Abstract
Whether a given target state can be prepared by starting with a simple product state and acting with a finite-depth quantum circuit is a key question in condensed matter physics and quantum information science. It underpins classifications of topological phases, as well as the understanding of topological quantum codes, and has obvious relevance for device implementations. Traditionally, this question assumes that the quantum circuit is made up of unitary gates that are geometrically local. Inspired by the advent of noisy intermediate-scale quantum devices, we reconsider this question with -local gates, i.e., gates that act on no more than degrees of freedom but are not restricted to be geometrically local. First, we construct explicit finite-depth circuits of symmetric -local gates that create symmetry-protected topological (SPT) states from an initial product state. Our construction applies to SPT states protected by global symmetries or subsystem symmetries but not to those with higher-form symmetries, which we conjecture remain nontrivial. Next, we show how to implement arbitrary translationally invariant quantum cellular automata in any dimension using finite-depth circuits of -local gates. These results imply that the topological classifications of SPT phases and quantum cellular automata both collapse to a single trivial phase in the presence of -local interactions. We furthermore argue that SPT phases are fragile to generic -local symmetric perturbations. We conclude by discussing the implications for other phases, such as fracton phases, and surveying future directions. Our analysis opens a new experimentally motivated conceptual direction examining the stability of phases and the feasibility of state preparation without the assumption of geometric locality.
- Received 10 January 2023
- Accepted 20 December 2023
DOI:https://doi.org/10.1103/PRXQuantum.5.010304
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
A major goal of condensed matter physics is to classify all phases of matter. Sorting physical systems into phases and describing their universal properties leads to an understanding of the immense richness exhibited by many-body quantum systems, which can then be harnessed for new technologies. Most studies of the classification of phases are rooted in the assumption of locality, which says that a given particle interacts only with its neighboring particles. This is a natural and fundamental assumption in typical condensed matter settings. Recently, however, there has been a proliferation of synthetic many-body quantum systems, sometimes called “quantum simulators,” in which long-range interactions that couple distant particles are naturally present. This calls into question the relevance of the traditional classification of phases to the physics occurring within these devices.
Here we study how the classification of phases is modified in the presence of interactions that couple arbitrarily far-separated particles. We find that such interactions completely trivialize a major class of phases of matter, the so-called symmetry-protected topological phases of matter, and also trivialize the classification of locality-preserving unitary operators, also known as quantum cellular automata. Our methods also provide efficient methods to generate representatives of these phases of matter in quantum simulators.
This work represents a first step toward a classification of phases that is relevant to the physics occurring in quantum simulators, with broad implications for condensed matter physics, quantum information, and quantum computation.
