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Stephen DT, Ho WW, Wei TC, Raussendorf R, Verresen R. Universal Measurement-Based Quantum Computation in a One-Dimensional Architecture Enabled by Dual-Unitary Circuits. PHYSICAL REVIEW LETTERS 2024; 132:250601. [PMID: 38996243 DOI: 10.1103/physrevlett.132.250601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Accepted: 05/14/2024] [Indexed: 07/14/2024]
Abstract
A powerful tool emerging from the study of many-body quantum dynamics is that of dual-unitary circuits, which are unitary even when read "sideways," i.e., along the spatial direction. Here, we show that this provides the ideal framework to understand and expand on the notion of measurement-based quantum computation (MBQC). In particular, applying a dual-unitary circuit to a many-body state followed by appropriate measurements effectively implements quantum computation in the spatial direction. We show how the dual-unitary dynamics generated by the dynamics of the paradigmatic one-dimensional kicked Ising chain with certain parameter choices generate resource states for universal deterministic MBQC. Specifically, after k time steps, equivalent to a depth-k quantum circuit, we obtain a resource state for universal MBQC on ∼3k/4 encoded qubits. Our protocol allows generic quantum circuits to be "rotated" in space-time and gives new ways to exchange between resources like qubit number and coherence time in quantum computers. Beyond the practical advantages, we also interpret the dual-unitary evolution as generating an infinite sequence of new symmetry-protected topological phases with spatially modulated symmetries, which gives a vast generalization of the well-studied one-dimensional cluster state and shows that our protocol is robust to symmetry-respecting deformations.
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Foligno A, Kos P, Bertini B. Quantum Information Spreading in Generalized Dual-Unitary Circuits. PHYSICAL REVIEW LETTERS 2024; 132:250402. [PMID: 38996275 DOI: 10.1103/physrevlett.132.250402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/17/2023] [Revised: 02/26/2024] [Accepted: 05/08/2024] [Indexed: 07/14/2024]
Abstract
We study the spreading of quantum information in a recently introduced family of brickwork quantum circuits that generalizes the dual-unitary class. These circuits are unitary in time, while their spatial dynamics is unitary only in a restricted subspace. First, we show that local operators spread at the speed of light as in dual-unitary circuits, i.e., the butterfly velocity takes the maximal value allowed by the geometry of the circuit. Then, we prove that the entanglement spreading can still be characterized exactly for a family of compatible initial states (in fact, for an extension of the compatible family of dual-unitary circuits) and that the asymptotic entanglement slope is again independent on the Rényi index. Remarkably, however, we find that the entanglement velocity is generically smaller than 1. We use these properties to find a closed-form expression for the entanglement-membrane line tension.
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Cecile G, De Nardis J, Ilievski E. Squeezed Ensembles and Anomalous Dynamic Roughening in Interacting Integrable Chains. PHYSICAL REVIEW LETTERS 2024; 132:130401. [PMID: 38613285 DOI: 10.1103/physrevlett.132.130401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/06/2023] [Accepted: 02/28/2024] [Indexed: 04/14/2024]
Abstract
It is widely accepted that local subsystems in isolated integrable quantum systems equilibrate to generalized Gibbs ensembles. Here, we identify a particular class of initial states in interacting integrable models that evade canonical generalized thermalization. Particularly, we demonstrate that in the easy-axis regime of the quantum XXZ chain, pure nonequilibrium initial states that lack magnetic fluctuations instead locally relax to squeezed generalized Gibbs ensembles governed by nonlocal equilibrium Hamiltonians, representing exotic equilibrium states with subextensive charge fluctuations that violate the self-affine scaling. At the isotropic point, we find exceptional behavior and explicit dependence on the initial state. Particularly, we find that relaxation from the Néel state is governed by extensive fluctuations and a superdiffusive dynamical exponent compatible with the Kardar-Parisi-Zhang universality. On the other hand, there are other nonfluctuating initial states that display diffusive scaling, e.g., a product state of spin singlets. Our predictions provide examples of anomalous quantum transport and fluctuations in strictly quantum states which can be directly tested in state-of-the-art cold atomic experimental settings.
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Affiliation(s)
- Guillaume Cecile
- Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université, 95302 Cergy-Pontoise Cedex, France
| | - Jacopo De Nardis
- Laboratoire de Physique Théorique et Modélisation, CNRS UMR 8089, CY Cergy Paris Université, 95302 Cergy-Pontoise Cedex, France
| | - Enej Ilievski
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
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Pilatowsky-Cameo S, Dag CB, Ho WW, Choi S. Complete Hilbert-Space Ergodicity in Quantum Dynamics of Generalized Fibonacci Drives. PHYSICAL REVIEW LETTERS 2023; 131:250401. [PMID: 38181361 DOI: 10.1103/physrevlett.131.250401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/10/2023] [Revised: 10/20/2023] [Accepted: 11/01/2023] [Indexed: 01/07/2024]
Abstract
Ergodicity of quantum dynamics is often defined through statistical properties of energy eigenstates, as exemplified by Berry's conjecture in single-particle quantum chaos and the eigenstate thermalization hypothesis in many-body settings. In this work, we investigate whether quantum systems can exhibit a stronger form of ergodicity, wherein any time-evolved state uniformly visits the entire Hilbert space over time. We call such a phenomenon complete Hilbert-space ergodicity (CHSE), which is more akin to the intuitive notion of ergodicity as an inherently dynamical concept. CHSE cannot hold for time-independent or even time-periodic Hamiltonian dynamics, owing to the existence of (quasi)energy eigenstates which precludes exploration of the full Hilbert space. However, we find that there exists a family of aperiodic, yet deterministic drives with minimal symbolic complexity-generated by the Fibonacci word and its generalizations-for which CHSE can be proven to occur. Our results provide a basis for understanding thermalization in general time-dependent quantum systems.
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Affiliation(s)
- Saúl Pilatowsky-Cameo
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Ceren B Dag
- ITAMP, Harvard-Smithsonian Center for Astrophysics, Cambridge, Massachusetts 02138, USA
- Department of Physics, Harvard University, 17 Oxford Street Cambridge, Massachusetts 02138, USA
| | - Wen Wei Ho
- Department of Physics, National University of Singapore, Singapore 117542
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
| | - Soonwon Choi
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Dowling N, Kos P, Modi K. Scrambling Is Necessary but Not Sufficient for Chaos. PHYSICAL REVIEW LETTERS 2023; 131:180403. [PMID: 37977605 DOI: 10.1103/physrevlett.131.180403] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Revised: 08/01/2023] [Accepted: 09/14/2023] [Indexed: 11/19/2023]
Abstract
We show that out-of-time-order correlators (OTOCs) constitute a probe for local-operator entanglement (LOE). There is strong evidence that a volumetric growth of LOE is a faithful dynamical indicator of quantum chaos, while OTOC decay corresponds to operator scrambling, often conflated with chaos. We show that rapid OTOC decay is a necessary but not sufficient condition for linear (chaotic) growth of the LOE entropy. We analytically support our results through wide classes of local-circuit models of many-body dynamics, including both integrable and nonintegrable dual-unitary circuits. We show sufficient conditions under which local dynamics leads to an equivalence of scrambling and chaos.
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Affiliation(s)
- Neil Dowling
- School of Physics & Astronomy, Monash University, Clayton, Victoria 3800, Australia
| | - Pavel Kos
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, 85748 Garching
| | - Kavan Modi
- School of Physics & Astronomy, Monash University, Clayton, Victoria 3800, Australia
- Quantum for New South Wales, Sydney 2000 New South Wales Australia
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McGinley M, Fava M. Shadow Tomography from Emergent State Designs in Analog Quantum Simulators. PHYSICAL REVIEW LETTERS 2023; 131:160601. [PMID: 37925705 DOI: 10.1103/physrevlett.131.160601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/12/2023] [Accepted: 09/11/2023] [Indexed: 11/07/2023]
Abstract
We introduce a method that allows one to infer many properties of a quantum state-including nonlinear functions such as Rényi entropies-using only global control over the constituent degrees of freedom. In this protocol, the state of interest is first entangled with a set of ancillas under a fixed global unitary, before projective measurements are made. We show that when the unitary is sufficiently entangling, a universal relationship between the statistics of the measurement outcomes and properties of the state emerges, which can be connected to the recently discovered phenomeonon of emergent quantum state designs in chaotic systems. Thanks to this relationship, arbitrary observables can be reconstructed using the same number of experimental repetitions that would be required in classical shadow tomography [Huang et al., Nat. Phys. 16, 1050 (2020)NPAHAX1745-247310.1038/s41567-020-0932-7]. Unlike previous approaches to shadow tomography, our protocol can be implemented using only global Hamiltonian evolution, as opposed to qubit-selective logic gates, which makes it particularly well suited to analog quantum simulators, including ultracold atoms in optical lattices and arrays of Rydberg atoms.
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Affiliation(s)
- Max McGinley
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- T.C.M. Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Michele Fava
- Rudolf Peierls Centre for Theoretical Physics, Clarendon Laboratory, Parks Road, Oxford OX1 3PU, United Kingdom
- Philippe Meyer Institute, Physics Department, École Normale Supérieure (ENS), Université PSL, 24 rue Lhomond, F-75231 Paris, France
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Casagrande HP, Xing B, Dalmonte M, Rodriguez A, Balachandran V, Poletti D. Complexity of spin configuration dynamics due to unitary evolution and periodic projective measurements. Phys Rev E 2023; 108:044128. [PMID: 37978657 DOI: 10.1103/physreve.108.044128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Accepted: 09/22/2023] [Indexed: 11/19/2023]
Abstract
We study the Hamiltonian dynamics of a many-body quantum system subjected to periodic projective measurements, which leads to probabilistic cellular automata dynamics. Given a sequence of measured values, we characterize their dynamics by performing a principal component analysis (PCA). The number of principal components required for an almost complete description of the system, which is a measure of complexity we refer to as PCA complexity, is studied as a function of the Hamiltonian parameters and measurement intervals. We consider different Hamiltonians that describe interacting, noninteracting, integrable, and nonintegrable systems, including random local Hamiltonians and translational invariant random local Hamiltonians. In all these scenarios, we find that the PCA complexity grows rapidly in time before approaching a plateau. The dynamics of the PCA complexity can vary quantitatively and qualitatively as a function of the Hamiltonian parameters and measurement protocol. Importantly, the dynamics of PCA complexity present behavior that is considerably less sensitive to the specific system parameters for models which lack simple local dynamics, as is often the case in nonintegrable models. In particular, we point out a figure of merit that considers the local dynamics and the measurement direction to predict the sensitivity of the PCA complexity dynamics to the system parameters.
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Affiliation(s)
- Heitor P Casagrande
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - Bo Xing
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
| | - Marcello Dalmonte
- Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Alex Rodriguez
- Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
| | - Vinitha Balachandran
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
- Institute of High-Performance Computing, Agency for Science, Technology, and Research (A*STAR), 138632, Singapore
| | - Dario Poletti
- Science, Mathematics and Technology Cluster, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
- Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, 34151 Trieste, Italy
- EPD Pillar, Singapore University of Technology and Design, 8 Somapah Road, 487372 Singapore
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Rampp MA, Moessner R, Claeys PW. From Dual Unitarity to Generic Quantum Operator Spreading. PHYSICAL REVIEW LETTERS 2023; 130:130402. [PMID: 37067305 DOI: 10.1103/physrevlett.130.130402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Accepted: 02/21/2023] [Indexed: 06/19/2023]
Abstract
Dual-unitary circuits are paradigmatic examples of exactly solvable yet chaotic quantum many-body systems, but solvability naturally goes along with a degree of nongeneric behavior. By investigating the effect of weakly broken dual unitarity on the spreading of local operators, we study whether, and how, small deviations from dual unitarity recover fully generic many-body dynamics. We present a discrete path-integral formula for the out-of-time-order correlator and recover a butterfly velocity smaller than the light-cone velocity, v_{B}<v_{LC}, and a diffusively broadening operator front, two generic features of ergodic quantum spin chains absent in dual-unitary circuit dynamics. The butterfly velocity and diffusion constant are determined by a small set of microscopic quantities, and the operator entanglement of the gates has a crucial role.
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Affiliation(s)
- Michael A Rampp
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Roderich Moessner
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
| | - Pieter W Claeys
- Max Planck Institute for the Physics of Complex Systems, 01187 Dresden, Germany
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