Abstract
The quantum imaginary time evolution is a powerful algorithm for preparing the ground and thermal states on near-term quantum devices. However, algorithmic errors induced by Trotterization and local approximation severely hinder its performance. Here we propose a deep reinforcement learning-based method to steer the evolution and mitigate these errors. In our scheme, the well-trained agent can find the subtle evolution path where most algorithmic errors cancel out, enhancing the fidelity significantly. We verified the method’s validity with the transverse-field Ising model and the Sherrington-Kirkpatrick model. Numerical calculations and experiments on a nuclear magnetic resonance quantum computer illustrate the efficacy. The philosophy of our method, eliminating errors with errors, sheds light on error reduction on near-term quantum devices.
Highlights
The quantum imaginary time evolution is a powerful algorithm for preparing the ground and thermal states on near-term quantum devices
We propose a deep reinforcement learning-based method to steer the quantum imaginary time evolution (QITE) and mitigate algorithmic errors
We have proposed an Reinforcement learning (RL)-based framework to steer the QITE algorithm for preparing a k-UGS state
Summary
The quantum imaginary time evolution is a powerful algorithm for preparing the ground and thermal states on near-term quantum devices. The philosophy of our method, eliminating errors with errors, sheds light on error reduction on near-term quantum devices. The quantum imaginary time evolution (QITE) is a promising near-term algorithm to find the ground state of a given Hamiltonian. It has been applied to prepare thermal states, simulate open quantum systems, and calculate finite temperature properties[17–19]. A pure quantum state is said to be k-UGS if it is the unique ground state of a k-local Hamiltonian H^ 1⁄4 ∑mj1⁄41 h^1⁄2j, where each local term h^1⁄2j acts on at most k neighboring qubits. The final state after long-time imaginary time evolution lim eÀβH^ Ψ ð1Þ β!1 init has very high fidelity with the k-UGS state.
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