Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session J09: Open Quantum Systems II |
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Sponsoring Units: DQI Chair: Peter Groszkowski, University of Chicago Room: 106 |
Tuesday, March 3, 2020 2:30PM - 2:42PM |
J09.00001: Master equation approach to study Non-Markovian dynamics of open quantum systems Yusui Chen A full understanding of the decoherence dynamics of an open quantum system is of crucial importance for quantum information theory and quantum computing. In the last two decades, most theoretical and experimental research is replied on the Born-Markov approximation, a no-memory and quasi-static process. The associated Lindblad master equation has the great success in explaining some phenomena, e.g. the long-time limit steady state, quantum-classical transition. However, the recently achieved strong coupling between system and environment in many experiments breaks the Born-Markov approximation and forces one to study the decoherence in a strong non-Markovian and non-equilibrium regime. The major difficulty is raised up by lack of the technique to deal with the large number of degrees of freedom of the colored noisy environment. Starting from stochastic Schrödinger equations, we demonstrate a systematical method to derive the exact time convolution-less master equation for various open quantum systems, e.g. qubit systems, multi-level systems, and harmonic oscillator systems. Our methods can also be extended to the optomechanical systems and other non-linear coupling systems. |
Tuesday, March 3, 2020 2:42PM - 2:54PM |
J09.00002: Markovian Entanglement Dynamics under Locally Scrambled Quantum Evolution Wei-Ting Kuo, Ahmed Akhtar, Daniel Arovas, Yizhuang You We study the time evolution of quantum entanglement for a specific class of quantum dynamics, namely the locally scrambled quantum dynamics, where each step of the unitary evolution is drawn from a random ensemble that is invariant under on-site basis transformations. In this case, the average entanglement entropy follows Markovian dynamics that the entanglement property of the future state can be predicted solely based on the entanglement properties of the current state and the unitary operator at each step. We introduce the entanglement feature formulation to concisely organize the entanglement entropies over all subsystems into a many-body wave function, which allows us to describe the entanglement dynamics using an imaginary-time Schrodinger equation, such that various tools developed in quantum many-body physics can be applied. In addition to Haar random circuits and Brownian circuits, we also study a new type of circuit — fractional swap circuit in which the two local qudits are partially exchanged and partially staying on the same site. We further investigate the bipartite operator mutual information and tripartite operator mutual information of the fractional swap circuit and compare with different CFT results. |
Tuesday, March 3, 2020 2:54PM - 3:06PM |
J09.00003: Critical Properties of the Measurement-Induced Transition in Random Quantum Circuits Aidan Zabalo, Michael Gullans, Justin Wilson, Sarang Gopalakrishnan, David Huse, Jed Pixley A transition was observed in random quantum circuits with local projective measurements where the entanglement entropy (EE) goes from volume law to area law scaling as the measurement rate, p, is increased above a critical value, pc. Attempts to extract the critical properties through finite size scaling of the EE has proven difficult due to the logarithmic divergence at criticality. We study the tripartite mutual information (TMI) as an alternative diagnostic of the transition that is finite at criticality while maintaining a volume law for p<pc and vanishing for p>pc. Our intuition for the Haar random circuit is guided by results on stabilizer circuits which can be simulated at much larger sizes. We find that the TMI has weaker finite size effects when compared to other quantities. Our numerics of the Haar random circuit suggests pc≈0.17 and the critical exponent ν≈1.3 for Renyi indices n≥1, which are smaller than previously reported results. We also find a strong Renyi index dependence of the coefficient of the logarithmic divergence α(n)=1.0(1)/n+0.7(1). |
Tuesday, March 3, 2020 3:06PM - 3:18PM |
J09.00004: Boundary Theory of a Deformed AKLT Model on the Square Lattice John Martyn, Kohtaro Kato, Angelo Lucia The 1D AKLT model is a paradigm of antiferromagnetism initially devised as a modification to the Heisenberg model, and its ground state is a quintessential example of symmetry protected topological order. On a 2D lattice, the AKLT model is particularly interesting because it also exhibits symmetry protected topological order, and can act as a resource for universal quantum computation. In contrast to the 1D case, the existence of the spectral gap in 2D, which guarantees the robustness of the model, remains an open problem despite extensive analyses. Recently, it has been shown that one can deduce this spectral gap by analyzing its boundary theory via a tensor network representation of the ground state. In this work, we present a method to calculate the boundary state of the 2D AKLT model in terms of a classical loop model, where loops, vertices, and crossings are each given a weight. We use numerical techniques to sample configurations of loops and subsequently evaluate the boundary state and boundary Hamiltonian on a square lattice. As a result, we evidence a spectral gap, and also indicate the presence of several different phases by varying the weights of the model. |
Tuesday, March 3, 2020 3:18PM - 3:30PM |
J09.00005: Basic construction of a tensor network library Thomas Baker, Alexandre Foley, Agustin Di Paolo, Martin P Thompson We present a template tensor network code written in the programming language julia. The code is simple, short, and is also is efficient, competing in speed with some implementations in lower-level languages. The code can provide an efficient means to learn tensor networks as it is well documented for users of all levels, and the code can be used to check other libraries in development. A large number of algorithms have been implemented. Given time, new algorithms developed while creating this library will be discussed. |
Tuesday, March 3, 2020 3:30PM - 3:42PM |
J09.00006: Tree tensor network study of out-of-time-order correlators on a sparse graph Christopher White, Brian Swingle The SYK model, which consists of Majorana fermions with random few-fermion all-to-all interactions, is a paradigmatic model of a "fast scrambler". Recent work (Bentsen, Gu, and Lucas: PNAS 116, 6689) argued that all-to-all connectivity is not necessary: rather, interactions on a sparse connectivity graph are sufficient. Because many such graphs are locally treelike, they are amenable to treatment with tree tensor networks. In this talk I will describes a study of out-of-time-order correlators using tree tensor networks; I will also comment on some methodological subtleties. |
Tuesday, March 3, 2020 3:42PM - 3:54PM |
J09.00007: Sparsity of the stabilizer projector decomposition of a density matrix and robustness of magic Yifei Huang, Peter Love We extend the stabilizer rank of state vectors to mixed states and define the rank(minimal l_0 norm) for stabilizer projector decomposition of a density matrix and show its advantage over the rank of Pauli decomposition. Both improvements on the scaling over standard orthonomal basis(computational basis for state vector and Pauli basis for density matrix) come from the fact that stabilizer states form a densely overcomplete basis. In comparison with Monte Carlo simulation that scales with Robustness of Magic(minimal l_1 norm), we analyse the strong simulation cost of noisy Clifford+T circuits with respect to the rank. Using results from compressed sensing, we explore the sparsity condition where the minimal l_0 and l_1 norm are reached at the same decomposition. |
Tuesday, March 3, 2020 3:54PM - 4:06PM |
J09.00008: Single T gate in a Clifford circuit drives transition to universal entanglement spectrum statistics Shiyu Zhou, Zhicheng Yang, Alioscia Hamma, Claudio Chamon Clifford circuits are insufficient for universal quantum computation or creating t-designs with t bigger than 4. While the entanglement entropy is not a telltale of this insufficiency, the entanglement spectrum is: the entanglement levels are Poisson-distributed for circuits restricted to the Clifford gate-set, while the levels follow Wigner-Dyson statistics when universal gates are used. In this paper we show, using finite-size scaling analysis of different measures of level spacing statistics, that in the thermodynamic limit, inserting a single T gate in the middle of a random Clifford circuit is sufficient to alter the entanglement spectrum from a Poisson to a Wigner-Dyson distribution. |
Tuesday, March 3, 2020 4:06PM - 4:18PM |
J09.00009: Recurrences in nonlinear few-body entanglement dynamics Alexander Kiral, Arjendu Kishore Pattanayak We study quantum tunneling for an initially pure coherent spin state in a many-body spin system. This manifests as dynamics which transforms it into a non-classical (in our case highly entangled) state that later recoheres. We develop a metric to determine the existence of tunneling as well as spectral techniques to predict rates of tunneling for an initial coherent state. We discover that the locations of tunneling reflect phase space structures that come from symmetries of the Hamiltonian. This can be visualized through the Husimi representation of stationary states which allows us to connect to other dynamical variables such as periodicity, entanglement, and chaos. |
Tuesday, March 3, 2020 4:18PM - 4:30PM |
J09.00010: Entanglement spectrum and entropy in non-Hermitian systems Po-Yao Chang, Jhih-Shih You, Xueda Wen, Shinsei Ryu In this talk, we study both the entanglement spectrum and the entanglement entropy by use of a biothogonal basis in non-Hermitian free fermion systems. We show the entanglement spectrum can characterize topological features in the non-Hermitian Su-Schrieffer-Heeger model with parity and time reversal symmetry. In addition, we find the entanglement entropy at the critical point of this model has a logarithmic scaling with corresponding central charge c=-2, which can be described by the non-unitary conformal field theory. |
Tuesday, March 3, 2020 4:30PM - 4:42PM |
J09.00011: GPU-accelerated simulations of realistic quantum systems with a focus on Quantum Information and Computation. Aleksander Lasek, Hugo V Lepage, Crispin H.W. Barnes, David R M Arvidsson Shukur In this talk we present our method of numerically simulating realistic quantum systems. With recent increases in GPU processing power, we are able to simulate two-particle 2D systems on thousands of spatial sites in a reasonable time. |
Tuesday, March 3, 2020 4:42PM - 4:54PM |
J09.00012: Unified Quantum Parallel Computing Theory and Discrete Time Crystals Cheng-Hsiao Wu
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Tuesday, March 3, 2020 4:54PM - 5:06PM |
J09.00013: Error rates in interacting Kitaev chains at finite temperature John Stenger, Roger Mong, David Pekker As proposed by Alexey Kiteav, a topological one-dimensional superconducting wire hosts Majorana zero modes, which could be used to store and process quantum information in a topologically protected manner. At finite temperatures (or quasi-particle densities), Kitaev’s model remains topologically protected because it is integrable. However, in the presence of interactions and finite temperature, topological protection is lifted. We investigate how error rates depend on interactions and temperature using TEBD and perturbation theory. These results are significant to experimental efforts to build a Majorana zero mode qubit. |
Tuesday, March 3, 2020 5:06PM - 5:18PM |
J09.00014: Time dependent variational principle with ancillary global Krylov subspace Mingru Yang, Steven Robert White We propose an improved scheme to do the time dependent variational principle (TDVP) in finite matrix product states (MPS) for two-dimensional systems or one-dimensional systems with long range interactions. We present a method to represent the time-evolving state in a MPS with its bond dimension increased by state-averaging with global Krylov vectors. We show that the projection error is significantly reduced so that precise time evolution can still be obtained even if a larger time step is used. |
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