Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session S50: Quantum Circuits and Entanglement DynamicsRecordings Available
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Sponsoring Units: DCMP Chair: Kasra Sardashti, Clemson University Room: McCormick Place W-474A |
Thursday, March 17, 2022 8:00AM - 8:12AM |
S50.00001: Entanglement phase transitions in non-unitary Gaussian fermionic circuits Hassan Shapourian, chao-ming Jian, Bela Bauer, Andreas W Ludwig Random quantum circuits with projective measurements are known to be a useful tool for simulating non-unitary quantum dynamics which results in a variety of non-equilibrium steady-state phases with different scaling laws for the entanglement entropy. In this talk, we consider a variant of such circuits based on random tensor networks of non-interacting fermions which exhibit two phases, logarithmic scaling law and area law, as the tensor parameters are tuned. We introduce several quantities to identify these two phases and characterize the critical theory at the phase transitions. Using these quantities, we present phase diagrams for a generic parametrization of tensors and discuss the effect of the Born rule on the critical theory. |
Thursday, March 17, 2022 8:12AM - 8:24AM |
S50.00002: Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits. Utkarsh Agrawal, Aidan Zabalo, Kun Chen, Justin Wilson, Andrew Potter, Sarang Gopalakrishnan, Jed Pixley, Romain Vasseur Monitored quantum circuits can exhibit an entanglement transition as a function of the rate of measurements, stemming from the competition between scrambling unitary dynamics and disentangling projective measurements. We study how entanglement dynamics in non-unitary quantum circuits can be enriched in the presence of charge conservation, using a combination of exact numerics and a mapping onto a statistical mechanics model of constrained hard-core random walkers. We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement, distinguished by whether measurements can efficiently reveal the total charge of the system. We study numerically the critical behavior of the charge-sharpening and entanglement transitions in U(1) circuits, and show that they exhibit emergent Lorentz invariance and can also be diagnosed using scalable local ancilla probes. Our statistical mechanical mapping technique readily generalizes to arbitrary Abelian groups. |
Thursday, March 17, 2022 8:24AM - 8:36AM |
S50.00003: Entanglement negativity and measurement-induced phases in open quantum circuits Zack Weinstein, Yimu Bao, Zala Lenarcic, Soonwon Choi, Ehud Altman Recent works on monitored random quantum circuits have revealed a dynamical phase transition between volume law and area law entangled steady states. To determine whether large scale entanglement and measurement-induced transitions can survive in the presence of realistic decoherence processes, we investigate how these measurement-induced phases are affected by coupling to dephasing channels at the system boundaries. We employ the logarithmic negativity as a metric of mixed-state entanglement in the resulting open system dynamics, where the bipartite entanglement entropy loses meaning as an entanglement measure. Although the presence of decoherence in the unitary circuit without measurements results in area law negativity as expected from Page's theorem, we find numerically that the addition of measurements can stabilize a phase with power law scaling of negativity. This new measurement-induced phase can be understood analytically within an effective statistical mechanics model, where the power law negativity arises as the free energy cost of the measurement-induced finite temperature fluctuations of domain walls. Our work provides insight on the ability to maintain large-scale quantum coherence in nontrivial open quantum systems, an important ingredient for quantum computation. |
Thursday, March 17, 2022 8:36AM - 8:48AM |
S50.00004: Information encoding transition in random classical circuits and its instability toward gate quantization Anasuya N Lyons, Soonwon Choi, Ehud Altman We formulate a semi-classical circuit model to clarify the role of quantum entanglement in the recently discovered encoding phase transitions in quantum circuits with measurements. As a starting point we define a random circuit model with nearest neighbor classical gates interrupted by erasure errors. In analogy with the quantum setting, this system undergoes a purification transition at a critical error rate above which the classical information entropy in the output state vanishes. We show that this phase transition is in the directed percolation universality class, consistent with the fact that having zero entropy is an absorbing state of the dynamics; this classical circuit cannot generate entropy. Adding an arbitrarily small density of quantum gates in presence of errors eliminates the transition by destroying the absorbing state: the quantum gates generate internal entanglement, which in presence of errors is converted to classical entropy. We describe the universal properties of this instability in an effective model of the semi-classical circuit. Our model highlights the crucial differences between information dynamics in classical and quantum circuits. |
Thursday, March 17, 2022 8:48AM - 9:00AM |
S50.00005: Stabilizing Criticality and Long-Ranged Entanglement in Measurement-Only Dynamics Sagar Vijay, Ali Lavasani, Zhu-Xi Luo Quantum circuit dynamics with local, projective measurements provide a way of realizing a rich spectrum of entangled states of quantum matter. We study a (2+1)-dimensional quantum circuit involving only repeated, local projective measurements, and demonstrate that this circuit stabilizes a phase with (i) a logarithmic violation of area-law entanglement which coexists with (ii) true long-ranged entanglement, as quantified by the conditional mutual information. This phase provides a non-equilibrium generalization of a gapless spin liquid state which can arise as a stable, zero-temperature phase of quantum matter in two spatial dimensions. We relate the entanglement properties of this highly-entangled, critical phase to a classical loop ensemble in three spatial dimensions. A phase transition out of this long-range-entangled phase can be driven by tuning the rate of different local projective measurements, and which we study in numerical simulations of these dynamics. |
Thursday, March 17, 2022 9:00AM - 9:12AM |
S50.00006: Spacetime duality between localization transitions and measurement-induced transitions Tsung-Cheng Lu, Tarun Grover Time evolution of quantum many-body systems typically leads to a state with maximal entanglement allowed by symmetries. Two distinct routes to impede entanglement growth are inducing localization via spatial disorder, or subjecting the system to non-unitary evolution, e.g., via projective measurements. Here we employ the idea of space-time rotation of a circuit to explore the relation between systems that fall into these two classes. In particular, by space-time rotating unitary Floquet circuits that display a localization transition, we construct non-unitary circuits that display a rich variety of entanglement scaling and phase transitions. One outcome of our approach is a non-unitary circuit for free fermions in 1d that exhibits an entanglement transition from logarithmic scaling to volume-law scaling. This transition is accompanied by a `purification transition' analogous to that seen in hybrid projective-unitary circuits. We follow a similar strategy to construct a non-unitary 2d Clifford circuit that shows a transition from area to volume-law entanglement scaling. Similarly, we space-time rotate a 1d spin chain that hosts many-body localization to obtain a non-unitary circuit that exhibits an entanglement transition. Finally, we introduce an unconventional correlator and argue that if a unitary circuit hosts a many-body localization transition, then the correlator is expected to be singular in its non-unitary counterpart as well. |
Thursday, March 17, 2022 9:12AM - 9:24AM |
S50.00007: Finite time teleportation phase transition in random quantum circuits Yimu Bao, Maxwell B Block, Ehud Altman How long does it take to entangle two distant qubits in a quantum circuit evolved by generic unitary dynamics? We show that if the time evolution is followed by measurement of all but the two infinitely separated test qubits, then the entanglement between them can undergo a phase transition and become nonzero at a finite critical time tc. The fidelity of teleporting a quantum state from an input qubit to an infinitely distant output qubit shows the same critical onset. Specifically, these finite time transitions occur in short-range interacting two-dimensional random unitary circuits and in sufficiently long-range interacting one-dimensional circuits. The phase transition is understood by mapping the random continuous-time evolution to a finite temperature thermal state of an effective spin Hamiltonian, where the inverse temperature equals the evolution time in the circuit. In this framework, the entanglement between two distant qubits at times t>tc corresponds to the emergence of long-range ferromagnetic spin correlations below the critical temperature. We verify these predictions using numerical simulation of Clifford circuits and propose potential realizations in existing platforms for quantum simulation. |
Thursday, March 17, 2022 9:24AM - 9:36AM |
S50.00008: Universal correlations in quantum trajectories of the transverse field Ising model Rohith Sajith, Zack Weinstein, Ehud Altman While the universal properties of quantum systems near a critical point are well understood in equilibrium, determining robust signatures of quantum criticality in nonequilibrium systems remains an ongoing challenge. Motivated by recent works on measurement-induced dynamical phase transitions in quantum circuits, we investigate the effect of repeated measurements of an edge spin in a transverse field Ising spin chain, which is initialized in its ground state and tuned across the quantum critical point. While the continuous monitoring drives the system out of equilibrium and destroys criticality in traditional observables obtained from the averaged density matrix, we find that signatures of quantum critical behavior can nevertheless be seen in individual measurement trajectories of the system. Using a combination of numerical simulations and field-theoretic techniques, we identify observables nonlinear in the density matrix, which remain sensitive to universal CFT behavior in the nonequilibrium monitored system. This work provides a step towards exploring critical behavior in monitored systems accessible to experiments. |
Thursday, March 17, 2022 9:36AM - 9:48AM |
S50.00009: Mixed state dynamics in a random quantum channel Zhi Li, Shengqi Sang, Timothy Hsieh Generic open quantum systems will become thermalized due to interactions with the environment. Here, as a minimal model, we considered the mixed state dynamics for a qudit chain under a random depolarization channel. We find that the system reaches thermalization within a system-independent time scale. As a result, various correlation and entanglement measures obey an area law: the maximal value is bounded by the boundary instead of the volume. |
Thursday, March 17, 2022 9:48AM - 10:00AM |
S50.00010: Phase Transitions in the Classical Simulability of Open Quantum Systems Fariha Azad We study the evolution of an open quantum system using a Langevin unravelling of the density matrix evolution over matrix product states. As the strength of coupling to and temperature of the environment is increased, we find a transition where the entanglement of the individual trajectories saturates, permitting a classical simulation of the system for all times. This is the Hamiltonian counterpart of the saturation in entanglement found in random circuits with projective measurements. If a system is open, there is a limit to the advantage in simulating its behaviour on a quantum computer, even when that evolution harbours important quantum effects. |
Thursday, March 17, 2022 10:00AM - 10:12AM |
S50.00011: Quantum-inspired tools in classical many-body dynamics Andrea Pizzi, Daniel Malz, Andreas Nunnenkamp, Johannes Knolle The exponentially large Hilbert space of quantum many-body systems provides a natural playground to explore how correlations spread dynamically. As a prominent example, the case of unitary dynamics following a quantum quench has been extensively studied in terms of entanglement entropy, that can describe correlations in a comprehensive (nonlocal) way. By contrast, in the case of classical dynamics the attention has remained limited mostly to order parameters and few-body correlation functions. However, the phase space of a classical many-body system can also be exponentially large, which begs the question about the dynamics of correlations beyond few-body observables in a classical setting. Here, we show that many of the salient features of the entanglement dynamics following a quantum quench (e.g., linear growth to an extensive value) also emerge in classical Hamiltonian dynamics, both for the mutual information and for a suitably defined classical analogue of the entanglement entropy. To demonstrate the generality of our approach, we then apply it in the setting of cellular automata. Looking ahead, our study opens new possibilities across physics, information theory, and statistics. |
Thursday, March 17, 2022 10:12AM - 10:24AM |
S50.00012: Simulating a measurement-induced phase transition with superconducting qubit arrays Gonzalo Martín Vázquez, Taneli Tolpanen, Matti Silveri The use of quantum computing is limited until the full development of large-scale fault-tolerant quantum computers. However, state-of-the-art quantum devices can be exploited for quantum simulations to explore exotic and novel physics. Recently, new phase transitions have been described in the entanglement properties of many-body dynamics when unitary evolution is interleaved by measurements, exhibiting universal properties that point to unexplored critical phenomena. Superconducting circuits, in particular arrays of superconducting transmon devices, are among the most promising platforms for quantum simulations. We show numerically that superconducting circuit systems modeled by an attractive Bose Hubbard model interspersed with measurements exhibit a phase transition, from volume-law to area-law, in the entanglement properties of the set of steady-state trajectories, which depends on the probability of measuring. Interestingly, the dispersion in the number of bosons in the half of the array can exhibit a behavior similar to that of entanglement entropy, indicating that it is an experimental candidate to avoid post-selection issues. We also implement the theory of the replica method to describe the model and obtain analytical results that agree with the numerical simulations. |
Thursday, March 17, 2022 10:24AM - 10:36AM |
S50.00013: Measurement-Induced Phase Transition in the Monitored Sachdev-Ye-Kitaev Model Chunxiao Liu, Shao-Kai Jian, Xiao Chen, Brian Swingle, Pengfei Zhang We construct Brownian Sachdev-Ye-Kitaev (SYK) chains subjected to continuous monitoring and explore possible entanglement phase transitions therein. We analytically derive the effective action in the large-N limit and show that an entanglement transition is caused by the symmetry breaking in the enlarged replica space. In the noninteracting case with SYK2 chains, the model features a continuous O(2) symmetry between two replicas and a transition corresponding to spontaneous breaking of that symmetry upon varying the measurement rate. In the symmetry broken phase at low measurement rate, the emergent replica criticality associated with the Goldstone mode leads to a log-scaling entanglement entropy that can be attributed to the free energy of vortices. In the symmetric phase at higher measurement rate, the entanglement entropy obeys area-law scaling. In the interacting case, the continuous O(2) symmetry is explicitly lowered to a discrete C4 symmetry, giving rise to volume-law entanglement entropy in the symmetry-broken phase due to the enhanced linear free energy cost of domain walls compared to vortices. The interacting transition is described by C4 symmetry breaking. We also verify the large-N critical exponents by numerically solving the Schwinger-Dyson equation. |
Thursday, March 17, 2022 10:36AM - 10:48AM |
S50.00014: Fast-Scrambling and Operator Confinement Using an Auxiliary Qubit Joseph C Szabo, Nandini Trivedi We study a locally interacting spin-1/2 system coupled to a single, central qubit. All spins develop effective all-to-all interactions through shared interaction with the auxiliary qubit, where stronger coupling continuously degrades any sense of locality. We obtain the operator and entanglement dynamics in a nonintegrable ring-star, spin-1/2 Ising model with tunable ancilla coupling. As the interaction with the central spin increases across all sites, we find a surprising transition from super-ballistic scrambling and information growth to continuously restricted sub-ballistic entanglement and increasingly inhibited operator growth. We provide exact dynamics of small systems working with non-equilibrium and effective infinite temperature states, and additionally contribute analytic early-time expansions that support the observed rapid scrambling to quantum-zeno transition. |
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