Deterministic Constant-Depth Preparation of the AKLT State on a Quantum Processor Using Fusion Measurements

• Main Authors: Crane, E. (Author), Girvin, S.M (Author), Smith, K.C (Author), Wiebe, N. (Author)
• Format: Article
• Language: English
• Published: American Physical Society 2023
• Subjects: Constant-depth circuits; Correlation lengths; Deterministics; Ground state; Matrix product state; Measurement-based quantum computation; Preparation method; Quantum computers; Quantum entanglement; Quantum processors; Speed up; System size; Topological phase; Topology
• Online Access: View Fulltext in Publisher; View in Scopus
• ISBN: 26913399 (ISSN)
• DOI: 10.1103/PRXQuantum.4.020315

The ground state of the spin-1 Affleck, Kennedy, Lieb, and Tasaki (AKLT) model is a paradigmatic example of both a matrix product state and a symmetry-protected topological phase and additionally holds promise as a resource state for measurement-based quantum computation. Having a nonzero correlation length, the AKLT state cannot be exactly prepared by a constant-depth unitary circuit composed of local gates. In this work, we demonstrate that this no-go limit can be evaded by augmenting a constant-depth circuit with fusion measurements, such that the total preparation time is independent of system size and entirely deterministic. We elucidate our preparation scheme using the language of tensor networks and, furthermore, show that the Z2×Z2 symmetry of the AKLT state directly affords this speed-up over previously known preparation methods. To demonstrate the practical advantage of measurement-assisted preparation on noisy intermediate-scale quantum (NISQ) devices, we carry out our protocol on an IBM Quantum processor. We measure both the string order and entanglement spectrum of prepared AKLT chains and, employing these as metrics, find improved results over the known (purely unitary) sequential preparation approach. We conclude with a demonstration of quantum teleportation using the AKLT state prepared by our measurement-assisted scheme. This work thus serves to provide an efficient strategy to prepare a specific resource in the form of the AKLT state and, more broadly, experimentally demonstrates the possibility for realizable improvement in state preparation afforded by measurement-based circuit depth reduction strategies on NISQ-era devices. © 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"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.