Abstract
Quantum simulation on emerging quantum hardware is a topic of intense interest. While many studies focus on computing ground state properties or simulating unitary dynamics of closed systems, open quantum systems are an interesting target of study owing to their ubiquity and rich physical behavior. However, their non-unitary dynamics are also not natural to simulate on digital quantum devices. Here, we report algorithms for the digital quantum simulation of the dynamics of open quantum systems governed by a Lindblad equation using adaptations of the quantum imaginary time evolution (QITE) algorithm. We demonstrate the algorithms on IBM Quantum's hardware with simulations of the spontaneous emission of a two level system and the dissipative transverse field Ising model. Our work advances efforts to simulate the dynamics of open quantum systems on quantum hardware.
Highlights
The development of quantum algorithms to simulate the dynamics of quantum many-body systems is a topic of interest owing to advances in quantum hardware [1–3]
Theoretical works examined the resources required for efficient quantum simulation of Markovian dynamics [23–25], concluding that arbitrary quantum channels can be efficiently simulated by combining elementary quantum channels
We demonstrate these algorithms on IBM Quantum hardware for two cases: the spontaneous emission of a two-level system in a heat bath at zero temperature, and the dissipative transverse field Ising model on two sites
Summary
The development of quantum algorithms to simulate the dynamics of quantum many-body systems is a topic of interest owing to advances in quantum hardware [1–3]. Determining the Kraus operators of a general system requires either computing the full unitary evolution of both the system and environment or casting a master equation into an operator-sum representation for the density operator The latter procedure can be approximated analogously to Trotterization [29,31], but requires either reset of ancillae qubits or a qubit overhead that scales linearly with the number of time steps in the simulation. The second algorithm expresses the density operator in terms of an ansatz that is preserved during both real- and imaginary–time evolution We demonstrate these algorithms on IBM Quantum hardware for two cases: the spontaneous emission of a two-level system in a heat bath at zero temperature, and the dissipative transverse field Ising model on two sites. We observe good agreement between the exact and hardware results, showing that the dynamics of open quantum systems are accessible on near-term quantum hardware
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