Exact and Efficient Simulation of Concordant Computation

TL;DR

This paper develops a new framework for the exact and efficient classical simulation of concordant quantum computations, extending previous results to larger gates and qudits, and analyzing the computational complexity involved.

Contribution

It introduces a novel theoretical framework for simulating concordant quantum computations efficiently and exactly, broadening the class of simulatable circuits beyond previous work.

Findings

Efficient classical simulation is possible for a larger class of concordant computations.

The paper provides alternative, exact proofs for previous simulation results.

It analyzes the arithmetic complexity involved in solving equations during simulation.

Abstract

Concordant computation is a circuit-based model of quantum computation for mixed states, that assumes that all correlations within the register are discord-free (i.e. the correlations are essentially classical) at every step of the computation. The question of whether concordant computation always admits efficient simulation by a classical computer was first considered by B. Eastin in quant-ph/1006.4402v1, where an answer in the affirmative was given for circuits consisting only of one- and two-qubit gates. Building on this work, we develop the theory of classical simulation of concordant computation. We present a new framework for understanding such computations, argue that a larger class of concordant computations admit efficient simulation, and provide alternative proofs for the main results of quant-ph/1006.4402v1 with an emphasis on the exactness of simulation which is crucial for this model. We include detailed analysis of the arithmetic complexity for solving equations in the simulation, as well as extensions to larger gates and qudits. We explore the limitations of our approach, and discuss the challenges faced in developing efficient classical simulation algorithms for all concordant computations.