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arXiv:2307.14325 · Physical Review Research

Simulation of open quantum systems via low-depth convex unitary evolutions

Joseph Peetz, Scott E. Smart, Spyros Tserkis, Prineha Narang

Published Jun 10, 2024• 12 citations
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Abstract

Simulating physical systems on quantum devices is one of the most promising applications of quantum technology. Current quantum approaches to simulating open quantum systems are still practically challenging on NISQ-era devices, because they typically require ancilla qubits and extensive controlled sequences. In this work, we propose a hybrid quantum-classical approach for simulating a class of open system dynamics called random-unitary channels. These channels naturally decompose into a series of convex unitary evolutions, which can then be efficiently sampled and run as independent circuits. The method does not require deep ancilla frameworks and thus can be implemented with lower noise costs. We implement simulations of open quantum systems up to dozens of qubits and with large channel ranks. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.023263

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Quantum simulation of open quantum systems in the noisy intermediate-scale quantum (NISQ) era is hindered by the non-unitary nature of dissipative dynamics and the limited quantum resources available on near-term quantum processors. In this work, we propose a resource-efficient algorithm for simulating Lindbladian dynamics on NISQ devices. For open quantum systems with Pauli dissipations, we first derive a compact and stable mixed-unitary adjoint channel that approximates the target dissipative dynamics and enables ancilla-free implementation through trajectory sampling. To further reduce the circuit depth required for implementing the sampled trajectories, we introduce an adaptive variational quantum trajectory compression framework. In this framework, a depth-adaptive parameterized quantum circuit is trained to approximate repeated Trotterized Hamiltonian simulation operators, which are then used to replace repeated unitary segments appearing in the sampled trajectories. Importantly, the training procedure can also be performed without auxiliary qubits. Numerical simulations of the dissipative quantum XYXYXY model demonstrate the accuracy and resource efficiency of the proposed algorithm. Our results provide a practical route toward ancilla-free and depth-reduced simulation of open quantum systems on near-term quantum hardware.
Abstract Quantum simulation algorithms often require numerous ancilla qubits and deep circuits, prohibitive for near-term hardware. We introduce a framework for simulating quantum channels using ensembles of low-depth circuits in place of many-qubit dilations. This naturally enables simulations of open systems, which we demonstrate by preparing damped many-qubit GHZ states on ibm_hanoi. The technique further inspires two Hamiltonian simulation algorithms with gate counts that are asymptotically independent of the spectral precision target, reducing resource requirements by several orders of magnitude for a benchmark system.
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