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  1. Free, publicly-accessible full text available April 1, 2023
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  3. Abstract Quantum many-body systems away from equilibrium host a rich variety of exotic phenomena that are forbidden by equilibrium thermodynamics. A prominent example is that of discrete time crystals 1–8 , in which time-translational symmetry is spontaneously broken in periodically driven systems. Pioneering experiments have observed signatures of time crystalline phases with trapped ions 9,10 , solid-state spin systems 11–15 , ultracold atoms 16,17 and superconducting qubits 18–20 . Here we report the observation of a distinct type of non-equilibrium state of matter, Floquet symmetry-protected topological phases, which are implemented through digital quantum simulation with an array of programmable superconductingmore »qubits. We observe robust long-lived temporal correlations and subharmonic temporal response for the edge spins over up to 40 driving cycles using a circuit of depth exceeding 240 and acting on 26 qubits. We demonstrate that the subharmonic response is independent of the initial state, and experimentally map out a phase boundary between the Floquet symmetry-protected topological and thermal phases. Our results establish a versatile digital simulation approach to exploring exotic non-equilibrium phases of matter with current noisy intermediate-scale quantum processors 21 .« less
    Free, publicly-accessible full text available July 21, 2023
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  10. null (Ed.)
    We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a path of length n , we show that there exists a constant ϵ ≈ 0.034 such that the quantum routing time is at most ( 1 − ϵ ) n , whereas any swap-based protocol needs at least time n − 1 . This represents the first known quantum advantage over swap-based routing methods and also gives improved quantum routing times for realistic architectures such asmore »grids. Furthermore, we show that our algorithm approaches a quantum routing time of 2 n / 3 in expectation for uniformly random permutations, whereas swap-based protocols require time n asymptotically. Additionally, we consider sparse permutations that route k ≤ n qubits and give algorithms with quantum routing time at most n / 3 + O ( k 2 ) on paths and at most 2 r / 3 + O ( k 2 ) on general graphs with radius r .« less
    Free, publicly-accessible full text available August 31, 2022