Abstract
The current generation of noisy intermediate-scale quantum computers introduces new opportunities to study quantum many-body systems. In this paper, we show that quantum circuits can provide a dramatically more efficient representation than current classical numerics of the quantum states generated under nonequilibrium quantum dynamics. For quantum circuits, we perform both real- and imaginary-time evolution using an optimization algorithm that is feasible on near-term quantum computers. We benchmark the algorithms by finding the ground state and simulating a global quench of the transverse-field Ising model with a longitudinal field on a classical computer. Furthermore, we implement (classically optimized) gates on a quantum processing unit and demonstrate that our algorithm effectively captures real-time evolution.
- Received 14 September 2020
- Revised 16 December 2020
- Accepted 18 February 2021
DOI:https://doi.org/10.1103/PRXQuantum.2.010342
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
The first quantum computers have recently shown specific capabilities beyond those of classical computers, demonstrating what has been termed quantum supremacy. Nevertheless, the question remains whether quantum computers can be used to solve practical problems, particularly while these devices remain relatively small scale and noisy. To achieve this, new quantum algorithms must be developed to efficiently simulate relevant physical problems on such machines. In this work, we demonstrate such a framework for studying condensed-matter systems and provide new insights into the complexity of quantum states.
The power of quantum computers and the difficulty of studying condensed-matter physics both stem from the immense complexity of the quantum states of many particles. In this work, we show that our inability to represent a range of physically relevant quantum states may be due to the restrictions of our classical computers. By proposing a new representation that is tailor made for these quantum devices, we demonstrate that we can achieve a dramatic exponential reduction in the number of parameters required to specify a quantum state. We focus upon a one-dimensional system where we develop methods for studying both ground states and nonequilibrium quantum dynamics that can be applied directly on a quantum computer.
The tools that we develop in this paper may help us more deeply understand the complexity of physically relevant quantum states. Furthermore, these tools are scalable, flexible, and may provide practical methods for simulating physical systems in higher dimensions.
