How to fault-tolerantly realize any quantum circuit with local operations

• URL: http://arxiv.org/abs/2402.13863v1
• Date: Wed, 21 Feb 2024 15:12:40 GMT
• Title: How to fault-tolerantly realize any quantum circuit with local operations
• Authors: Shin Ho Choe and Robert Koenig
• Abstract summary: We show how to realize a general quantum circuit involving gates between arbitrary pairs of qubits. We prove that circuit-level local noise modeling is equivalent to local noise in the original circuit.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show how to realize a general quantum circuit involving gates between arbitrary pairs of qubits by means of geometrically local quantum operations and efficient classical computation. We prove that circuit-level local stochastic noise modeling an imperfect implementation of our derived schemes is equivalent to local stochastic noise in the original circuit. Our constructions incur a constant-factor increase in the quantum circuit depth and a polynomial overhead in the number of qubits: To execute an arbitrary quantum circuit on $n$ qubits, we give a 3D quantum fault-tolerance architecture involving $O(n^{3/2} \log^3 n)$ qubits, and a quasi-2D architecture using $O(n^2 \log^3 n)$ qubits. Applied to recent fault-tolerance constructions, this gives a fault-tolerance threshold theorem for universal quantum computations with local operations, a polynomial qubit overhead and a quasi-polylogarithmic depth overhead. More generally, our transformation dispenses with the need for considering the locality of operations when designing schemes for fault-tolerant quantum information processing.

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