NotionNext BLOGQEC decoding project
Project: Error decoding with multiple logical qubits
"Error decoding with multiple logical qubits" refers to the critical process of identifying and correcting errors that occur in a quantum computing system that involves multiple logical qubits. Quantum error correction is essential for ensuring the accuracy and reliability of quantum computations.
In quantum computing, errors can arise due to various factors such as noise, imperfections in hardware, and environmental interference. These errors can corrupt the information stored in qubits and lead to inaccurate results. Quantum error correction techniques aim to mitigate the impact of these errors and enable the preservation of quantum information.
Decoding is a crucial step in the error correction process. It involves analyzing the syndrome measurements obtained from the quantum system and determining the most likely error or errors that occurred. The syndrome measurements are obtained by measuring the stabilizer generators of the error-correcting code. These generators are designed to detect specific types of errors and provide information about the presence and location of errors.
In the context of multiple logical qubits, error decoding becomes more complex. Each logical qubit represents a quantum state that is encoded across multiple physical qubits. Errors can affect the individual physical qubits, leading to errors in the encoded logical qubits. Decoding algorithms for multiple logical qubits need to take into account the interdependencies between the physical qubits and their corresponding logical qubits.
The goal of error decoding with multiple logical qubits is to identify the errors that occurred and apply appropriate recovery operations to correct them. This process requires sophisticated decoding algorithms that can handle the complexity of multiple logical qubits and efficiently determine the most likely error configuration.
By successfully decoding and correcting errors in a quantum computing system with multiple logical qubits, the accuracy and reliability of quantum computations can be significantly improved. This is crucial for the advancement and practical implementation of quantum technologies in various fields, such as cryptography, optimization, and simulation.
The pipeline as implemented in the compiler:
procedure 1st:
QEC 1 logical qubit with surface code
PyMatching is a fast Python/C++ library for decoding quantum error correcting (QEC) codes using the Minimum Weight Perfect Matching (MWPM) decoder.
MWPM decoder : how to use PyMatching; use a small surface code for example
what’s the process and the principle[3].
Stim :
Stim is a tool for high performance simulation and analysis of quantum stabilizer circuits, especially quantum error correction (QEC) circuits.
procedure 2nd:
multiple logical qubits simulation
decoding
How does uf/mwpm deal with the measurement error? Is there any literature that describes it in detail (e.g., how the 3d syndrome graph is constructed, how the edge weight is handled, how uf/mwpm gets the corrected information it needs after the decoding is done, etc.)?
- UF and MWPM decoders construct a 3D syndrome graph (matching graph) that incorporates multiple rounds of syndrome measurements [1][2][9][12]. This allows the decoders to account for measurement errors.
- In the syndrome graph, vertices correspond to non-trivial syndrome measurements, and edges correspond to possible error events that could have caused the observed syndrome changes [1][9]. The edge weights represent the probability of the corresponding errors.
- For each fault location (e.g. CNOT gates, idling, state preparation, measurements) in the syndrome extraction circuits, all possible Pauli errors are considered. If propagating a Pauli error results in two syndrome changes, an edge is added between the corresponding vertices in the graph [9].
- The syndrome graph spans multiple rounds of measurements. Vertical edges are added between vertices in consecutive rounds to represent measurement errors [2][9][12].
- UF and MWPM are run on this syndrome graph to find a set of edges (error correction operations) that restore the code to the error-free state [1][2][13]. MWPM finds the minimum weight perfect matching while UF grows clusters to find likely error chains.
- After decoding, the identified Pauli errors from the matching/clustering are applied as corrections to the data qubits [2][13]. Only corrections from the "commit" region of the graph are applied, as those have high confidence.
- Leftover unresolved syndrome bits and artificially generated syndrome bits from the "buffer" region are passed to the next decoding round [12].
Some specific papers that go into details of this process:
- [2] provides an introduction to syndrome graphs and the UF decoder
- [9][12] describe the sliding window technique and the commit/buffer regions
- [13] explains the belief propagation based methods to calculate edge weights
- [18] gives an overview of real-time decoding using these techniques
Citations:
[1] https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.4.043086
[2] https://repository.tudelft.nl/islandora/object/uuid:94823249-e114-4fc0-bae9-4c80d503296f/datastream/OBJ/download
[3] https://par.nsf.gov/servlets/purl/10211647
[4] https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.4.043086
[5] https://github.com/yuewuo/fusion-blossom
[6] https://arxiv.org/html/2307.14989v4
[7] https://arxiv.org/abs/2203.15304
[8] https://iopscience.iop.org/article/10.1088/2058-9565/ace64d/meta
[9] https://iopscience.iop.org/article/10.1088/2058-9565/ace64d
[10] https://arxiv.org/abs/2311.16082
[11] https://memlab.ece.gatech.edu/papers/ISCA_2023_1.pdf
[12] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10624853/
[13] https://journals.aps.org/prx/pdf/10.1103/PhysRevX.13.031007
[14] https://arxiv.org/abs/2309.15354
[15] https://arxiv.org/pdf/2211.03288.pdf
[16] https://www.researchgate.net/publication/370775474_Fusion_Blossom_Fast_MWPM_Decoders_for_QEC
[17] https://arxiv.org/pdf/2107.13589.pdf
[18] https://research.tudelft.nl/files/166442756/Battistel_2023_Nano_Futures_7_032003.pdf
[19] https://repository.tudelft.nl/islandora/object/uuid%3A94823249-e114-4fc0-bae9-4c80d503296f
[20] https://www.researchgate.net/publication/362429184_Techniques_for_combining_fast_local_decoders_with_global_decoders_under_circuit-level_noise
surface code:[1]A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, “Surface codes: Towards practical large-scale quantum computation,” Phys. Rev. A, vol. 86, no. 3, p. 032324, Sep. 2012, doi: 10.1103/PhysRevA.86.032324.[2]C. Horsman, A. G. Fowler, S. Devitt, and R. V. Meter, “Surface code quantum computing by lattice surgery,” New J. Phys., vol. 14, no. 12, p. 123011, Dec. 2012, doi: 10.1088/1367-2630/14/12/123011.Decoding algorithms for surface codes:[3]A. deMarti iOlius, P. Fuentes, R. Orús, P. M. Crespo, and J. E. Martinez, “Decoding algorithms for surface codes,” Sep. 2023, doi: 10.48550/arXiv.2307.14989.Not only these reference papers, but you can also find more references from these papers.
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Name | Title | Abstract | Tags | URL | Year |
iOlius等, 2023 | Decoding algorithms for surface codes | Quantum technologies have the potential to solve computationally hard problems that are intractable via classical means. Unfortunately, the unstable nature of quantum information makes it prone to errors. For this reason, quantum error correction is an invaluable tool to make quantum information reliable and enable the ultimate goal of fault-tolerant quantum computing. Surface codes currently stand as the most promising candidates to build error corrected qubits given their two-dimensional architecture, a requirement of only local operations, and high tolerance to quantum noise. Decoding algorithms are an integral component of any error correction scheme, as they are tasked with producing accurate estimates of the errors that affect quantum information, so that it can subsequently be corrected. A critical aspect of decoding algorithms is their speed, since the quantum state will suffer additional errors with the passage of time. This poses a connundrum-like tradeoff, where decoding performance is improved at the expense of complexity and viceversa. In this review, a thorough discussion of state-of-the-art surface code decoding algorithms is provided. The core operation of these methods is described along with existing variants that show promise for improved results. In addition, both the decoding performance, in terms of error correction capability, and decoding complexity, are compared. A review of the existing software tools regarding surface code decoding is also provided. | /reading, Quantum physics, 🌟🌟🌟 | 2023 | |
Wu等, 2022 | A synthesis framework for stitching surface code with superconducting quantum devices | Quantum error correction (QEC) is the central building block of fault-tolerant quantum computation but the design of QEC codes may not always match the underlying hardware. To tackle the discrepancy between the quantum hardware and QEC codes, we propose a synthesis framework that can implement and optimize the surface code onto superconducting quantum architectures. In particular, we divide the surface code synthesis into three key subroutines. The first two optimize the mapping of data qubits and ancillary qubits including syndrome qubits on the connectivity-constrained superconducting architecture, while the last subroutine optimizes the surface code execution by rescheduling syndrome measurements. Our experiments on mainstream superconducting architectures demonstrate the effectiveness of the proposed synthesis framework. Especially, the surface codes synthesized by the proposed automatic synthesis framework can achieve comparable or even better error correction capability than manually designed QEC codes. | Quantum Computing, Quantum Error Correction, compiler, 🌟, 👌 | 2022 | |
Google Quantum AI等, 2023 | Suppressing quantum errors by scaling a surface code logical qubit | Abstract Practical quantum computing will require error rates well below those achievable with physical qubits. Quantum error correction 1,2 offers a path to algorithmically relevant error rates by encoding logical qubits within many physical qubits, for which increasing the number of physical qubits enhances protection against physical errors. However, introducing more qubits also increases the number of error sources, so the density of errors must be sufficiently low for logical performance to improve with increasing code size. Here we report the measurement of logical qubit performance scaling across several code sizes, and demonstrate that our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. We find that our distance-5 surface code logical qubit modestly outperforms an ensemble of distance-3 logical qubits on average, in terms of both logical error probability over 25 cycles and logical error per cycle ((2.914 ± 0.016)% compared to (3.028 ± 0.023)%). To investigate damaging, low-probability error sources, we run a distance-25 repetition code and observe a 1.7 × 10 −6 logical error per cycle floor set by a single high-energy event (1.6 × 10 −7 excluding this event). We accurately model our experiment, extracting error budgets that highlight the biggest challenges for future systems. These results mark an experimental demonstration in which quantum error correction begins to improve performance with increasing qubit number, illuminating the path to reaching the logical error rates required for computation. | /reading, 🌟, 👌 | 2023 | |
Liyanage等, 2023 | Scalable Quantum Error Correction for Surface Codes using FPGA | A fault-tolerant quantum computer must decode and correct errors faster than they appear. The faster errors can be corrected, the more time the computer can do useful work. The Union-Find (UF) decoder is promising with an average time complexity slightly higher than O(d3). We report a distributed version of the UF decoder that exploits parallel computing resources for further speedup. Using an FPGA-based implementation, we empirically show that this distributed UF decoder has a sublinear average time complexity with regard to d, given O(d3) parallel computing resources. The decoding time per measurement round decreases as d increases, a first time for a quantum error decoder. The implementation employs a scalable architecture called Helios that organizes parallel computing resources into a hybrid tree-grid structure. We are able to implement d up to 21 with a Xilinx VCU129 FPGA, for which an average decoding time is 11.5 ns per measurement round under phenomenological noise of 0.1%, significantly faster than any existing decoder implementation. Since the decoding time per measurement round of Helios decreases with d, Helios can decode a surface code of arbitrarily large d without a growing backlog. | 🌟 | 2023 | |
Vittal等, 2023 | Astrea: Accurate Quantum Error-Decoding via Practical Minimum-Weight Perfect-Matching | Quantum devices suffer from high error rates, which makes them ineffective for running practical applications. Quantum computers can be made fault tolerant using Quantum Error Correction (QEC), which protects quantum information by encoding logical qubits using data qubits and parity qubits. The data qubits collectively store the quantum information and the parity qubits are measured periodically to produce a syndrome, which is decoded by a classical decoder to identify the location and type of errors. To prevent errors from accumulating and causing a logical error, decoders must accurately identify errors in real-time, necessitating the use of hardware solutions because software decoders are slow. Ideally, a real-time decoder must match the performance of the Minimum-Weight Perfect Matching (MWPM) decoder. However, due to the complexity of the underlying Blossom algorithm, state-of-the-art real-time decoders either use lookup tables, which are not scalable, or use approximate decoding, which significantly increases logical error rates. In this paper, we leverage two key insights to enable practical real-time MWPM decoding. First, for near-term implementations (with redundancies up to distance d = 7) of surface codes, the Hamming weight of the syndromes tends to be quite small (less than or equal to 10). For this regime, we propose Astrea, which simply performs a brute-force search for the few hundred possible options to perform accurate decoding within a few nanoseconds (1ns average, 456ns worst-case), thus representing the first decoder to be able to do MWPM in real-time up-to distance 7. Second, even for codes that produce syndromes with higher Hamming weights (e.g. d = 9) the search for optimal pairings can be made more efficient by simply discarding the weights that denote significantly lower probability than the logical error-rate of the code. For this regime, we propose a greedy design called Astrea-G, which filters high-cost weights and reorders the search from high-likelihood pairings to low-likelihood pairings to produce the most likely decoding within 1μs (average 450ns). Our evaluations show that Astrea-G provides similar logical error-rates as the software-based MWPM for up-to d = 9 codes while meeting the real-time decoding latency constraints. | Quantum Error Correction, Real-Time Decoding, error decoding, 🌟, 👌 | 2023 | |
Higgott, 2021 | PyMatching: A Python package for decoding quantum codes with minimum-weight perfect matching | This paper introduces PyMatching, a fast open-source Python package for decoding quantum error-correcting codes with the minimum-weight perfect matching (MWPM) algorithm. PyMatching includes the standard MWPM decoder as well as a variant, which we call local matching, that restricts each syndrome defect to be matched to another defect within a local neighbourhood. The decoding performance of local matching is almost identical to that of the standard MWPM decoder in practice, while reducing the computational complexity approximately quadratically. We benchmark the performance of PyMatching, showing that local matching is several orders of magnitude faster than implementations of the full MWPM algorithm using NetworkX or Blossom V for problem sizes typically considered in error correction simulations. PyMatching and its dependencies are open-source, and it can be used to decode any quantum code for which syndrome defects come in pairs using a simple Python interface. PyMatching supports the use of weighted edges, hook errors, boundaries and measurement errors, enabling fast decoding and simulation of fault-tolerant quantum computing. | Quantum physics, ⛔ No INSPIRE recid found, 🌟🌟🌟 | 2021 | |
Barber等, 2023 | A real-time, scalable, fast and highly resource efficient decoder for a quantum computer | Quantum computers promise to solve computing problems that are currently intractable using traditional approaches. This can only be achieved if the noise inevitably present in quantum computers can be efficiently managed at scale. A key component in this process is a classical decoder, which diagnoses the errors occurring in the system. If the decoder does not operate fast enough, an exponential slowdown in the logical clock rate of the quantum computer occurs. Additionally, the decoder must be resource efficient to enable scaling to larger systems and potentially operate in cryogenic environments. Here we introduce the Collision Clustering decoder, which overcomes both challenges. We implement our decoder on both an FPGA and ASIC, the latter ultimately being necessary for any cost-effective scalable solution. We simulate a logical memory experiment on large instances of the leading quantum error correction scheme, the surface code, assuming a circuit-level noise model. The FPGA decoding frequency is above a megahertz, a stringent requirement on decoders needed for e.g. superconducting quantum computers. To decode an 881 qubit surface code it uses only 4.5\% of the available logical computation elements. The ASIC decoding frequency is also above a megahertz on a 1057 qubit surface code, and occupies 0.06 mm^2 area and consumes 8 mW of power. Our decoder is optimised to be both highly performant and resource efficient, while its implementation on hardware constitutes a viable path to practically realising fault-tolerant quantum computers. | Quantum physics, 🌟, 👌 | 2023 | |
Kolmogorov, 2009 | Blossom V: a new implementation of a minimum cost perfect matching algorithm | We describe a new implementation of the Edmonds’s algorithm for computing a perfect matching of minimum cost, to which we refer as Blossom V. A key feature of our implementation is a combination of two ideas that were shown to be effective for this problem: the “variable dual updates” approach of Cook and Rohe (INFORMS J Comput 11(2):138–148, 1999) and the use of priority queues. We achieve this by maintaining an auxiliary graph whose nodes correspond to alternating trees in the Edmonds’s algorithm. While our use of priority queues does not improve the worst-case complexity, it appears to lead to an efficient technique. In the majority of our tests Blossom V outperformed previous implementations of Cook and Rohe (INFORMS J Comput 11(2):138–148, 1999) and Mehlhorn and Schäfer (J Algorithmics Exp (JEA) 7:4, 2002), sometimes by an order of magnitude. We also show that for large VLSI instances it is beneficial to update duals by solving a linear program, contrary to a conjecture by Cook and Rohe. | /reading, 68R10, ⛔ No INSPIRE recid found, 🌟🌟🌟 | 2009 | |
Wu & Zhong, 2023 | Fusion Blossom: Fast MWPM Decoders for QEC | The Minimum-Weight Perfect Matching (MWPM) decoder is widely used in Quantum Error Correction (QEC) decoding. Despite its high accuracy, existing implementations of the MWPM decoder cannot catch up with quantum hardware, e.g., 1 million measurements per second for superconducting qubits. They suffer from a backlog of measurements that grows exponentially and as a result, cannot realize the power of quantum computation. We design and implement a fast MWPM decoder, called Parity Blossom, which reaches a time complexity almost proportional to the number of defect measurements. We further design and implement a parallel version of Parity Blossom called Fusion Blossom. Given a practical circuit-level noise of 0.1%, Fusion Blossom can decode a million measurement rounds per second up to a code distance of 33. Fusion Blossom also supports stream decoding mode that reaches a 0.7 ms decoding latency at code distance 21 regardless of the measurement rounds. | /reading, Computer Science - Data Structures and Algorithms, Computer Science - Distributed; Parallel; and Cluster Computing, Quantum physics, 🌟🌟🌟 | 2023 | |
Higgott & Gidney, 2023 | Sparse Blossom: correcting a million errors per core second with minimum-weight matching | In this work, we introduce a fast implementation of the minimum-weight perfect matching (MWPM) decoder, the most widely used decoder for several important families of quantum error correcting codes, including surface codes. Our algorithm, which we call sparse blossom, is a variant of the blossom algorithm which directly solves the decoding problem relevant to quantum error correction. Sparse blossom avoids the need for all-to-all Dijkstra searches, common amongst MWPM decoder implementations. For 0.1% circuit-level depolarising noise, sparse blossom processes syndrome data in both X and Z bases of distance-17 surface code circuits in less than one microsecond per round of syndrome extraction on a single core, which matches the rate at which syndrome data is generated by superconducting quantum computers. Our implementation is open-source, and has been released in version 2 of the PyMatching library. | /reading, Quantum physics, 🌟🌟🌟 | 2023 | |
Battistel等, 2023 | Real-time decoding for fault-tolerant quantum computing: progress, challenges and outlook | Quantum computing is poised to solve practically useful problems which are computationally intractable for classical supercomputers. However, the current generation of quantum computers are limited by errors that may only partially be mitigated by developing higher-quality qubits. Quantum error correction (QEC) will thus be necessary to ensure fault tolerance. QEC protects the logical information by cyclically measuring syndrome information about the errors. An essential part of QEC is the decoder, which uses the syndrome to compute the likely effect of the errors on the logical degrees of freedom and provide a tentative correction. The decoder must be accurate, fast enough to keep pace with the QEC cycle (e.g. on a microsecond timescale for superconducting qubits) and with hard real-time system integration to support logical operations. As such, real-time decoding is essential to realize fault-tolerant quantum computing and to achieve quantum advantage. In this work, we highlight some of the key challenges facing the implementation of real-time decoders while providing a succinct summary of the progress to-date. Furthermore, we lay out our perspective for the future development and provide a possible roadmap for the field of real-time decoding in the next few years. As the quantum hardware is anticipated to scale up, this perspective article will provide a guidance for researchers, focusing on the most pressing issues in real-time decoding and facilitating the development of solutions across quantum, nano and computer science. | 🌟, 👌 | 2023 | |
Delfosse & Nickerson, 2021 | Almost-linear time decoding algorithm for topological codes | In order to build a large scale quantum computer, one must be able to correct errors extremely fast. We design a fast decoding algorithm for topological codes to correct for Pauli errors and erasure and combination of both errors and erasure. Our algorithm has a worst case complexity of O(n \alpha(n)), where n is the number of physical qubits and \alpha is the inverse of Ackermann's function, which is very slowly growing. For all practical purposes, \alpha(n) \leq 3. We prove that our algorithm performs optimally for errors of weight up to (d-1)/2 and for loss of up to d-1 qubits, where d is the minimum distance of the code. Numerically, we obtain a threshold of 9.9\% for the 2d-toric code with perfect syndrome measurements and 2.6\% with faulty measurements. | /reading, Quantum physics, UF decoder, 🌟🌟🌟 | 2021 | |
Edmonds, 1965 | Paths, Trees, and Flowers | A graph G for purposes here is a finite set of elements called vertices and a finite set of elements called edges such that each edge meets exactly two vertices, called the end-points of the edge. An edge is said to join its end-points. A matching in G is a subset of its edges such that no two meet the same vertex. We describe an efficient algorithm for finding in a given graph a matching of maximum cardinality. This problem was posed and partly solved by C. Berge; see Sections 3.7 and 3.8. | /reading, ⛔ No INSPIRE recid found, 🌟🌟🌟 | 1965 | |
Mondal & Parhi, 2023 | Quantum Circuits for Stabilizer Error Correcting Codes: A Tutorial | Quantum computers have the potential to provide exponential speedups over their classical counterparts. Quantum principles are being applied to fields such as communications, information processing, and artificial intelligence to achieve quantum advantage. However, quantum bits are extremely noisy and prone to decoherence. Thus, keeping the qubits error free is extremely important toward reliable quantum computing. Quantum error correcting codes have been studied for several decades and methods have been proposed to import classical error correcting codes to the quantum domain. However, circuits for such encoders and decoders haven't been explored in depth. This paper serves as a tutorial on designing and simulating quantum encoder and decoder circuits for stabilizer codes. We present encoding and decoding circuits for five-qubit code and Steane code, along with verification of these circuits using IBM Qiskit. We also provide nearest neighbour compliant encoder and decoder circuits for the five-qubit code. | /reading, Electrical Engineering and Systems Science - Signal Processing, Quantum physics, reading, 🌟🌟🌟 | 2023 | |
Kitaev, 2003 | Fault-tolerant quantum computation by anyons | ㅤ | 🌟 | 2003 | |
Wu等, 2022 | An interpretation of Union-Find Decoder on Weighted Graphs | Union-Find (UF) and Minimum-Weight Perfect Matching (MWPM) are popular decoder designs for surface codes. The former has significantly lower time complexity than the latter but is considered somewhat inferior, in terms of decoding accuracy. In this work we present an interpretation of UF decoders that explains why UF and MWPM decoders perform closely in some cases: the UF decoder is an approximate implementation of the blossom algorithm used for MWPM. This interpretation allows a generalization of UF decoders for weighted decoding graphs and explains why UF decoders achieve high accuracy for certain surface codes. | /reading, Quantum physics, 🌟🌟🌟 | 2022 | |
Bonilla Ataides等, 2021 | The XZZX surface code | Performing large calculations with a quantum computer will likely require a fault-tolerant architecture based on quantum error-correcting codes. The challenge is to design practical quantum error-correcting codes that perform well against realistic noise using modest resources. Here we show that a variant of the surface code—the XZZX code—offers remarkable performance for fault-tolerant quantum computation. The error threshold of this code matches what can be achieved with random codes (hashing) for every single-qubit Pauli noise channel; it is the first explicit code shown to have this universal property. We present numerical evidence that the threshold even exceeds this hashing bound for an experimentally relevant range of noise parameters. Focusing on the common situation where qubit dephasing is the dominant noise, we show that this code has a practical, high-performance decoder and surpasses all previously known thresholds in the realistic setting where syndrome measurements are unreliable. We go on to demonstrate the favourable sub-threshold resource scaling that can be obtained by specialising a code to exploit structure in the noise. We show that it is possible to maintain all of these advantages when we perform fault-tolerant quantum computation. | Quantum information, Qubits, 🌟 | 2021 | |
Edmonds & Johnson, 1973 | Matching, Euler tours and the Chinese postman | ㅤ | /reading, ⛔ No INSPIRE recid found, 🌟🌟🌟 | 1973 | |
Fowler, 2014 | Minimum weight perfect matching of fault-tolerant topological quantum error correction in average O(1) parallel time | Consider a 2-D square array of qubits of extent L\times L. We provide a proof that the minimum weight perfect matching problem associated with running a particular class of topological quantum error correction codes on this array can be exactly solved with a 2-D square array of classical computing devices, each of which is nominally associated with a fixed number N of qubits, in constant average time per round of error detection independent of L provided physical error rates are below fixed nonzero values, and other physically reasonable assumptions. This proof is applicable to the fully fault-tolerant case only, not the case of perfect stabilizer measurements. | /reading, Quantum physics, 🌟🌟🌟 | 2014 | |
Fowler等, 2012 | Towards practical classical processing for the surface code: Timing analysis | Topological quantum error-correction codes have high thresholds and are well suited to physical implementation. The minimum-weight perfect-matching algorithm can be used to efficiently handle errors in such codes. We perform a timing analysis of our current implementation of the minimum-weight perfect-matching algorithm. Our implementation performs the classical processing associated with an n×n lattice of qubits realizing a square surface code storing a single logical qubit of information in a fault-tolerant manner. We empirically demonstrate that our implementation requires only O(n2) average time per round of error correction for code distances ranging from 4 to 512 and a range of depolarizing error rates. We also describe tests we have performed to verify that it always obtains a true minimum-weight perfect matching. | /reading, ⛔ No INSPIRE recid found, 🌟🌟🌟 | 2012 | |
Zhang & Cubitt, 2023 | Quantum Error Transmutation | We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a pre-specified admissible set of errors on the code space. We call these quantum error transmuting codes. They are of particular interest for the simulation of noisy quantum systems, and for use in algorithms inherently robust to errors of a particular character. Necessary and sufficient algebraic conditions on the set of physical and admissible errors for error transmutation are derived, generalising the Knill-Laflamme quantum error correction conditions. We demonstrate how some existing codes, including fermionic encodings, have error transmuting properties to interesting classes of admissible errors. Additionally, we report on the existence of some new codes, including low-qubit and translation invariant examples. | /reading, Quantum physics, 🌟🌟🌟 | 2023 | |
Girvin, 2022 | Introduction to Quantum Error Correction and Fault Tolerance | These lecture notes from the 2019 Les Houches Summer School on 'Quantum Information Machines' are intended to provide an introduction to classical and quantum error correction with bits and qubits, and with continuous variable systems (harmonic oscillators). The focus on the latter will be on practical examples that can be realized today or in the near future with a modular architecture based on superconducting electrical circuits and microwave photons. The goal and vision is 'hardware-efficient' quantum error correction that does not require exponentially large hardware overhead in order to achieve practical and useful levels of fault tolerance and circuit depth. | Quantum physics, 🌟🌟🌟 | 2022 | |
Fowler等, 2012 | Surface codes: Towards practical large-scale quantum computation | This article provides an introduction to surface code quantum computing. We first estimate the size and speed of a surface code quantum computer. We then introduce the concept of the stabilizer, using two qubits, and extend this concept to stabilizers acting on a two-dimensional array of physical qubits, on which we implement the surface code. We next describe how logical qubits are formed in the surface code array and give numerical estimates of their fault-tolerance. We outline how logical qubits are physically moved on the array, how qubit braid transformations are constructed, and how a braid between two logical qubits is equivalent to a controlled-NOT. We then describe the single-qubit Hadamard, S and T operators, completing the set of required gates for a universal quantum computer. We conclude by briefly discussing physical implementations of the surface code. We include a number of appendices in which we provide supplementary information to the main text. | Quantum physics, 🌟🌟🌟, 👌 | 2012 | |
Gottesman, 2010 | An introduction to quantum error correction and fault-tolerant quantum computation | Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences from the theory of classical error-correcting codes. Many quantum codes can be described in terms of the stabilizer of the codewords. The stabilizer is a finite Abelian group, and allows a straightforward characterization of the error-correcting properties of the code. The stabilizer formalism for quantum codes also illustrates the relationships to classical coding theory, particularly classical codes over GF(4), the finite field with four elements. To build a quantum computer which behaves correctly in the presence of errors, we also need a theory of fault-tolerant quantum computation, instructing us how to perform quantum gates on qubits which are encoded in a quantum errorcorrecting code. The threshold theorem states that it is possible to create a quantum computer to perform an arbitrary quantum computation provided the error rate per physical gate or time step is below some constant threshold value. | ⛔ No INSPIRE recid found, 🌟 | 2010 | |
Pesah, 2023 | An interactive introduction to the surface code | Research blog | 🌟, 👌 | 2023 | |
Chamberland等, 2023 | Techniques for combining fast local decoders with global decoders under circuit-level noise | Abstract Implementing algorithms on a fault-tolerant quantum computer will require fast decoding throughput and latency times to prevent an exponential increase in buffer times between the applications of gates. In this work we begin by quantifying these requirements. We then introduce the construction of local neural network (NN) decoders using three-dimensional convolutions. These local decoders are adapted to circuit-level noise and can be applied to surface code volumes of arbitrary size. Their application removes errors arising from a certain number of faults, which serves to substantially reduce the syndrome density. Remaining errors can then be corrected by a global decoder, such as Blossom or union find, with their implementation significantly accelerated due to the reduced syndrome density. However, in the circuit-level setting, the corrections applied by the local decoder introduce many vertical pairs of highlighted vertices. To obtain a low syndrome density in the presence of vertical pairs, we consider a strategy of performing a syndrome collapse which removes many vertical pairs and reduces the size of the decoding graph used by the global decoder. We also consider a strategy of performing a vertical cleanup, which consists of removing all local vertical pairs prior to implementing the global decoder. By applying our local NN decoder and the vertical cleanup strategy to a d = 17 surface code volume, we show a 10 6 × speedup of the minimum-weight perfect matching decoder. Lastly, we estimate the cost of implementing our local decoders on field programmable gate arrays. | /reading, 🌟 | 2023 | |
Higgott等, 2023 | Improved Decoding of Circuit Noise and Fragile Boundaries of Tailored Surface Codes | ㅤ | /reading, 🌟 | 2023 | |
Terhal, 2015 | Quantum error correction for quantum memories | ㅤ | /reading, 🌟 | 2015 | |
Tuckett, 2020 | Tailoring surface codes Improvements in quantum error correction with biased noise | ㅤ | /reading, 🌟 | ㅤ | 2020 |
Hua等, 2021 | AutoBraid: A Framework for Enabling Efficient Surface Code Communication in Quantum Computing | Quantum computers can solve problems that are intractable using the most powerful classical computer. However, qubits are fickle and error prone. It is necessary to actively correct errors in the execution of a quantum circuit. Quantum error correction (QEC) codes are developed to enable fault-tolerant quantum computing. With QEC, one logical circuit is converted into an encoded circuit. Most studies on quantum circuit compilation focus on NISQ devices which have 10-100 qubits and are not fault-tolerant. In this paper, we focus on the compilation for fault-tolerant quantum hardware. In particular, we focus on optimizing communication parallelism for the surface code based QEC. The execution of surface code circuits involves non-trivial geometric manipulation of a large lattice of entangled physical qubits. A two-qubit gate in surface code is implemented as a virtual “pipe" in space-time called a braiding path. The braiding paths should be carefully routed to avoid congestion. Communication between qubits is considered the major bottleneck as it involves scheduling and searching for simultaneous paths between qubits. We provide a framework for efficiently scheduling braiding paths. We discover that for quantum programs with a local parallelism pattern, our framework guarantees an optimal solution, while the previous greedy-heuristic-based solution cannot. Moreover, we propose an extension to the local parallelism analysis framework to address the communication bottleneck. Our framework achieves orders of magnitude improvement after addressing the communication bottleneck. | /reading, 🌟🌟🌟, 👌 | 2021 | |
Javadi-Abhari等, 2017 | Optimized Surface Code Communication in Superconducting Quantum Computers | Quantum computing (QC) is at the cusp of a revolution. Machines with 100 quantum bits (qubits) are anticipated to be operational by 2020 [30, 73], and several-hundred-qubit machines are around the corner. Machines of this scale have the capacity to demonstrate quantum supremacy, the tipping point where QC is faster than the fastest classical alternative for a particular problem. Because error correction techniques will be central to QC and will be the most expensive component of quantum computation, choosing the lowest-overhead error correction scheme is critical to overall QC success. This paper evaluates two established quantum error correction codes-planar and double-defect surface codes-using a set of compilation, scheduling and network simulation tools. In considering scalable methods for optimizing both codes, we do so in the context of a full microarchitectural and compiler analysis. Contrary to previous predictions, we find that the simpler planar codes are sometimes more favorable for implementation on superconducting quantum computers, especially under conditions of high communication congestion. | /reading, Computers, Design-Space Exploration, ECC, Encoding, Lattices, Measurement uncertainty, Quantum Computing, Quantum mechanics, Qubit, 🌟 | ㅤ | 2017 |
Gottesman, 1998 | The Heisenberg Representation of Quantum Computers | Since Shor’s discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers — the difficulty of describing them on classical computers —also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation. | /unread, Quantum physics, 🌟, 👌 | 1998 | |
Wang等, 2023 | Transformer-QEC: Quantum Error Correction Code Decoding with Transferable Transformers | Quantum computing has the potential to solve problems that are intractable for classical systems, yet the high error rates in contemporary quantum devices often exceed tolerable limits for useful algorithm execution. Quantum Error Correction (QEC) mitigates this by employing redundancy, distributing quantum information across multiple data qubits and utilizing syndrome qubits to monitor their states for errors. The syndromes are subsequently interpreted by a decoding algorithm to identify and correct errors in the data qubits. This task is complex due to the multiplicity of error sources affecting both data and syndrome qubits as well as syndrome extraction operations. Additionally, identical syndromes can emanate from different error sources, necessitating a decoding algorithm that evaluates syndromes collectively. Although machine learning (ML) decoders such as multi-layer perceptrons (MLPs) and convolutional neural networks (CNNs) have been proposed, they often focus on local syndrome regions and require retraining when adjusting for different code distances. We introduce a transformer-based QEC decoder which employs self-attention to achieve a global receptive field across all input syndromes. It incorporates a mixed loss training approach, combining both local physical error and global parity label losses. Moreover, the transformer architecture's inherent adaptability to variable-length inputs allows for efficient transfer learning, enabling the decoder to adapt to varying code distances without retraining. Evaluation on six code distances and ten different error configurations demonstrates that our model consistently outperforms non-ML decoders, such as Union Find (UF) and Minimum Weight Perfect Matching (MWPM), and other ML decoders, thereby achieving best logical error rates. Moreover, the transfer learning can save over 10x of training cost. | Computer Science - Artificial Intelligence, Computer Science - Emerging Technologies, Computer Science - Hardware Architecture, Computer Science - Machine Learning, Quantum physics, 🌟🌟🌟, 👌 | 2023 | |
Bluvstein等, 2023 | Logical quantum processor based on reconfigurable atom arrays | Suppressing errors is the central challenge for useful quantum computing, requiring quantum error correction for large-scale processing. However, the overhead in the realization of error-corrected ``logical'' qubits, where information is encoded across many physical qubits for redundancy, poses significant challenges to large-scale logical quantum computing. Here we report the realization of a programmable quantum processor based on encoded logical qubits operating with up to 280 physical qubits. Utilizing logical-level control and a zoned architecture in reconfigurable neutral atom arrays, our system combines high two-qubit gate fidelities, arbitrary connectivity, as well as fully programmable single-qubit rotations and mid-circuit readout. Operating this logical processor with various types of encodings, we demonstrate improvement of a two-qubit logic gate by scaling surface code distance from d=3 to d=7, preparation of color code qubits with break-even fidelities, fault-tolerant creation of logical GHZ states and feedforward entanglement teleportation, as well as operation of 40 color code qubits. Finally, using three-dimensional [[8,3,2]] code blocks, we realize computationally complex sampling circuits with up to 48 logical qubits entangled with hypercube connectivity with 228 logical two-qubit gates and 48 logical CCZ gates. We find that this logical encoding substantially improves algorithmic performance with error detection, outperforming physical qubit fidelities at both cross-entropy benchmarking and quantum simulations of fast scrambling. These results herald the advent of early error-corrected quantum computation and chart a path toward large-scale logical processors. | /reading, Condensed Matter - Quantum Gases, Physics - Atomic Physics, Quantum physics, 🌟🌟🌟 | 2023 | |
Evered等, 2023 | High-fidelity parallel entangling gates on a neutral-atom quantum computer | The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing1. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits2,3 and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture4. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions5. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction6,7. Our method uses fast, single-pulse gates based on optimal control8, atomic dark states to reduce scattering9 and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications10,11, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates12,13. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms14, error-corrected circuits7 and digital simulations15. | /reading, Quantum information, Qubits, 🌟 | 2023 | |
Litinski, 2019 | A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery | Given a quantum gate circuit, how does one execute it in a fault-tolerant architecture with as little overhead as possible? In this paper, we discuss strategies for surface-code quantum computing on small, intermediate and large scales. They are strategies for space-time trade-offs, going from slow computations using few qubits to fast computations using many qubits. Our schemes are based on surface-code patches, which not only feature a low space cost compared to other surface-code schemes, but are also conceptually simple, simple enough that they can be described as a tile-based game with a small set of rules. Therefore, no knowledge of quantum error correction is necessary to understand the schemes in this paper, but only the concepts of qubits and measurements. As an example, assuming a physical error rate of 10^{-4} and a code cycle time of 1 \mus, a classically intractable 100-qubit quantum computation with a T count of 10^8 and a T depth of 10^6 can be executed in 4 hours using 55,000 qubits, in 22 minutes using 120,000 qubits, or in 1 second using 330,000,000 qubits. | /reading, Condensed Matter - Mesoscale and Nanoscale Physics, Quantum physics, surface code, ⛔ No INSPIRE recid found, 🌟🌟🌟 | 2019 | |
Horsman等, 2012 | Surface code quantum computing by lattice surgery | ㅤ | /reading, 🌟🌟🌟 | 2012 | |
Campbell等, 2017 | Roads towards fault-tolerant universal quantum computation | A practical quantum computer must not merely store information, but also process it. To prevent errors introduced by noise from multiplying and spreading, a fault-tolerant computational architecture is required. Current experiments are taking the first steps toward noise-resilient logical qubits. But to convert these quantum devices from memories to processors, it is necessary to specify how a universal set of gates is performed on them. The leading proposals for doing so, such as magic-state distillation and colour-code techniques, have high resource demands. Alternative schemes, such as those that use high-dimensional quantum codes in a modular architecture, have potential benefits, but need to be explored further. | /reading, Information theory and computation, Quantum information, Qubits, 🌟🌟🌟, 👌 | 2017 | |
Fowler & Gidney, 2019 | Low overhead quantum computation using lattice surgery | When calculating the overhead of a quantum algorithm made fault-tolerant using the surface code, many previous works have used defects and braids for logical qubit storage and state distillation. In this work, we show that lattice surgery reduces the storage overhead by over a factor of 4, and the distillation overhead by nearly a factor of 5, making it possible to run algorithms with 10^8 T gates using only 3.7\times 10^5 physical qubits capable of executing gates with error p\sim 10^{-3}. These numbers strongly suggest that defects and braids in the surface code should be deprecated in favor of lattice surgery. | /reading, Quantum physics, 🌟🌟🌟 | 2019 | |
Erhard等, 2021 | Entangling logical qubits with lattice surgery | The development of quantum computing architectures from early designs and current noisy devices to fully fledged quantum computers hinges on achieving fault tolerance using quantum error correction1–4. However, these correction capabilities come with an overhead for performing the necessary fault-tolerant logical operations on logical qubits (qubits that are encoded in ensembles of physical qubits and protected by error-correction codes)5–8. One of the most resource-efficient ways to implement logical operations is lattice surgery9–11, where groups of physical qubits, arranged on lattices, can be merged and split to realize entangling gates and teleport logical information. Here we report the experimental realization of lattice surgery between two qubits protected via a topological error-correction code in a ten-qubit ion-trap quantum information processor. In this system, we can carry out the necessary quantum non-demolition measurements through a series of local and entangling gates, as well as measurements on auxiliary qubits. In particular, we demonstrate entanglement between two logical qubits and we implement logical state teleportation between them. The demonstration of these operations—fundamental building blocks for quantum computation—through lattice surgery represents a step towards the efficient realization of fault-tolerant quantum computation. | /reading, Quantum information, Qubits, 🌟 | 2021 | |
Tomita & Svore, 2014 | Low-distance surface codes under realistic quantum noise | Experimental implementation of the surface code will be a significant milestone for quantum computing. We develop a circuit and a decoder targeted for near-term implementation of a distance-3 surface code. We simulate the code under amplitude and phase damping and compare the threshold to a Pauli-twirl approximation. We find that the approximation yields a pessimistic threshold estimate. From numerical Monte Carlo simulations, we identify the gate and measurement speeds required to achieve reliable error correction. For superconductor devices, a qubit encoded in a 17-qubit surface code demonstrates a lower error rate than an unencoded qubit assuming gate times of 5–40 ns and T1 times of at least 1–2 μs. If T1≥10 ns, the difference is significant and can be experimentally measured, allowing near-term implementation and verification of a small surface code. For ion trap devices, gates times of 1 μs and T1≥40 ms admit measurable differences in error rate. | /reading, 🌟 | 2014 | |
Watkins等, 2023 | A High Performance Compiler for Very Large Scale Surface Code Computations | We present the first high performance compiler for very large scale quantum error correction: it translates an arbitrary quantum circuit to surface code operations based on lattice surgery. Our compiler offers an end to end error correction workflow implemented by a pluggable architecture centered around an intermediate representation of lattice surgery instructions. Moreover, the compiler supports customizable circuit layouts, can be used for quantum benchmarking and includes a quantum resource estimator. The compiler can process millions of gates using a streaming pipeline at a speed geared towards real-time operation of a physical device. We compiled within seconds 80 million logical surface code instructions, corresponding to a high precision Clifford+T implementation of the 128-qubit Quantum Fourier Transform (QFT). Our code is open-sourced at \url{https://github.com/latticesurgery-com}. | Quantum physics, 🌟🌟🌟, 👌 | 2023 | |
Zhu等, 2023 | Ecmas: Efficient Circuit Mapping and Scheduling for Surface Code | As the leading candidate of quantum error correction codes, surface code suffers from significant overhead, such as execution time. Reducing the circuit's execution time not only enhances its execution efficiency but also improves fidelity. However, finding the shortest execution time is NP-hard. In this work, we study the surface code mapping and scheduling problem. To reduce the execution time of a quantum circuit, we first introduce two novel metrics: Circuit Parallelism Degree and Chip Communication Capacity to quantitatively characterize quantum circuits and chips. Then, we propose a resource-adaptive mapping and scheduling method, named Ecmas, with customized initialization of chip resources for each circuit. Ecmas can dramatically reduce the execution time in both double defect and lattice surgery models. Furthermore, we provide an additional version Ecmas-ReSu for sufficient qubits, which is performance-guaranteed and more efficient. Extensive numerical tests on practical datasets show that Ecmas outperforms the state-of-the-art methods by reducing the execution time by 51.5% on average for double defect model. Ecmas can reach the optimal result in most benchmarks, reducing the execution time by up to 13.9% for lattice surgery model. | /reading, Quantum physics, 🌟🌟🌟 | 2023 | |
Beverland等, 2022 | Surface Code Compilation via Edge-Disjoint Paths | We provide an efficient algorithm to compile quantum circuits for fault-tolerant execution. We target surface codes, which form a two-dimensional grid of logical qubits with nearest-neighbor logical operations. Embedding an input circuit’s qubits in surface codes can result in long-range two-qubit operations across the grid. We show how to prepare many long-range Bell pairs on qubits connected by edge-disjoint paths of ancillae in constant depth that can be used to perform these long-range operations. This forms one core part of our edge-disjoint path compilation (EDPC) algorithm, by easily performing many parallel long-range Clifford operations in constant depth. It also allows us to establish a connection between surface code compilation and several well-studied edge-disjoint path problems. Similar techniques allow us to perform non-Clifford single-qubit rotations far from magic state distillation factories. In this case, we can easily find the maximum set of paths by a max-flow reduction, which forms the other major part of EDPC. EDPC has the best asymptotic worst-case performance guarantees on the circuit depth for compiling parallel operations when compared to related compilation methods based on swap gates and network coding. EDPC also shows a quadratic depth improvement over sequential Pauli-based compilation for parallel rotations requiring magic resources. We implement EDPC and find significantly improved performance for circuits built from parallel controlled-not (cnot) gates, and for circuits that implement the multicontrolled X gate CkNOT. | /reading, 🌟 | 2022 | |
Paler & Fowler, 2020 | OpenSurgery for Topological Assemblies | Surface quantum error-correcting codes are the leading proposal for fault-tolerance within quantum computers. We present OpenSurgery, a scalable tool for the preparation of circuits protected by the surface code operated through lattice surgery. Lattice surgery is considered a resource efficient method to implement surface code computations. Resource efficiency refers to the number of physical qubits and the time necessary for executing a quantum computation. OpenSurgery is a first step towards methods that aid quantum algorithm design informed by the realities of the hardware architectures. OpenSurgery can: 1) lay out arbitrary quantum circuits, 2) estimate the quantum resources used for their execution, 3) visualise the resulting 3D topological assemblies. Source code is available at http://www.github.com/alexandrupaler/opensurgery. | /reading, 🌟🌟🌟 | 2020 | |
Paler, 2019 | SurfBraid: A concept tool for preparing and resource estimating quantum circuits protected by the surface code | The first generations of quantum computers will execute fault-tolerant quantum circuits, and it is very likely that such circuits will use surface quantum error correcting codes. To the best of our knowledge, no complete design automation tool for such circuits is currently available. This is to a large extent because such circuits have three dimensional layouts (e.g. two dimensional hardware and time axis as a third dimension) and their optimisation is still ongoing research. This work introduces SurfBraid, a tool for the automatic design of surface code protected quantum circuits -- it includes a complete workflow that compiles an arbitrary quantum circuit into an intermediary Clifford+T equivalent representation which is further synthesised and optimised to surface code protected structures (for the moment, braided defects). SurfBraid is arguably the first flexible (modular structure, extensible through user provided scripts) and interactive (automatically updating the results based on user interaction, browser based) tool for such circuits. One of the prototype's methodological novelty is its capability to automatically estimate the resources necessary for executing large fault-tolerant circuits. A prototype implementation and the corresponding source code are available at https://alexandrupaler.github.io/quantjs/. | /reading, Computer Science - Emerging Technologies, Quantum physics, 🌟🌟🌟 | 2019 | |
Melko & Carrasquilla, 2024 | Language models for quantum simulation | A key challenge in the effort to simulate today’s quantum computing devices is the ability to learn and encode the complex correlations that occur between qubits. Emerging technologies based on language models adopted from machine learning have shown unique abilities to learn quantum states. We highlight the contributions that language models are making in the effort to build quantum computers and discuss their future role in the race to quantum advantage. | Information theory and computation, Quantum physics, 🌟🌟🌟, 👌 | 2024 | |
Paler等, 2017 | Fault-tolerant, high-level quantum circuits: form, compilation and description | ㅤ | /reading, 🌟 | 2017 | |
Campbell, 2024 | A series of fast-paced advances in Quantum Error Correction | Over the past few years, and most notably in 2023, quantum error correction has made big strides, shifting the community focus from noisy applications to what can be achieved with early error-corrected quantum computers. But despite the breakthroughs in experiments with trapped ions, superconducting circuits and reconfigurable atom arrays there are still several technological challenges — unique to each platform — to overcome. | Quantum information, Qubits, 🌟, 👌 | 2024 | |
Delfosse & Zémor, 2020 | Linear-time maximum likelihood decoding of surface codes over the quantum erasure channel | ㅤ | /reading, UF decoder, 🌟 | 2020 | |
Quillen, 不详 | PHY265 Lecture notes: Introducing Quantum Error Correction | ㅤ | tutorial, 🌟 | ㅤ | ㅤ |
Cain等, 2024 | Correlated decoding of logical algorithms with transversal gates | Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation of logical qubits using transversal gates (Bluvstein et al., Nature 626, 58-65 (2024)), we show that the performance of logical algorithms can be substantially improved by decoding the qubits jointly to account for physical error propagation during transversal entangling gates. We find that such correlated decoding improves the performance of both Clifford and non-Clifford transversal entangling gates, and explore two decoders offering different computational runtimes and accuracies. By considering deep logical Clifford circuits, we find that correlated decoding can significantly improve the space-time cost by reducing the number of rounds of noisy syndrome extraction per gate. These results demonstrate that correlated decoding provides a major advantage in early fault-tolerant computation, and indicate it has considerable potential to reduce the space-time cost in large-scale logical algorithms. | Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Statistical Mechanics, Quantum physics, 🌟🌟🌟 | 2024 | |
Lin等, 2024 | Spatially parallel decoding for multi-qubit lattice surgery | Running quantum algorithms protected by quantum error correction requires a real time, classical decoder. To prevent the accumulation of a backlog, this decoder must process syndromes from the quantum device at a faster rate than they are generated. Most prior work on real time decoding has focused on an isolated logical qubit encoded in the surface code. However, for surface code, quantum programs of utility will require multi-qubit interactions performed via lattice surgery. A large merged patch can arise during lattice surgery -- possibly as large as the entire device. This puts a significant strain on a real time decoder, which must decode errors on this merged patch and maintain the level of fault-tolerance that it achieves on isolated logical qubits. These requirements are relaxed by using spatially parallel decoding, which can be accomplished by dividing the physical qubits on the device into multiple overlapping groups and assigning a decoder module to each. We refer to this approach as spatially parallel windows. While previous work has explored similar ideas, none have addressed system-specific considerations pertinent to the task or the constraints from using hardware accelerators. In this work, we demonstrate how to configure spatially parallel windows, so that the scheme (1) is compatible with hardware accelerators, (2) supports general lattice surgery operations, (3) maintains the fidelity of the logical qubits, and (4) meets the throughput requirement for real time decoding. Furthermore, our results reveal the importance of optimally choosing the buffer width to achieve a balance between accuracy and throughput -- a decision that should be influenced by the device's physical noise. | /reading, Computer Science - Emerging Technologies, Computer Science - Hardware Architecture, Quantum physics, 🌟 | 2024 |
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Last update: 2024-8-16