Unitary Dilation Strategy Towards Efficient and Exact Simulation of Non-Unitary Quantum Evolutions

TL;DR

This paper presents a novel unitary dilation method using Lagrange-Sylvester interpolation to efficiently and exactly simulate non-unitary quantum evolutions, significantly reducing measurement costs in quantum simulations.

Contribution

The authors introduce an exact single-ancilla unitary decomposition technique for non-unitary operators based on Lagrange-Sylvester interpolation, improving efficiency and precision.

Findings

Exact representation of non-unitary operators without approximation errors

Significant reduction in measurement costs for quantum simulations

Applicable to open quantum system simulations

Abstract

Simulating quantum systems with their environments often requires non-unitary operations, and mapping these to quantum devices often involves expensive dilations or prohibitive measurement costs to achieve desired precisions. Building on prior work with a finite-differences strategy, we introduce an efficient and exact single-ancilla unitary decomposition technique that addresses these challenges. Our approach is based on Lagrange-Sylvester interpolation, akin to analytical differentiation techniques for functional interpolation. As a result, we can exactly express any arbitrary non-unitary operator with no finite approximation error using an easily computable decomposition. This can lead to several orders of magnitude reduction in the measurement cost, which is highly desirable for practical quantum computations of open systems.