Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes

Zheng, Yuqian; Lai, Ching-Yi; Brun, Todd A.; Kwek, Leong‐Chuan

doi:10.1088/2058-9565/aba34d

Cited by 15 publications

(8 citation statements)

References 56 publications

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“…, n. Given the tableau of U , Aaronson and Gottesman provided a circuit synthesis algorithm that decomposes U to a circuit that contains 11 stages of computation in the sequence -H-C-P-C-P-C-H-P-C-P-C- [38], where -H-, -P-, and -C-stand for stages composed of only Hadamard, Phase, and CNOT gates, respectively. (This is further improved to a nine-stage circuit by Maslov and Roetteler [39], which can be utilized in fault-tolerant quantum computation [40].) Consequently, any Clifford circuit can be decomposed into O(n 2 / log n) Clifford gates with circuit depth O(n) [41] or O(n 2 ) Clifford gates with circuit depth O(log n) [42].…”

Section: B a Circuit Synthesis Methodsmentioning

confidence: 99%

“…Since a Clifford circuit can be implemented with depth logarithmic in the number of qubits [42], we have the first statement. As for the second statement, we simply use the gate teleportation technique [44], [40] to implement a Clifford circuit with a corresponding ancillary state. If this ancillary state can be prepared offline, the teleportation part can be done in constant depth.…”

Section: Characterizing Quantum Circuits Of Some T Gates a Expanded S...mentioning

confidence: 99%

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Learning Quantum Circuits of Some T Gates

Lai

Cheng

2022

IEEE Trans. Inform. Theory

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In this paper, we study the problem of learning quantum circuits of a certain structure. If the unknown target is an n-qubit Clifford circuit, we devise an algorithm to reconstruct its circuit representation by using O(n 2 ) queries to it. It is unknown for decades how to handle circuits beyond the Clifford group for which the stabilizer formalism cannot be applied. Herein, we study quantum circuits of T -depth one given the all-zero state as an input. We show that their output states can be represented by some stabilizer pseudomixtures. By analyzing the algebraic structure of the stabilizer pseudomixture, we can reconstruct the output state of an unknown T -depth one quantum circuit on input |0 n from the outcomes of Pauli measurements and Bell measurements. If the number of T gates is of the order O(log n), our algorithm requires O(n 2 ) queries. Our results greatly extend the previous known facts that stabilizer states can be efficiently identified based on the stabilizer formalism. Hence, the proposed expanded stabilizer formalism and our analysis might pave the way towards learning quantum circuits beyond the Clifford structure.

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Section: B a Circuit Synthesis Methodsmentioning

confidence: 99%

Section: Characterizing Quantum Circuits Of Some T Gates a Expanded S...mentioning

confidence: 99%

Learning Quantum Circuits of Some T Gates

Lai

Cheng

2022

IEEE Trans. Inform. Theory

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“…While Ref. [42] establishes a method to perform quantum computation using faulttolerant gate teleportation [49], the cost associated with the distillation of the requisite resource state [50] is not understood well in the practical regime of interest.…”

Section: Introductionmentioning

confidence: 99%

Low-overhead fault-tolerant quantum computing using long-range connectivity

Cohen,

Kim,

Bartlett

et al. 2021

Preprint

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Vast numbers of qubits will be needed for large-scale quantum computing using today's faulttolerant architectures due to the overheads associated with quantum error correction. We present a scheme for low-overhead fault-tolerant quantum computation based on quantum low-density paritycheck (LDPC) codes, where the capability of performing long-range entangling interactions allows a large number of logical qubits to be encoded with a modest number of physical qubits. In our approach, quantum logic gates operate via logical Pauli measurements that preserve both the protection of the LDPC codes as well as the low overheads in terms of required number of additional ancilla qubits. Compared with the surface code architecture, resource estimates for our scheme indicate order-of-magnitude improvements in the overheads for encoding and processing around one hundred logical qubits, meaning fault-tolerant quantum computation at this scale may be achievable with a few thousand physical qubits at achievable error rates.

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“…This method destructively measures all the logical qubits in a code block. Alternatively, one can measure a subset of logical qubits by moving them to an ancilla block which is then measured destructively [Got13, NFB17, BVC + 17], or using a Steane-type ancillary block [ZLBK20]. Here, we design measurement sequences that perform logical measurements without any extra ancillary block, eliminating the time and space required for ancilla preparation.…”

Section: Introductionmentioning

confidence: 99%

Short Shor-style syndrome sequences

Delfosse¹,

Reichardt²

2020

Preprint

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We optimize fault-tolerant quantum error correction to reduce the number of syndrome bit measurements. Speeding up error correction will also speed up an encoded quantum computation, and should reduce its effective error rate. We give both code-specific and general methods, using a variety of techniques and in a variety of settings. We design new quantum error-correcting codes specifically for efficient error correction, e.g., allowing single-shot error correction. For codes with multiple logical qubits, we give methods for combining error correction with partial logical measurements. There are tradeoffs in choosing a code and error-correction technique. While to date most work has concentrated on optimizing the syndrome-extraction procedure, we show that there are also substantial benefits to optimizing how the measured syndromes are chosen and used.As an example, we design single-shot measurement sequences for fault-tolerant quantum error correction with the 16-qubit extended Hamming code. Our scheme uses 10 syndrome bit measurements, compared to 40 measurements with the Shor scheme. We design single-shot logical measurements as well: any logical Z measurement can be made together with fault-tolerant error correction using only 11 measurements. For comparison, using the Shor scheme a basic implementation of such a non-destructive logical measurement uses 63 measurements.We also offer ten open problems, the solutions of which could lead to substantial improvements of fault-tolerant error correction.

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Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes

Cited by 15 publications

References 56 publications

Learning Quantum Circuits of Some T Gates

Learning Quantum Circuits of Some T Gates

Low-overhead fault-tolerant quantum computing using long-range connectivity

Short Shor-style syndrome sequences

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