Imaginary Time Propagation on a Quantum Chip

Abstract

Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems, and the heart of a number of numerical methods that have been used with great success in quantum chemistry, condensed matter and nuclear physics. We propose an algorithm to implement imaginary time propagation on a quantum computer. Our algorithm is devised in the context of an efficient encoding into an optimized gate, drawing on the underlying characteristics of the quantum device, of a unitary operation in an extended Hilbert space. However, we proved that for simple problems it can be successfully applied to standard digital quantum machines. This work paves the way for porting quantum many-body methods based on imaginary-time propagation to near-term quantum devices, enabling the future quantum simulation of the ground states of a broad class of microscopic systems.

12 pages, 8 figures, 3 tables

References in corpus (6)

• QuTiP 2: A Python framework for the dynamics of open quantum systems
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Local chiral effective field theory interactions and quantum Monte Carlo applications
• Preparation of excited states for nuclear dynamics on a quantum computer
• Noise-Resilient Quantum Dynamics Using Symmetry-Preserving Ansatzes
• Ground States via Spectral Combing on a Quantum Computer

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