Pieceable fault tolerant conversion between 5-qubit code and 7-CSS code
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Pieceable fault tolerant conversion between 5-qubit code and 7-CSS code Chen Lin1 · GuoWu Yang1
· QingBin Luo2 · XiaoYu Li3
Received: 10 December 2019 / Accepted: 26 June 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract We propose a non-transversal but pieceable fault tolerant conversion circuit that is used to convert encoded information between five-qubit code and seven-qubit CSS code. Since a syndrome extraction circuit requiring fewer ancillary qubit resources would facilitate the realization of large-scale quantum computations, we further adapt a flag-assisted fault tolerant syndrome measurement scheme to reduce the cost of ancillary preparation. Numerical simulations are also performed to further analyze the performance of our conversion method. Keywords Fault tolerant quantum computation · Quantum error correction code · Round-robin circuit
1 Introduction Practical quantum computation may be coming soon [19,21]. Consequently, the prospect of large-scale quantum computers has generated interest, as they can solve certain problems exponentially faster than computers using the best known classic algorithms [10,11,24]. However, given the limitations of current quantum computers, called noisy intermediate-scale quantum computers (NISQ), high-fidelity quantum circuits for the compiling of certain quantum algorithms always require very large quantum computers [5,14,22].
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GuoWu Yang [email protected]
1
Big Data Research Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, People’s Republic of China
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School of Information Engineering, Hubei Minzu University, Enshi 44500, People’s Republic of China
3
School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu 610054, People’s Republic of China 0123456789().: V,-vol
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C. Lin et al.
Specifically, by combining physical qubits through the use of error-correcting codes [15,20], single-qubit quantum information can be encoded by a logical qubit. Any logical circuit can be implemented in a fault tolerant manner through periodic syndrome measurement and error correction [13]. It has also been proved that when the physical error rate p phy is below a certain constant threshold [2,9,14], any quantum circuit consisting of n physical elementary components (measurement, gate and state preparation) can be simulated in a fault tolerant manner with a cost up to O( poly(log( nε )n)), where ε is the desired accuracy [18,20]. In practical applications, however, it is desirable to choose smaller codes to store the information in long-term memory. When we want to handle the quantum information with a quantum circuit, it is appropriate to convert the code under the information to some code that has a simple construction of a fault tolerant encoded logical gate. For example, the 7-qubit CSS code [4,28] requires more resources than the 5-qubit code for storing information because the former use
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