Abstract
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 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.
- Received 2 November 2022
- Accepted 27 March 2023
DOI:https://doi.org/10.1103/PRXQuantum.4.020315
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 preparation of many-body entangled states is a universally important ingredient for the proposed use cases of quantum computers, from fundamental science (e.g., quantum chemistry and condensed-matter physics) to applications such as quantum machine learning. However, preparing certain entangled states with local unitary gates—the primary ingredient of quantum algorithms—comes at a great cost: for many states with nontrivial topological properties, the depth of the preparation circuit increases with the size of the state. This presents a major roadblock for the high-fidelity preparation of large classically intractable entangled states, particularly on current noisy intermediate-scale quantum (NISQ) devices, which are limited to relatively shallow circuit depths due to decoherence.
In this work, we present a way around this limitation. By expanding our toolbox to include measurements in addition to local unitary gates, we theoretically and experimentally demonstrate that we can speed up the preparation of one of the most paradigmatic entangled states in condensed-matter physics: the Affleck, Kennedy, Lieb, and Tasaki (AKLT) state. In particular, we show that it becomes possible to deterministically prepare the AKLT state with a circuit the depth of which is independent of the size of the state, a theoretical impossibility with local unitary gates alone. We carry out our scheme on IBM Quantum processors and, notably, we find that it outperforms purely unitary preparation.
This work presents the most efficient known scheme to prepare the AKLT state (useful for tasks such as measurement-based quantum computation) while more broadly serving as the first experimental demonstration of using measurements to speed up state preparation on a NISQ-era device. That we find a clear improvement over purely unitary preparation hints at the significant potential of measurement-based circuit-depth-reduction strategies for NISQ-era applications, an exciting direction that requires further research.
