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Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on verification of an analog quantum simulation, in which the verifier need only run an $O\left({\lambda }^2\right)$-time classical computation, and the prover need only prepare $O\left(1\right)$samples of a history state and perform $O\left({\lambda }^2\right)$single-qubit measurements, for a security parameter $\lambda$. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations. Published by the American Physical Society2025 

Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes that affects code performance and ease of physical realization. For device architectures restricted to two-dimensional (2D) local gates, naively implementing the high-rate codes suitable for low-overhead fault-tolerant quantum computing incurs prohibitive overhead. In this work, we present an error-correction protocol built on a bilayer architecture that aims to reduce operational overheads when restricted to 2D local gates by measuring some generators less frequently than others. We investigate the family of bivariate-bicycle qLDPC codes and show that they are well suited for a parallel syndrome-measurement scheme using fast routing with local operations and classical communication (LOCC). Through circuit-level simulations, we find that in some parameter regimes, bivariate-bicycle codes implemented with this protocol have logical error rates comparable to the surface code while using fewer physical qubits. Published by the American Physical Society2025 

We study the problem of implementing arbitrary permutations of qubits under interaction constraints in quantum systems that allow for arbitrarily fast local operations and classical communication (LOCC). In particular, we show examples of speedups over swap-based and more general unitary routing methods by distributing entanglement and using LOCC to perform quantum teleportation. We further describe an example of an interaction graph for which teleportation gives a logarithmic speedup in the worst-case routing time over swap-based routing. We also study limits on the speedup afforded by quantum teleportation—showing an $O\left(\sqrt{NlogN}\right)$upper bound on the separation in routing time for any interaction graph—and give tighter bounds for some common classes of graphs. Published by the American Physical Society2024