Building a Fault-Tolerant Quantum Computer Using Concatenated Cat Codes

Chamberland, Christopher; Noh, Kyungjoo; Arrangoiz-Arriola, Patricio; Campbell, Earl T.; Hann, Connor T.; Iverson, Joseph; Putterman, Harald; Bohdanowicz, Thomas C.; Flammia, Steven T.; Keller, Andrew J.; Refael, Gil; Preskill, John; Jiang, Liang; Safavi-Naeini, Amir H.; Painter, Oskar; Brandão, Fernando G. S. L.

doi:10.1103/prxquantum.3.010329

Cited by 176 publications

(97 citation statements)

References 114 publications

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“…Alternative approaches to MSD for achieving universality, such as code-switching [21,[42][43][44], have been proposed. Such alternative approaches are not always compatible with the 2D hardware constraints and have been shown to require larger resource overhead costs in their implementation [29,45,46].…”

Section: Fault-tolerant |H -Type Magic State Preparation Using Smt So...mentioning

confidence: 99%

“…However, the surface code still provides lower overhead costs to achieve a given logical error rate for most studied realistic noise models [29]. Since the methods of Section III are used to prepare magic states encoded in the color code, in Section IV we show how magic states encoded in the color code can be converted to magic states encoded in the surface code.…”

Section: Introductionmentioning

confidence: 99%

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Finding fault-tolerant Clifford circuits using satisfiability modulo theories solvers and decoding merged color-surface codes

Shutty,

Chamberland

2022

Preprint

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Universal fault-tolerant quantum computers will require the use of efficient protocols to implement encoded operations necessary in the execution of algorithms. In this work, we show how SMT solvers can be used to automate the construction of Clifford circuits with certain fault-tolerance properties and apply our techniques to a fault-tolerant magic state preparation protocol. Part of the protocol requires converting magic states encoded in the color code to magic states encoded in the surface code. Since the teleportation step involves decoding a color code merged with a surface code, we develop a new decoding algorithm applicable to such codes.

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Section: Fault-tolerant |H -Type Magic State Preparation Using Smt So...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finding fault-tolerant Clifford circuits using satisfiability modulo theories solvers and decoding merged color-surface codes

Shutty,

Chamberland

2022

Preprint

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“…2, we convert all gates to Toffoli gates and make a comparison between PLAQ and spiltoperator estimates. We choose to work in units of Toffoli gates instead of T -gates since recent, low-overhead magic state distillation factories output Toffoli states [40,41]. The Toffoli count for PLAQ can be reproduced from Table II by assuming that 2 T -gates can be performed using 1 Toffoli gate (given access to a catalyst [36,40,42]) so that the total Toffoli count is N TOF + (N T /2).…”

Section: Phase Estimationmentioning

confidence: 99%

“…The physical qubit requirements and algorithm runtime for specific architectures is discussed further in the companion paper Ref. [41] VI. CONCLUSIONS…”

Section: Fig (2imentioning

confidence: 99%

Early fault-tolerant simulations of the Hubbard model

Campbell

2020

Preprint

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“…In the Noisy Intermediate-Scale Quantum (or NISQ) era, quantum computers are still rapidly evolving but still present several limitations: Firstly, quantum computing as a field has not yet settled on a particular physical realization for quantum hardware [25]; leading candidate implementations include those constructed from superconducting qubits [26], VOLUME 4, 2016 [27], [28], [29], [30], [19], trapped-ion qubits [31], [32], [33], [34], as well as other proposals [35], [36], [37], [38], [39]. Secondly, many devices exhibit fixed and finite connectivity constraints between neighboring qubits (a notable exception to this is trapped-ion technology, in which one can in principle produce "all-to-all" connectivity [31]).…”

Section: Introductionmentioning

confidence: 99%

Topological-Graph Dependencies and Scaling Properties of a Heuristic Qubit-Assignment Algorithm

Steinberg

Feld

Almudéver

et al. 2022

IEEE Trans. Quantum Eng.

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The qubit-mapping problem aims to assign and route qubits of a quantum circuit onto a NISQ device in an optimized fashion, with respect to some cost function. Finding an optimal solution to this problem is known to scale exponentially in computational complexity; as such, it is imperative to investigate scalable qubit-mapping solutions for NISQ computation. In this work, a noise-aware heuristic qubit-assignment algorithm (which assigns initial placements for qubits in a quantum algorithm to qubits on a NISQ device, but does not route qubits during the quantum algorithm's execution) is presented and compared against the optimal brute-force solution, as well as a trivial qubit assignment, with the aim to quantify the performance of our heuristic qubit-assignment algorithm. We find that for small, connectedgraph algorithms, our heuristic-assignment algorithm faithfully lies in between the effective upper and lower bounds given by the brute-force and trivial qubit-assignment algorithms. Additionally, we find that the topological-graph properties of quantum algorithms with over six qubits play an important role in our heuristic qubit-assignment algorithm's performance on NISQ devices. Finally, we investigate the scaling properties of our heuristic algorithm for quantum processors with up to 100 qubits; here, the algorithm was found to be scalable for quantum-algorithms which admit path-like graphs. Our findings show that as the size of the quantum processor in our simulation grows, so do the benefits from utilizing the heuristic qubitassignment algorithm, under particular constraints for our heuristic algorithm. This work thus characterizes the performance of a heuristic qubit-assignment algorithm with respect to the topological-graph and scaling properties of a quantum algorithm which one may wish to run on a given NISQ device.

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Building a Fault-Tolerant Quantum Computer Using Concatenated Cat Codes

Cited by 176 publications

References 114 publications

Finding fault-tolerant Clifford circuits using satisfiability modulo theories solvers and decoding merged color-surface codes

Finding fault-tolerant Clifford circuits using satisfiability modulo theories solvers and decoding merged color-surface codes

Early fault-tolerant simulations of the Hubbard model

Topological-Graph Dependencies and Scaling Properties of a Heuristic Qubit-Assignment Algorithm

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