Simulating Open Quantum Systems Using Hamiltonian Simulations

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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• Accuracy guarantees and quantum advantage in analogue open quantum simulation with and without noise
• Simulating spin biology using a digital quantum computer: Prospects on a near-term quantum hardware emulator
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• Design nearly optimal quantum algorithm for linear differential equations via Lindbladians
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• Simulation of bilayer Hamiltonians based on monitored quantum trajectories
• Learning the dynamics of Markovian open quantum systems from experimental data
• Simple and efficient end-to-end quantum thermal and ground state preparation
• Strong symmetries in collision models and physical dilations of covariant quantum maps
• Computational Complexity and Simulability of Non-Hermitian Quantum Dynamics
• Quantum Signal Processing and Quantum Singular Value Transformation on $U(N)$
• A Randomized Method for Simulating Lindblad Equations and Thermal State Preparation
• Quantum Simulation of Two-Level $PT$-Symmetric Systems Using Hermitian Hamiltonians
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