01872nas a2200145 4500008004100000245006400041210006300105260001300168520141700181100002301598700002701621700002101648700002001669856003701689 2024 eng d00aZero-temperature entanglement membranes in quantum circuits0 aZerotemperature entanglement membranes in quantum circuits c4/3/20243 a

In chaotic quantum systems, the entanglement of a region A can be described in terms of the surface tension of a spacetime membrane pinned to the boundary of A. Here, we interpret the tension of this entanglement membrane in terms of the rate at which information "flows" across it. For any orientation of the membrane, one can define (generically nonunitary) dynamics across the membrane; we explore this dynamics in various space-time translation-invariant (STTI) stabilizer circuits in one and two spatial dimensions. We find that the flux of information across the membrane in these STTI circuits reaches a steady state. In the cases where this dynamics is nonunitary and the steady state flux is nonzero, this occurs because the dynamics across the membrane is unitary in a subspace of extensive entropy. This generalized unitarity is present in a broad class of STTI stabilizer circuits, and is also present in some special non-stabilizer models. The existence of multiple unitary (or generalized unitary) directions forces the entanglement membrane tension to be a piecewise linear function of the orientation of the membrane; in this respect, the entanglement membrane behaves like an interface in a zero-temperature classical lattice model. We argue that entanglement membranes in random stabilizer circuits that produce volume-law entanglement are also effectively at zero temperature.

1 aSommers, Grace, M.1 aGopalakrishnan, Sarang1 aGullans, Michael1 aHuse, David, A. uhttps://arxiv.org/abs/2404.0297501491nas a2200157 4500008004100000245005900041210005800100260001300158490000800171520102800179100001901207700002201226700002001248700002801268856003701296 2023 eng d00aNon-Abelian symmetry can increase entanglement entropy0 aNonAbelian symmetry can increase entanglement entropy c1/3/20230 v1073 a

The pillars of quantum theory include entanglement and operators' failure to commute. The Page curve quantifies the bipartite entanglement of a many-body system in a random pure state. This entanglement is known to decrease if one constrains extensive observables that commute with each other (Abelian ``charges''). Non-Abelian charges, which fail to commute with each other, are of current interest in quantum thermodynamics. For example, noncommuting charges were shown to reduce entropy-production rates and may enhance finite-size deviations from eigenstate thermalization. Bridging quantum thermodynamics to many-body physics, we quantify the effects of charges' noncommutation -- of a symmetry's non-Abelian nature -- on Page curves. First, we construct two models that are closely analogous but differ in whether their charges commute. We show analytically and numerically that the noncommuting-charge case has more entanglement. Hence charges' noncommutation can promote entanglement.

1 aMajidy, Shayan1 aLasek, Aleksander1 aHuse, David, A.1 aHalpern, Nicole, Yunger uhttps://arxiv.org/abs/2209.1430301641nas a2200181 4500008004100000245008700041210006900128260001400197520106300211100001801274700002301292700002101315700002001336700002701356700002001383700001901403856003701422 2022 eng d00aInfinite-randomness criticality in monitored quantum dynamics with static disorder0 aInfiniterandomness criticality in monitored quantum dynamics wit c5/27/20223 a

We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in their entanglement structure, but the nature of the critical point differs drastically from the case with constant measurement rate. In particular, at the critical measurement rate, we find that the entanglement of a subsystem of size ℓ scales as S∼ℓ√; moreover, the dynamical critical exponent z=∞. The MIPT is flanked by Griffiths phases with continuously varying dynamical exponents. We argue for this infinite-randomness scenario on general grounds and present numerical evidence that it captures some features of the universal critical properties of MIPT using large-scale simulations of Clifford circuits. These findings demonstrate that the relevance and irrelevance of perturbations to the MIPT can naturally be interpreted using a powerful heuristic known as the Harris criterion. 

1 aZabalo, Aidan1 aWilson, Justin, H.1 aGullans, Michael1 aVasseur, Romain1 aGopalakrishnan, Sarang1 aHuse, David, A.1 aPixley, J., H. uhttps://arxiv.org/abs/2205.1400201727nas a2200205 4500008004100000245008700041210006900128260001400197490000800211520109000219100001801309700002101327700002301348700002001371700002701391700002701418700002001445700001901465856003701484 2022 eng d00aOperator Scaling Dimensions and Multifractality at Measurement-Induced Transitions0 aOperator Scaling Dimensions and Multifractality at MeasurementIn c2/11/20220 v1283 a

Repeated local measurements of quantum many body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar values of the critical exponents, making it unclear if there is only one underlying universality class. Here, we directly probe the properties of the conformal field theories governing these MIPTs using a numerical transfer-matrix method, which allows us to extract the effective central charge, as well as the first few low-lying scaling dimensions of operators at these critical points. Our results provide convincing evidence that the generic and Clifford MIPTs for qubits lie in different universality classes and that both are distinct from the percolation transition for qudits in the limit of large onsite Hilbert space dimension. For the generic case, we find strong evidence of multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

1 aZabalo, Aidan1 aGullans, Michael1 aWilson, Justin, H.1 aVasseur, Romain1 aLudwig, Andreas, W. W.1 aGopalakrishnan, Sarang1 aHuse, David, A.1 aPixley, J., H. uhttps://arxiv.org/abs/2107.0339301625nas a2200229 4500008004100000245008800041210006900129260001400198520092400212100001801136700002101154700001601175700002101191700001601212700002201228700001801250700002501268700002101293700002001314700002401334856003701358 2021 eng d00aObservation of measurement-induced quantum phases in a trapped-ion quantum computer0 aObservation of measurementinduced quantum phases in a trappedion c6/10/20213 a

Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped ion quantum computer, where the system evolution is represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerent threshold. We probe the "pure" phase, where the system is rapidly projected to a deterministic state conditioned on the measurement outcomes, and the "mixed" or "coding" phase, where the initial state becomes partially encoded into a quantum error correcting codespace. We find convincing evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition clearly emerge.

1 aNoel, Crystal1 aNiroula, Pradeep1 aZhu, Daiwei1 aRisinger, Andrew1 aEgan, Laird1 aBiswas, Debopriyo1 aCetina, Marko1 aGorshkov, Alexey, V.1 aGullans, Michael1 aHuse, David, A.1 aMonroe, Christopher uhttps://arxiv.org/abs/2106.0588102376nas a2200157 4500008004100000245005000041210004900091260001500140520192200155100002102077700002202098700002002120700001702140700002402157856003702181 2020 eng d00aQuantum coding with low-depth random circuits0 aQuantum coding with lowdepth random circuits c10/19/20203 a

Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity in D≥1 spatial dimensions to generate quantum error-correcting codes. For random stabilizer codes and the erasure channel, we find strong evidence that a depth O(logN) random circuit is necessary and sufficient to converge (with high probability) to zero failure probability for any finite amount below the channel capacity for any D. Previous results on random circuits have only shown that O(N1/D) depth suffices or that O(log3N) depth suffices for all-to-all connectivity (D→∞). We then study the critical behavior of the erasure threshold in the so-called moderate deviation limit, where both the failure probability and the distance to the channel capacity converge to zero with N. We find that the requisite depth scales like O(logN) only for dimensions D≥2, and that random circuits require O(N−−√) depth for D=1. Finally, we introduce an "expurgation" algorithm that uses quantum measurements to remove logical operators that cause the code to fail by turning them into either additional stabilizers or into gauge operators in a subsystem code. With such targeted measurements, we can achieve sub-logarithmic depth in D≥2 spatial dimensions below capacity without increasing the maximum weight of the check operators. We find that for any rate beneath the capacity, high-performing codes with thousands of logical qubits are achievable with depth 4-8 expurgated random circuits in D=2 dimensions. These results indicate that finite-rate quantum codes are practically relevant for near-term devices and may significantly reduce the resource requirements to achieve fault tolerance for near-term applications. 

1 aGullans, Michael1 aKrastanov, Stefan1 aHuse, David, A.1 aJiang, Liang1 aFlammia, Steven, T. uhttps://arxiv.org/abs/2010.0977502166nas a2200205 4500008004100000245008500041210006900126260001500195520153900210100001701749700001501766700002101781700002101802700001901823700001901842700001701861700002001878700002401898856003801922 2016 eng d00aMany-body localization in a quantum simulator with programmable random disorder0 aManybody localization in a quantum simulator with programmable r c2016/06/063 a

When a system thermalizes it loses all local memory of its initial conditions. This is a general feature of open systems and is well described by equilibrium statistical mechanics. Even within a closed (or reversible) quantum system, where unitary time evolution retains all information about its initial state, subsystems can still thermalize using the rest of the system as an effective heat bath. Exceptions to quantum thermalization have been predicted and observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize in spite of strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. Here we experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium. We observe the essential signatures of MBL: memory retention of the initial state, a Poissonian distribution of energy level spacings, and entanglement growth in the system at long times. Our platform can be scaled to higher numbers of spins, where detailed modeling of MBL becomes impossible due to the complexity of representing such entangled quantum states. Moreover, the high degree of control in our experiment may guide the use of MBL states as potential quantum memories in naturally disordered quantum systems.

1 aSmith, Jacob1 aLee, Aaron1 aRicherme, Philip1 aNeyenhuis, Brian1 aHess, Paul, W.1 aHauke, Philipp1 aHeyl, Markus1 aHuse, David, A.1 aMonroe, Christopher uhttp://arxiv.org/abs/1508.07026v1