Variational Quantum Algorithm for Unitary Dilation

TL;DR

This paper presents a hybrid quantum-classical algorithm for efficiently implementing approximate unitary dilations of non-unitary operators, improving noise resilience and resource efficiency for simulating open quantum systems on near-term quantum devices.

Contribution

It introduces a novel variational framework embedding non-unitary operators into unitary matrices with a parameterized circuit, validated on superconducting hardware.

Findings

Reduces quantum resource requirements compared to standard methods

Enhances robustness against device noise

Achieves high-fidelity simulation of non-unitary processes

Abstract

We introduce a hybrid quantum-classical framework for efficiently implementing approximate unitary dilations of non-unitary operators with enhanced noise resilience. The method embeds a target non-unitary operator into a subblock of a unitary matrix generated by a parameterized quantum circuit with universal expressivity, while a classical optimizer adjusts circuit parameters under the global unitary constraint. As a representative application, we consider the non-unitary propagator of a Lindbladian superoperator acting on the vectorized density matrix, which is relevant for simulating open quantum systems. We further validate the approach experimentally on superconducting devices in the Quafu quantum cloud computing cluster. Compared with standard dilation protocols, our method significantly reduces quantum resource requirements and improves robustness against device noise, achieving high-fidelity simulation. Its generality also enables compatibility with non-Markovian dynamics and Kraus-operator-based evolutions, providing a practical pathway for the noise-resilient simulation of non-unitary processes on near-term quantum hardware.