Fault-tolerant circuit synthesis for universal fault-tolerant quantum
computing
- URL: http://arxiv.org/abs/2206.02691v1
- Date: Mon, 6 Jun 2022 15:43:36 GMT
- Title: Fault-tolerant circuit synthesis for universal fault-tolerant quantum
computing
- Authors: Yongsoo Hwang
- Abstract summary: We present a quantum circuit synthesis algorithm for implementing universal fault-tolerant quantum computing based on geometricd codes.
We show how to synthesize the set of universal fault-tolerant protocols for $[[7,1,3]]$ Steane code and the syndrome measurement protocol of $[[23, 1, 7]]$ Golay code.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We present a quantum circuit synthesis algorithm for implementing universal
fault-tolerant quantum computing based on concatenated codes. To realize
fault-tolerant quantum computing, the fault-tolerant quantum protocols should
be transformed into executable quantum circuits based on the nearest-neighbor
interaction. Unlike topological codes that are defined based on local
operations fundamentally, for the concatenated codes, it is possible to obtain
the circuits composed of the local operations by applying the quantum circuit
synthesis. However, by the existing quantum circuit synthesis developed for
ordinary quantum computational algorithms, the fault-tolerant of the protocol
may not be preserved in the resulting circuit. Besides, we have to consider
something more to implement the quantum circuit of universal fault-tolerant
quantum computing. First, we have not to propagate quantum errors on data
qubits when selecting a qubit move path (a sequence of \emph{SWAP} gates) to
satisfy the geometric locality constraint. Second, the circuit should be
self-contained so that it is possible to act independently regardless of the
situation. Third, for universal fault-tolerant quantum computing, we require
multiple fault-tolerant quantum circuits of multiple fault-tolerant quantum
protocols acting on the same input, a logical data qubit. Last, we need to
recall fault-tolerant protocols such as syndrome measure and encoder implicitly
include classical control processing conditioned on the measurement outcomes,
and therefore have to partition the quantum circuits in time flow to execute
the classical control as the architect intended. We propose the circuit
synthesis method resolving the requirements and show how to synthesize the set
of universal fault-tolerant protocols for $[[7,1,3]]$ Steane code and the
syndrome measurement protocol of $[[23, 1, 7]]$ Golay code.
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