Quantum circuit design for accurate simulation of qudit channels

TL;DR

This paper presents a classical algorithm that efficiently designs quantum circuits for simulating arbitrary qudit channels with high accuracy on fault-tolerant quantum computers, optimizing for error tolerance and resource use.

Contribution

It introduces a novel classical decomposition method for quantum channels into generalized extreme channels, enabling efficient circuit design for qudit simulation.

Findings

Circuit run-time scales logarithmically with error tolerance

Resource requirements are quadratic in Hilbert space dimension

Algorithm achieves high-precision simulation within fault-tolerant constraints

Abstract

We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm distance. The classical algorithm is constructed by decomposing a quantum channel into a convex combination of generalized extreme channels by optimization of a set of nonlinear coupled algebraic equations. The resultant circuit is a randomly chosen generalized extreme channel circuit whose run-time is logarithmic with respect to the error tolerance and quadratic with respect to Hilbert space dimension, which requires only a single ancillary qudit plus classical dits.