Source-linked AI summary
Quantum Simulation of Open Quantum Systems Using a Unitary Decomposition of Operators
Anthony W. Schlimgen, Kade Head-Marsden, LeeAnn M. Sager, Prineha Narang, David A. Mazziotti
TL;DR
Open-system evolution uses non-unitary operators, challenging quantum computers built from unitary gates. The paper decomposes operators into at most four unitary operators and reports agreement with exact classical solutions in zero- and finite-temperature amplitude damping simulations.
Problem
Open-system evolution uses non-unitary operators, challenging quantum computers whose fundamental gates are unitary.
Source: p. 1Method
The algorithm represents an operator’s action as a sum of at most four strictly unitary operators, with the decomposition exact as epsilon approaches zero.
Source: p. 1Results
Simulated dynamics in zero- and finite-temperature amplitude damping channels agree with the exact classical solutions.
Source: pp. 3–4Takeaways & Limitations
The formalism also applies to quantum-chemistry and physics operators such as Hamiltonians and dipoles, offering an alternative to Trotterization.
Source: p. 4Because populations are scaled by epsilon, generally below one, accurate statistics on noisy devices can require many samples.
Source: p. 2
Abstract
from arXiv · showhide
Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open quantum system employs a non-unitary operator, the simulation of open quantum systems presents a challenge for universal quantum computers constructed from only unitary operators or gates. Here we present a general algorithm for implementing the action of any non-unitary operator on an arbitrary state on a quantum device. We show that any quantum operator can be exactly decomposed as a linear combination of at most four unitary operators. We demonstrate this method on a two-level system in both zero and finite temperature amplitude damping channels. The results are in agreement with classical calculations, showing promise in simulating non-unitary operations on intermediate-term and future quantum devices.