Simulating Open Quantum Systems Using Hamiltonian Simulations

• URL: http://arxiv.org/abs/2311.15533v3
• Date: Wed, 24 Apr 2024 20:53:43 GMT
• Title: Simulating Open Quantum Systems Using Hamiltonian Simulations
• Authors: Zhiyan Ding, Xiantao Li, Lin Lin,
• Abstract summary: We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged Hilbert space that can approximate the Lindblad dynamics up to an arbitrarily high order. This unitary representation can then be simulated using a quantum circuit that involves only Hamiltonian simulation and tracing out the ancilla qubits.
• Score: 4.328210085579236
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged Hilbert space that can approximate the Lindblad dynamics up to an arbitrarily high order. This unitary representation can then be simulated using a quantum circuit that involves only Hamiltonian simulation and tracing out the ancilla qubits. There is no need for additional postselection in measurement outcomes, ensuring a success probability of one at each stage. Our method can be directly generalized to the time-dependent setting. We provide numerical examples that simulate both time-independent and time-dependent Lindbladian dynamics with accuracy up to the third order.

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