Quantum State Preparation and Non-Unitary Evolution with Diagonal Operators

TL;DR

This paper introduces a dilation-based quantum algorithm that efficiently simulates non-unitary operations using a single ancilla qubit, enabling high-fidelity preparation of sub-normalized states and modeling open quantum system dynamics.

Contribution

The authors develop a novel dilation algorithm utilizing SVD to implement non-unitary operators with minimal qubit overhead, suitable for noisy intermediate-scale quantum devices.

Findings

Successfully prepared sub-normalized states with high fidelity

Simulated open quantum system dynamics accurately on quantum hardware

Limited gate complexity by focusing on diagonal unitaries in dilated space

Abstract

Realizing non-unitary transformations on unitary-gate based quantum devices is critically important for simulating a variety of physical problems including open quantum systems and subnormalized quantum states. We present a dilation based algorithm to simulate non-unitary operations using probabilistic quantum computing with only one ancilla qubit. We utilize the singular-value decomposition (SVD) to decompose any general quantum operator into a product of two unitary operators and a diagonal non-unitary operator, which we show can be implemented by a diagonal unitary operator in a 1-qubit dilated space. While dilation techniques increase the number of qubits in the calculation, and thus the gate complexity, our algorithm limits the operations required in the dilated space to a diagonal unitary operator, which has known circuit decompositions. We use this algorithm to prepare random sub-normalized two-level states on a quantum device with high fidelity. Furthermore, we present the accurate non-unitary dynamics of two-level open quantum systems in a dephasing channel and an amplitude damping channel computed on a quantum device. The algorithm presented will be most useful for implementing general non-unitary operations when the SVD can be readily computed, which is the case with most operators in the noisy intermediate-scale quantum computing era.