Browsing by Author "Brun, Todd A."

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Constant depth fault-tolerant Clifford circuits for multi-qubit large block codes
(2020-10-01)
Zheng, Yi-Cong
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Lai, Ching-Yi
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Brun, Todd A.
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Kwek, Leong-Chuan
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電信工程研究所
Fault-tolerant quantum computation (FTQC) schemes using large block codes that encodek> 1 qubits innphysical qubits can potentially reduce the resource overhead to a great extent because of their high encoding rate. However, the fault-tolerant (FT) logical operations for the encoded qubits are difficult to find and implement, which usually takes not only a very large resource overhead but also longin situcomputation time. In this paper, we focus on Calderbank-Shor-Steane [[n,k,d]] (CSS) codes and their logical FT Clifford circuits. We show that the depth of an arbitrary logical Clifford circuit can be implemented fault-tolerantly inO(1) stepsin situvia either Knill or Steane syndrome measurement circuit, with the qualified ancilla states efficiently prepared. Particularly, for those codes satisfyingk/n similar to Theta(1), the resource scaling for Clifford circuits implementation on the logical level can be the same as on the physical level up to a constant, which is independent of code distanced. With a suitable pipeline to produce ancilla states, our scheme requires only a modest resource cost in physical qubits, physical gates, and computation time for very large scale FTQC.
Quantum Data-Syndrome Codes
(2020-03-01)
Ashikhmin, Alexei
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Lai, Ching-Yi
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Brun, Todd A.
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傳播研究所
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Institute of Communication Studies
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of measured error syndromes. To obtain reliable error syndromes using imperfect physical circuits, we propose syndrome measurement (SM) and quantum data-syndrome (DS) codes. SM codes protect syndrome with linearly dependent redundant stabilizer measurements. DS codes generalize this idea for simultaneous correction of both data qubits and syndrome bits errors. We study fundamental properties of quantum DS codes, including split weight enumerators, generalized MacWilliams identities, and linear programming bounds. In particular, we derive Singleton and Hamming-type upper bounds on the minimum distance of degenerate quantum DS codes. Then we study random DS codes and show that random DS codes with a relatively small additional syndrome measurements achieve the Gilbert-Varshamov bound of stabilizer codes. Finally, we propose a family of CSS-type quantum DS codes based on classical cyclic codes, which include the Steane code and the quantum Golay code.