%0 Journal Article %J Physical Review B %D 2021 %T Conformal field theories are magical %A Christopher David White %A ChunJun Cao %A Brian Swingle %X
"Magic" is the degree to which a state cannot be approximated by Clifford gates. We study mana, a measure of magic, in the ground state of the Z3 Potts model, and argue that it is a broadly useful diagnostic for many-body physics. In particular we find that the q=3 ground state has large mana at the model's critical point, and that this mana resides in the system's correlations. We explain the form of the mana by a simple tensor-counting calculation based on a MERA representation of the state. Because mana is present at all length scales, we conclude that the conformal field theory describing the 3-state Potts model critical point is magical. These results control the difficulty of preparing the Potts ground state on an error-corrected quantum computer, and constrain tensor network models of AdS-CFT.
%B Physical Review B %V 103 %P 075145 %8 2/25/2021 %G eng %U https://arxiv.org/abs/2007.01303 %N 7 %R https://journals.aps.org/prb/pdf/10.1103/PhysRevB.103.075145 %0 Journal Article %J Nature Physics %D 2020 %T Accessing scrambling using matrix product operators %A Shenglong Xu %A Brian Swingle %XScrambling, a process in which quantum information spreads over a complex quantum system becoming inaccessible to simple probes, happens in generic chaotic quantum many-body systems, ranging from spin chains, to metals, even to black holes. Scrambling can be measured using out-of-time-ordered correlators (OTOCs), which are closely tied to the growth of Heisenberg operators. In this work, we present a general method to calculate OTOCs of local operators in local one-dimensional systems based on approximating Heisenberg operators as matrix-product operators (MPOs). Contrary to the common belief that such tensor network methods work only at early times, we show that the entire early growth region of the OTOC can be captured using an MPO approximation with modest bond dimension. We analytically establish the goodness of the approximation by showing that if an appropriate OTOC is close to its initial value, then the associated Heisenberg operator has low entanglement across a given cut. We use the method to study scrambling in a chaotic spin chain with 201 sites. Based on this data and OTOC results for black holes, local random circuit models, and non-interacting systems, we conjecture a universal form for the dynamics of the OTOC near the wavefront. We show that this form collapses the chaotic spin chain data over more than fifteen orders of magnitude.
%B Nature Physics %V 16 %P 199-204 %8 2/2020 %G eng %U https://arxiv.org/abs/1802.00801 %N 2 %R https://doi.org/10.1038/s41567-019-0712-4 %0 Journal Article %D 2020 %T Approximate recovery and relative entropy I. general von Neumann subalgebras %A Thomas Faulkner %A Stefan Hollands %A Brian Swingle %A Yixu Wang %XWe prove the existence of a universal recovery channel that approximately recovers states on a v. Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I v. Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary v. Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki-Masuda Lp norms. We comment on applications to the quantum null energy condition.
%8 6/14/2020 %G eng %U https://arxiv.org/abs/2006.08002 %0 Journal Article %D 2020 %T Approximate recovery and relative entropy I. general von Neumann subalgebras %A Thomas Faulkner %A Stefan Hollands %A Brian Swingle %A Yixu Wang %XWe prove the existence of a universal recovery channel that approximately recovers states on a v. Neumann subalgebra when the change in relative entropy, with respect to a fixed reference state, is small. Our result is a generalization of previous results that applied to type-I v. Neumann algebras by Junge at al. [arXiv:1509.07127]. We broadly follow their proof strategy but consider here arbitrary v. Neumann algebras, where qualitatively new issues arise. Our results hinge on the construction of certain analytic vectors and computations/estimations of their Araki-Masuda Lp norms. We comment on applications to the quantum null energy condition.
%8 6/14/2020 %G eng %U https://arxiv.org/abs/2006.08002 %0 Journal Article %J Journal of High Energy Physics %D 2020 %T Building Bulk Geometry from the Tensor Radon Transform %A ChunJun Cao %A Xiao-Liang Q %A Brian Swingle %A Eugene Tang %XUsing the tensor Radon transform and related numerical methods, we study how bulk geometries can be explicitly reconstructed from boundary entanglement entropies in the specific case of AdS3/CFT2. We find that, given the boundary entanglement entropies of a 2d CFT, this framework provides a quantitative measure that detects whether the bulk dual is geometric in the perturbative (near AdS) limit. In the case where a well-defined bulk geometry exists, we explicitly reconstruct the unique bulk metric tensor once a gauge choice is made. We then examine the emergent bulk geometries for static and dynamical scenarios in holography and in many-body systems. Apart from the physics results, our work demonstrates that numerical methods are feasible and effective in the study of bulk reconstruction in AdS/CFT.
%B Journal of High Energy Physics %V 2020 %P 1-50 %8 12/4/2020 %G eng %U https://arxiv.org/abs/2007.00004 %N 12 %0 Journal Article %D 2020 %T An exponential ramp in the quadratic Sachdev-Ye-Kitaev model %A Michael Winer %A Shao-Kai Jian %A Brian Swingle %XA long period of linear growth in the spectral form factor provides a universal diagnostic of quantum chaos at intermediate times. By contrast, the behavior of the spectral form factor in disordered integrable many-body models is not well understood. Here we study the two-body Sachdev-Ye-Kitaev model and show that the spectral form factor features an exponential ramp, in sharp contrast to the linear ramp in chaotic models. We find a novel mechanism for this exponential ramp in terms of a high-dimensional manifold of saddle points in the path integral formulation of the spectral form factor. This manifold arises because the theory enjoys a large symmetry group. With finite nonintegrable interaction strength, these delicate symmetries reduce to a relative time translation, causing the exponential ramp to give way to a linear ramp.
%8 6/26/2020 %G eng %U https://arxiv.org/abs/2006.15152 %0 Journal Article %D 2020 %T Information scrambling at finite temperature in local quantum systems %A Subhayan Sahu %A Brian Swingle %XThis paper investigates the temperature dependence of quantum information scrambling in local systems with an energy gap, m, above the ground state. We study the speed and shape of growing Heisenberg operators as quantified by out-of-time-order correlators, with particular attention paid to so-called contour dependence, i.e. dependence on the way operators are distributed around the thermal circle. We report large scale tensor network numerics on a gapped chaotic spin chain down to temperatures comparable to the gap which show that the speed of operator growth is strongly contour dependent. The numerics also show a characteristic broadening of the operator wavefront at finite temperature T. To study the behavior at temperatures much below the gap, we perform a perturbative calculation in the paramagnetic phase of a 2+1D O(N) non-linear sigma model, which is analytically tractable at large N. Using the ladder diagram technique, we find that operators spread at a speed T/m−−−−√ at low temperatures, T≪m. In contrast to the numerical findings of spin chain, the large N computation is insensitive to the contour dependence and does not show broadening of operator front. We discuss these results in the context of a recently proposed state-dependent bound on scrambling.
%8 5/21/2020 %G eng %U https://arxiv.org/abs/2005.10814 %0 Journal Article %D 2020 %T Information scrambling at finite temperature in local quantum systems %A Subhayan Sahu %A Brian Swingle %XThis paper investigates the temperature dependence of quantum information scrambling in local systems with an energy gap, m, above the ground state. We study the speed and shape of growing Heisenberg operators as quantified by out-of-time-order correlators, with particular attention paid to so-called contour dependence, i.e. dependence on the way operators are distributed around the thermal circle. We report large scale tensor network numerics on a gapped chaotic spin chain down to temperatures comparable to the gap which show that the speed of operator growth is strongly contour dependent. The numerics also show a characteristic broadening of the operator wavefront at finite temperature T. To study the behavior at temperatures much below the gap, we perform a perturbative calculation in the paramagnetic phase of a 2+1D O(N) non-linear sigma model, which is analytically tractable at large N. Using the ladder diagram technique, we find that operators spread at a speed T/m−−−−√ at low temperatures, T≪m. In contrast to the numerical findings of spin chain, the large N computation is insensitive to the contour dependence and does not show broadening of operator front. We discuss these results in the context of a recently proposed state-dependent bound on scrambling.
%8 5/21/2020 %G eng %U https://arxiv.org/abs/2005.10814 %0 Journal Article %J Phys. Rev. Lett. %D 2020 %T Minimal model for fast scrambling %A Ron Belyansky %A Przemyslaw Bienias %A Yaroslav A. Kharkov %A Alexey V. Gorshkov %A Brian Swingle %XWe study quantum information scrambling in spin models with both long-range all-to-all and short-range interactions. We argue that a simple global, spatially homogeneous interaction together with local chaotic dynamics is sufficient to give rise to fast scrambling, which describes the spread of quantum information over the entire system in a time that is logarithmic in the system size. This is illustrated in two exactly solvable models: (1) a random circuit with Haar random local unitaries and a global interaction and (2) a classical model of globally coupled non-linear oscillators. We use exact numerics to provide further evidence by studying the time evolution of an out-of-time-order correlator and entanglement entropy in spin chains of intermediate sizes. Our results can be verified with state-of-the-art quantum simulators.
%B Phys. Rev. Lett. %V 125 %8 9/22/2020 %G eng %U https://arxiv.org/abs/2005.05362 %N 130601 %R https://doi.org/10.1103/PhysRevLett.125.130601 %0 Journal Article %D 2020 %T Non-equilibrium steady state phases of the interacting Aubry-Andre-Harper model %A Yongchan Yoo %A Junhyun Lee %A Brian Swingle %XHere we study the phase diagram of the Aubry-Andre-Harper model in the presence of strong interactions as the strength of the quasiperiodic potential is varied. Previous work has established the existence of many-body localized phase at large potential strength; here, we find a rich phase diagram in the delocalized regime characterized by spin transport and unusual correlations. We calculate the non-equilibrium steady states of a boundary-driven strongly interacting Aubry-Andre-Harper model by employing the time-evolving block decimation algorithm on matrix product density operators. From these steady states, we extract spin transport as a function of system size and quasiperiodic potential strength. This data shows spin transport going from superdiffusive to subdiffusive well before the localization transition; comparing to previous results, we also find that the transport transition is distinct from a transition observed in the speed of operator growth in the model. We also investigate the correlation structure of the steady state and find an unusual oscillation pattern for intermediate values of the potential strength. The unusual spin transport and quantum correlation structure suggest multiple dynamical phases between the much-studied thermal and many-body-localized phases.
%8 5/21/2020 %G eng %U https://arxiv.org/abs/2005.10835 %0 Journal Article %J Phys. Rev. Lett. %D 2020 %T The operator Lévy flight: light cones in chaotic long-range interacting systems %A Tianci Zhou %A Shenglong Xu %A Xiao Chen %A Andrew Guo %A Brian Swingle %XWe propose a generic light cone phase diagram for chaotic long-range r−α interacting systems, where a linear light cone appears for α≥d+1/2 in d dimension. Utilizing the dephasing nature of quantum chaos, we argue that the universal behavior of the squared commutator is described by a stochastic model, for which the exact phase diagram is known. We provide an interpretation in terms of the Lévy flights and show that this suffices to capture the scaling of the squared commutator. We verify these phenomena in numerical computation of a long-range spin chain with up to 200 sites.
%B Phys. Rev. Lett. %V 124 %8 7/6/2020 %G eng %U https://arxiv.org/abs/1909.08646 %N 180601 %R https://doi.org/10.1103/PhysRevLett.124.180601 %0 Journal Article %D 2020 %T A Sparse Model of Quantum Holography %A Shenglong Xu %A Leonard Susskind %A Yuan Su %A Brian Swingle %XWe study a sparse version of the Sachdev-Ye-Kitaev (SYK) model defined on random hypergraphs constructed either by a random pruning procedure or by randomly sampling regular hypergraphs. The resulting model has a new parameter, k, defined as the ratio of the number of terms in the Hamiltonian to the number of degrees of freedom, with the sparse limit corresponding to the thermodynamic limit at fixed k. We argue that this sparse SYK model recovers the interesting global physics of ordinary SYK even when k is of order unity. In particular, at low temperature the model exhibits a gravitational sector which is maximally chaotic. Our argument proceeds by constructing a path integral for the sparse model which reproduces the conventional SYK path integral plus gapped fluctuations. The sparsity of the model permits larger scale numerical calculations than previously possible, the results of which are consistent with the path integral analysis. Additionally, we show that the sparsity of the model considerably reduces the cost of quantum simulation algorithms. This makes the sparse SYK model the most efficient currently known route to simulate a holographic model of quantum gravity. We also define and study a sparse supersymmetric SYK model, with similar conclusions to the non-supersymmetric case. Looking forward, we argue that the class of models considered here constitute an interesting and relatively unexplored sparse frontier in quantum many-body physics.
%8 8/5/2020 %G eng %U https://arxiv.org/abs/2008.02303 %0 Journal Article %D 2019 %T Butterfly effect in interacting Aubry-Andre model: thermalization, slow scrambling, and many-body localization %A Shenglong Xu %A Xiao Li %A Yi-Ting Hsu %A Brian Swingle %A Sankar Das Sarma %XThe many-body localization transition in quasiperiodic systems has been extensively studied in recent ultracold atom experiments. At intermediate quasiperiodic potential strength, a surprising Griffiths-like regime with slow dynamics appears in the absence of random disorder and mobility edges. In this work, we study the interacting Aubry-Andre model, a prototype quasiperiodic system, as a function of incommensurate potential strength using a novel dynamical measure, information scrambling, in a large system of 200 lattice sites. Between the thermal phase and the many-body localized phase, we find an intermediate dynamical phase where the butterfly velocity is zero and information spreads in space as a power-law in time. This is in contrast to the ballistic spreading in the thermal phase and logarithmic spreading in the localized phase. We further investigate the entanglement structure of the many-body eigenstates in the intermediate phase and find strong fluctuations in eigenstate entanglement entropy within a given energy window, which is inconsistent with the eigenstate thermalization hypothesis. Machine-learning on the entanglement spectrum also reaches the same conclusion. Our large-scale simulations suggest that the intermediate phase with vanishing butterfly velocity could be responsible for the slow dynamics seen in recent experiments.
%8 02/19/2019 %G eng %U https://arxiv.org/abs/1902.07199 %0 Journal Article %D 2019 %T Chaos in a quantum rotor model %A Gong Cheng %A Brian Swingle %XWe study scrambling in a model consisting of a number N of M-component quantum rotors coupled by random infinite-range interactions. This model is known to have both a paramagnetic phase and a spin glass phase separated by second order phase transition. We calculate in perturbation theory the squared commutator of rotor fields at different sites in the paramagnetic phase, to leading non-trivial order at large N and large M. This quantity diagnoses the onset of quantum chaos in this system, and we show that the squared commutator grows exponentially with time, with a Lyapunov exponent proportional to 1M. At high temperature, the Lyapunov exponent limits to a value set by the microscopic couplings, while at low temperature, the exponent exhibits a T4 dependence on temperature T.
%8 01/29/2019 %G eng %U https://arxiv.org/abs/1901.10446 %0 Journal Article %D 2019 %T A characterization of quantum chaos by two-point correlation functions %A Hrant Gharibyan %A Masanori Hanada %A Brian Swingle %A Masaki Tezuka %XWe propose a characterization of quantum many-body chaos: given a collection of simple operators, the set of all possible pair-correlations between these operators can be organized into a matrix with random-matrix-like spectrum. This approach is particularly useful for locally interacting systems, which do not generically show exponential Lyapunov growth of out-of-time-ordered correlators. We demonstrate the validity of this characterization by numerically studying the Sachdev-Ye-Kitaev model and a one-dimensional spin chain with random magnetic field (XXZ model).
%8 02/28/2019 %G eng %U https://arxiv.org/abs/1902.11086 %0 Journal Article %J Phys. Rev. X %D 2019 %T Locality, Quantum Fluctuations, and Scrambling %A Shenglong Xu %A Brian Swingle %XThermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be diagnosed by out-of-time-order correlators (OTOCs). However, the behavior of OTOCs of local operators in generic chaotic local Hamiltonians remains poorly understood, with some semiclassical and large N models exhibiting exponential growth of OTOCs and a sharp chaos wavefront and other random circuit models showing a diffusively broadened wavefront. In this paper we propose a unified physical picture for scrambling in chaotic local Hamiltonians. We construct a random time-dependent Hamiltonian model featuring a large N limit where the OTOC obeys a Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) type equation and exhibits exponential growth and a sharp wavefront. We show that quantum fluctuations manifest as noise (distinct from the randomness of the couplings in the underlying Hamiltonian) in the FKPP equation and that the noise-averaged OTOC exhibits a cross-over to a diffusively broadened wavefront. At small N we demonstrate that operator growth dynamics, averaged over the random couplings, can be efficiently simulated for all time using matrix product state techniques. To show that time-dependent randomness is not essential to our conclusions, we push our previous matrix product operator methods to very large size and show that data for a time-independent Hamiltonian model are also consistent with a diffusively-broadened wavefront.
%B Phys. Rev. X %V 9 %8 9/18/2019 %G eng %U https://arxiv.org/abs/1805.05376 %N 031048 %R https://doi.org/10.1103/PhysRevX.9.031048 %0 Journal Article %J Phys. Rev. A %D 2019 %T Product Spectrum Ansatz and the Simplicity of Thermal States %A John Martyn %A Brian Swingle %XCalculating the physical properties of quantum thermal states is a difficult problem for classical computers, rendering it intractable for most quantum many-body systems. A quantum computer, by contrast, would make many of these calculations feasible in principle, but it is still non-trivial to prepare a given thermal state or sample from it. It is also not known how to prepare special simple purifications of thermal states known as thermofield doubles, which play an important role in quantum many-body physics and quantum gravity. To address this problem, we propose a variational scheme to prepare approximate thermal states on a quantum computer by applying a series of two-qubit gates to a product mixed state. We apply our method to a non-integrable region of the mixed field Ising chain and the Sachdev-Ye-Kitaev model. We also demonstrate how our method can be easily extended to large systems governed by local Hamiltonians and the preparation of thermofield double states. By comparing our results with exact solutions, we find that our construction enables the efficient preparation of approximate thermal states on quantum devices. Our results can be interpreted as implying that the details of the many-body energy spectrum are not needed to capture simple thermal observables.
%B Phys. Rev. A %V 100 %8 2019/11/18 %G eng %U https://arxiv.org/abs/1812.01015 %N 032107 %R https://doi.org/10.1103/PhysRevA.100.032107 %0 Journal Article %D 2019 %T Quantum circuit approximations and entanglement renormalization for the Dirac field in 1+1 dimensions %A Freek Witteveen %A Volkher Scholz %A Brian Swingle %A Michael Walter %XThe multiscale entanglement renormalization ansatz describes quantum many-body states by a hierarchical entanglement structure organized by length scale. Numerically, it has been demonstrated to capture critical lattice models and the data of the corresponding conformal field theories with high accuracy. However, a rigorous understanding of its success and precise relation to the continuum is still lacking. To address this challenge, we provide an explicit construction of entanglement-renormalization quantum circuits that rigorously approximate correlation functions of the massless Dirac conformal field theory. We directly target the continuum theory: discreteness is introduced by our choice of how to probe the system, not by any underlying short-distance lattice regulator. To achieve this, we use multiresolution analysis from wavelet theory to obtain an approximation scheme and to implement entanglement renormalization in a natural way. This could be a starting point for constructing quantum circuit approximations for more general conformal field theories.
%8 05/21/2019 %G eng %U https://arxiv.org/abs/1905.08821 %0 Journal Article %D 2019 %T Quantum Gravity in the Lab: Teleportation by Size and Traversable Wormholes %A Adam R. Brown %A Hrant Gharibyan %A Stefan Leichenauer %A Henry W. Lin %A Sepehr Nezami %A Grant Salton %A Leonard Susskind %A Brian Swingle %A Michael Walter %XWith the long-term goal of studying quantum gravity in the lab, we propose holographic teleportation protocols that can be readily executed in table-top experiments. These protocols exhibit similar behavior to that seen in recent traversable wormhole constructions: information that is scrambled into one half of an entangled system will, following a weak coupling between the two halves, unscramble into the other half. We introduce the concept of "teleportation by size" to capture how the physics of operator-size growth naturally leads to information transmission. The transmission of a signal through a semi-classical holographic wormhole corresponds to a rather special property of the operator-size distribution we call "size winding". For more general setups (which may not have a clean emergent geometry), we argue that imperfect size winding is a generalization of the traversable wormhole phenomenon. For example, a form of signalling continues to function at high temperature and at large times for generic chaotic systems, even though it does not correspond to a signal going through a geometrical wormhole, but rather to an interference effect involving macroscopically different emergent geometries. Finally, we outline implementations feasible with current technology in two experimental platforms: Rydberg atom arrays and trapped ions.
%8 2019/11/14 %G eng %U https://arxiv.org/abs/1911.06314 %0 Journal Article %J JHEP04 %D 2019 %T Quantum Lyapunov Spectrum %A Hrant Gharibyan %A Masanori Hanada %A Brian Swingle %A Masaki Tezuka %XWe introduce a simple quantum generalization of the spectrum of classical Lyapunov exponents. We apply it to the SYK and XXZ models, and study the Lyapunov growth and entropy production. Our numerical results suggest that a black hole is not just the fastest scrambler, but also the fastest entropy generator. We also study the statistical features of the quantum Lyapunov spectrum and find universal random matrix behavior, which resembles the recently-found universality in classical chaos. The random matrix behavior is lost when the system is deformed away from chaos, towards integrability or a many-body localized phase. We propose that quantum systems holographically dual to gravity satisfy this universality in a strong form. We further argue that the quantum Lyapunov spectrum contains important additional information beyond the largest Lyapunov exponent and hence provides us with a better characterization of chaos in quantum systems.
%B JHEP04 %V 082 %8 04/10/2019 %G eng %U https://arxiv.org/abs/1809.01671 %R https://doi.org/10.1007/JHEP04(2019)082 %0 Journal Article %D 2019 %T Quenched vs Annealed: Glassiness from SK to SYK %A Christopher L. Baldwin %A Brian Swingle %XWe show that any SYK-like model with finite-body interactions among \textit{local} degrees of freedom, e.g., bosons or spins, has a fundamental difference from the standard fermionic model: the former fails to be described by an annealed free energy at low temperature. In this respect, such models more closely resemble spin glasses. We demonstrate this by two means: first, a general theorem proving that the annealed free energy is divergent at low temperature in any model with a tensor product Hilbert space; and second, a replica treatment of two prominent examples which exhibit phase transitions from an "annealed" phase to a "non-annealed" phase as a function of temperature. We further show that this effect appears only at O(N)'th order in a 1/N expansion, even though lower-order terms misleadingly seem to converge. Our results prove that the non-bosonic nature of the particles in SYK is an essential ingredient for its physics, highlight connections between local models and spin glasses, and raise important questions as to the role of fermions and/or glassiness in holography.
%8 11/26/2019 %G eng %U https://arxiv.org/abs/1911.11865 %0 Journal Article %D 2019 %T The Speed of Quantum Information Spreading in Chaotic Systems %A Josiah Couch %A Stefan Eccles %A Phuc Nguyen %A Brian Swingle %A Shenglong Xu %XWe present a general theory of quantum information propagation in chaotic quantum many-body systems. The generic expectation in such systems is that quantum information does not propagate in localized form; instead, it tends to spread out and scramble into a form that is inaccessible to local measurements. To characterize this spreading, we define an information speed via a quench-type experiment and derive a general formula for it as a function of the entanglement density of the initial state. As the entanglement density varies from zero to one, the information speed varies from the entanglement speed to the butterfly speed. We verify that the formula holds both for a quantum chaotic spin chain and in field theories with an AdS/CFT gravity dual. For the second case, we study in detail the dynamics of entanglement in two-sided Vaidya-AdS-Reissner-Nordstrom black branes. We also show that, with an appropriate decoding process, quantum information can be construed as moving at the information speed, and, in the case of AdS/CFT, we show that a locally detectable signal propagates at the information speed in a spatially local variant of the traversable wormhole setup.
%8 08/19/2019 %G eng %U https://arxiv.org/abs/1908.06993 %0 Journal Article %J Phys. Rev. D %D 2019 %T Thermalization and chaos in QED3 %A Julia Steinberg %A Brian Swingle %XWe study the real time dynamics of NF flavors of fermions coupled to a U(1) gauge field in 2+1 dimensions to leading order in a 1/NF expansion. For large enough NF, this is an interacting conformal field theory and describes the low energy properties of the Dirac spin liquid. We focus on thermalization and the onset of many-body quantum chaos which can be diagnosed from the growth of initally anti-commuting fermion field operators. We compute such anti-commutators in this gauge theory to leading order in 1/NF. We find that the anti-commutator grows exponentially in time and compute the quantum Lyapunov exponent. We briefly comment on chaos, locality, and gauge invariance.
%B Phys. Rev. D %V 99 %8 04/11/2019 %G eng %U https://arxiv.org/abs/1901.04984 %N 076007 %R https://doi.org/10.1103/PhysRevD.99.076007 %0 Journal Article %D 2019 %T Universal Constraints on Energy Flow and SYK Thermalization %A Ahmed Almheiri %A Alexey Milekhin %A Brian Swingle %8 12/10/2019 %G eng %U https://arxiv.org/abs/1912.04912 %0 Journal Article %D 2018 %T Black Hole Microstate Cosmology %A Sean Cooper %A Moshe Rozali %A Brian Swingle %A Mark Van Raamsdonk %A Christopher Waddell %A David Wakeham %XIn this note, we explore the possibility that certain high-energy holographic CFT states correspond to black hole microstates with a geometrical behind-the-horizon region, modelled by a portion of a second asymptotic region terminating at an end-of-the-world (ETW) brane. We study the time-dependent physics of this behind-the-horizon region, whose ETW boundary geometry takes the form of a closed FRW spacetime. We show that in many cases, this behind-the-horizon physics can be probed directly by looking at the time dependence of entanglement entropy for sufficiently large spatial CFT subsystems. We study in particular states defined via Euclidean evolution from conformal boundary states and give specific predictions for the behavior of the entanglement entropy in this case. We perform analogous calculations for the SYK model and find qualitative agreement with our expectations. A fascinating possibility is that for certain states, we might have gravity localized to the ETW brane as in the Randall-Sundrum II scenario for cosmology. In this case, the effective description of physics beyond the horizon could be a big bang/big crunch cosmology of the same dimensionality as the CFT. In this case, the d-dimensional CFT describing the black hole microstate would give a precise, microscopic description of the d-dimensional cosmological physics.
%G eng %U https://arxiv.org/abs/1810.10601 %0 Journal Article %J Journal of High Energy Physics %D 2018 %T Entanglement of purification: from spin chains to holography %A Phuc Nguyen %A Trithep Devakul %A Matthew G. Halbasch %A Michael P. Zaletel %A Brian Swingle %XPurification is a powerful technique in quantum physics whereby a mixed quantum state is extended to a pure state on a larger system. This process is not unique, and in systems composed of many degrees of freedom, one natural purification is the one with minimal entanglement. Here we study the entropy of the minimally entangled purification, called the entanglement of purification, in three model systems: an Ising spin chain, conformal field theories holographically dual to Einstein gravity, and random stabilizer tensor networks. We conjecture values for the entanglement of purification in all these models, and we support our conjectures with a variety of numerical and analytical results. We find that such minimally entangled purifications have a number of applications, from enhancing entanglement-based tensor network methods for describing mixed states to elucidating novel aspects of the emergence of geometry from entanglement in the AdS/CFT correspondence.
%B Journal of High Energy Physics %P 98 %8 2018/01/22 %G eng %U https://link.springer.com/article/10.1007%2FJHEP01%282018%29098#citeas %R 10.1007/JHEP01(2018)098 %0 Journal Article %J J. High Energ. Phys. %D 2018 %T Holographic Complexity of Einstein-Maxwell-Dilaton Gravity %A Brian Swingle %A Yixu Wang %XWe study the holographic complexity of Einstein-Maxwell-Dilaton gravity using the recently proposed "complexity = volume" and "complexity = action" dualities. The model we consider has a ground state that is represented in the bulk via a so-called hyperscaling violating geometry. We calculate the action growth of the Wheeler-DeWitt patch of the corresponding black hole solution at non-zero temperature and find that, in the presence of violations of hyperscaling, there is a parametric enhancement of the action growth rate. We partially match this behavior to simple tensor network models which can capture aspects of hyperscaling violation. We also exhibit the switchback effect in complexity growth using shockwave geometries and comment on a subtlety of our action calculations when the metric is discontinuous at a null surface.
%B J. High Energ. Phys. %V 106 %8 2018 %G eng %U https://arxiv.org/abs/1712.09826 %R https://doi.org/10.1007/JHEP09(2018)106 %0 Journal Article %J Phys. Rev. %D 2018 %T The quasiprobability behind the out-of-time-ordered correlator %A Nicole Yunger Halpern %A Brian Swingle %A Justin Dressel %XTwo topics, evolving rapidly in separate fields, were combined recently: The out-of-time-ordered correlator (OTOC) signals quantum-information scrambling in many-body systems. The Kirkwood-Dirac (KD) quasiprobability represents operators in quantum optics. The OTOC has been shown to equal a moment of a summed quasiprobability. That quasiprobability, we argue, is an extension of the KD distribution. We explore the quasiprobability's structure from experimental, numerical, and theoretical perspectives. First, we simplify and analyze the weak-measurement and interference protocols for measuring the OTOC and its quasiprobability. We decrease, exponentially in system size, the number of trials required to infer the OTOC from weak measurements. We also construct a circuit for implementing the weak-measurement scheme. Next, we calculate the quasiprobability (after coarse-graining) numerically and analytically: We simulate a transverse-field Ising model first. Then, we calculate the quasiprobability averaged over random circuits, which model chaotic dynamics. The quasiprobability, we find, distinguishes chaotic from integrable regimes. We observe nonclassical behaviors: The quasiprobability typically has negative components. It becomes nonreal in some regimes. The onset of scrambling breaks a symmetry that bifurcates the quasiprobability, as in classical-chaos pitchforks. Finally, we present mathematical properties. The quasiprobability obeys a Bayes-type theorem, for example, that exponentially decreases the memory required to calculate weak values, in certain cases. A time-ordered correlator analogous to the OTOC, insensitive to quantum-information scrambling, depends on a quasiprobability closer to a classical probability. This work not only illuminates the OTOC's underpinnings, but also generalizes quasiprobability theory and motivates immediate-future weak-measurement challenges.
%B Phys. Rev. %V A %8 04/2018 %G eng %U https://arxiv.org/abs/1704.01971 %N 97 %& 042105 %R https://doi.org/10.1103/PhysRevA.97.042105 %0 Journal Article %D 2018 %T Recovery Map for Fermionic Gaussian Channels %A Brian Swingle %A Yixu Wang %XA recovery map effectively cancels the action of a quantum operation to a partial or full extent. We study the Petz recovery map in the case where the quantum channel and input states are fermionic and Gaussian. Gaussian states are convenient because they are totally determined by their covariance matrix and because they form a closed set under so-called Gaussian channels. Using a Grassmann representation of fermionic Gaussian maps, we show that the Petz recovery map is also Gaussian and determine it explicitly in terms of the covariance matrix of the reference state and the data of the channel. As a by-product, we obtain a formula for the fidelity between two fermionic Gaussian states. We also discuss subtleties arising from the singularities of the involved matrices.
%G eng %U https://arxiv.org/abs/1811.04956 %0 Journal Article %J Phys. Rev. %D 2018 %T Resilience of scrambling measurements %A Brian Swingle %A Nicole Yunger Halpern %XMost experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian's negative counterpart (backwards time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum-chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol's effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.
%B Phys. Rev. %V A %8 2018/06/18 %G eng %U https://arxiv.org/abs/1802.01587 %N 97 %& 062113 %R https://doi.org/10.1103/PhysRevA.97.062113 %0 Journal Article %D 2018 %T Scrambling dynamics across a thermalization-localization quantum phase transition %A Subhayan Sahu %A Shenglong Xu %A Brian Swingle %XWe study quantum information scrambling, specifically the growth of Heisenberg operators, in large disordered spin chains using matrix product operator dynamics to scan across the thermalization-localization quantum phase transition. We observe ballistic operator growth for weak disorder, and a sharp transition to a phase with sub-ballistic operator spreading. The critical disorder strength for the ballistic to sub-ballistic transition is well below the many body localization phase transition, as determined from finite size scaling of energy eigenstate entanglement entropy in small chains. In contrast, we find that the operator dynamics is not very sensitive to the actual eigenstate localization transition. These data are discussed in the context of a universal form for the growing operator shape and substantiated with a simple phenomenological model of rare regions.
%G eng %U https://arxiv.org/abs/1807.06086 %0 Journal Article %D 2018 %T Subsystem Complexity and Holography %A Cesar A. Agón %A Matthew Headrick %A Brian Swingle %XWe study circuit complexity for spatial regions in holographic field theories. We study analogues based on the entanglement wedge of the bulk quantities appearing in the "complexity = volume" and "complexity = action" conjectures. We calculate these quantities for one exterior region of an eternal static neutral or charged black hole in general dimensions, dual to a thermal state on one boundary with or without chemical potential respectively, as well as for a shock wave geometry. We then define several analogues of circuit complexity for mixed states, and use tensor networks to gain intuition about them. We find a promising qualitative match between the holographic action and what we call the purification complexity, the minimum number of gates required to prepare an arbitrary purification of the given mixed state. On the other hand, the holographic volume does not appear to match any of our definitions of mixed-state complexity.
%G eng %U https://arxiv.org/abs/1804.01561 %0 Journal Article %D 2017 %T Entanglement Wedge Reconstruction via Universal Recovery Channels %A Jordan Cotler %A Patrick Hayden %A Geoffrey Penington %A Grant Salton %A Brian Swingle %A Michael Walter %XWe apply and extend the theory of universal recovery channels from quantum information theory to address the problem of entanglement wedge reconstruction in AdS/CFT. It has recently been proposed that any low-energy local bulk operators in a CFT boundary region's entanglement wedge can be reconstructed on that boundary region itself. Existing work arguing for this proposal relies on algebraic consequences of the exact equivalence between bulk and boundary relative entropies, namely the theory of operator algebra quantum error correction. However, bulk and boundary relative entropies are only approximately equal in bulk effective field theory, and in similar situations it is known that predictions from exact entropic equalities can be qualitatively incorrect. The framework of universal recovery channels provides a robust demonstration of the entanglement wedge reconstruction conjecture in addition to new physical insights. Most notably, we find that a bulk operator acting in a given boundary region's entanglement wedge can be expressed as the response of the boundary region's modular Hamiltonian to a perturbation of the bulk state in the direction of the bulk operator. This formula can be interpreted as a noncommutative version of Bayes' rule that attempts to undo the noise induced by restricting to only a portion of the boundary, and has an integral representation in terms of modular flows. To reach these conclusions, we extend the theory of universal recovery channels to finite-dimensional operator algebras and demonstrate that recovery channels approximately preserve the multiplicative structure of the operator algebra
%G eng %U https://arxiv.org/abs/1704.05839 %0 Journal Article %D 2017 %T Robust entanglement renormalization on a noisy quantum computer %A Isaac H. Kim %A Brian Swingle %XA method to study strongly interacting quantum many-body systems at and away from criticality is proposed. The method is based on a MERA-like tensor network that can be efficiently and reliably contracted on a noisy quantum computer using a number of qubits that is much smaller than the system size. We prove that the outcome of the contraction is stable to noise and that the estimated energy upper bounds the ground state energy. The stability, which we numerically substantiate, follows from the positivity of operator scaling dimensions under renormalization group flow. The variational upper bound follows from a particular assignment of physical qubits to different locations of the tensor network plus the assumption that the noise model is local. We postulate a scaling law for how well the tensor network can approximate ground states of lattice regulated conformal field theories in d spatial dimensions and provide evidence for the postulate. Under this postulate, a O(logd (1/δ))-qubit quantum computer can prepare a valid quantum-mechanical state with energy density δ above the ground state. In the presence of noise, δ = O( logd+1(1/)) can be achieved, where is the noise strength.
%8 2017/11/20 %G eng %U https://arxiv.org/abs/1711.07500