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The edge of a quantum critical system can exhibit multiple distinct types of boundary criticality. We use a numerical real-space renormalization group (RSRG) to study the boundary criticality of a 2d quantum Ising model with random exchange couplings and transverse fields, whose bulk exhibits an infinite randomness critical point. This approach enables an asymptotically numerically exact extraction of universal scaling data from very large systems with many thousands of spins that cannot be efficiently simulated directly. We identify three distinct classes of boundary criticality, and extract key scaling exponents governing boundary-boundary and boundary-bulk correlations and dynamics. We anticipate that this approach can be generalized to studying a broad class of (disordered) boundary criticality, including symmetry-enriched criticality and edge modes of gapless symmetry-protected topological states, in contexts were other numerical methods are restricted to one-dimensional chains.

There has been a growing trend that activities relating to clinical trials take place at locations other than traditional trial sites (hence decentralized clinical trials or DCTs), some of which are at settings of real-world clinical practice. Although there are numerous benefits of DCTs, this also brings some implications on a number of issues relating to the design, conduct, and analysis of DCTs. The Real-World Evidence Scientific Working Group of the American Statistical Association Biopharmaceutical Section has been reviewing the field of DCTs and provides in this paper considerations for decentralized trials from a statistical perspective. This paper first discusses selected critical decentralized elements that may have statistical implications on the trial and then summarizes regulatory guidance, framework, and initiatives on DCTs. More discussions are presented by focusing on the design (including construction of estimand), implementation, statistical analysis plan (including missing data handling), and reporting of safety events. Some additional considerations (e.g., ethical considerations, technology infrastructure, study oversight, data security and privacy, and regulatory compliance) are also briefly discussed. This paper is intended to provide statistical considerations for decentralized trials of medical products to support regulatory decision-making.

Trapped ions offer long coherence times and high fidelity, programmable quantum operations, making them a promising platform for quantum simulation of condensed matter systems, quantum dynamics, and problems related to high-energy physics. We review selected developments in trapped-ion qubits and architectures and discuss quantum simulation applications that utilize these emerging capabilities. This review emphasizes developments in digital (gate-based) quantum simulations that exploit trapped-ion hardware capabilities, such as flexible qubit connectivity, selective mid-circuit measurement, and classical feedback, to simulate models with long-range interactions, explore non-unitary dynamics, compress simulations of states with limited entanglement, and reduce the circuit depths required to prepare or simulate long-range entangled states., Comment: 34 pages, 5 figures, Review article for Annual Reviews of Condensed Matter Physics

Twisted MoTe$_2$ homobilayers exhibit transport signatures consistent with a fractional quantum spin Hall (FQSH) state. We describe a route to construct topological quantum memory elements, dubbed Cheshire qudits, formed from punching holes in such a FQSH state and using proximity-induced superconductivity to gap out the resulting helical edge states. Cheshire qudits encode quantum information in states that differ by a fractional topological "Cheshire" charge that is hidden from local detection within a condensate anyons. Control of inter-edge tunneling by gates enables both supercurrent-based readout of a Cheshire qudit, and capacitive measurement of the thermal entropy associated with its topological ground-space degeneracy. Additionally, we systematically classify different types of gapped boundaries, Cheshire qudits, and parafermionic twist defects for various Abelian and non-Abelian candidate FQSH orders that are consistent with the transport data, and describe experimental signatures to distinguish these orders.

Topological holography is a conjectured correspondence between the symmetry charges and defects of a $D$-dimensional system with the anyons in a $(D+1)$-dimensional topological order: the symmetry topological field theory (SymTFT). Topological holography is conjectured to capture the topological aspects of symmetry in gapped and gapless systems, with different phases corresponding to different gapped boundaries (anyon condensations) of the SymTFT. This correspondence was previously considered primarily for bosonic systems, excluding many phases of condensed matter systems involving fermionic electrons. In this work, we extend the SymTFT framework to establish a topological holography correspondence for fermionic systems. We demonstrate that this fermionic SymTFT framework captures the known properties of $1+1D$ fermion gapped phases and critical points, including the classification, edge-modes, and stacking rules of fermionic symmetry-protected topological phases (SPTs), and computation of partition functions of fermionic conformal field theories (CFTs). Beyond merely reproducing known properties, we show that the SymTFT approach can additionally serve as a practical tool for discovering new physics, and use this framework to construct a new example of a fermionic intrinsically gapless SPT phase characterized by an emergent fermionic anomaly., Comment: 44 pages, 19 figures

Unlike unitary dynamics, measurements of a subsystem can induce long-range entanglement via quantum teleportation. The amount of measurement-induced entanglement or mutual information depends jointly on the measurement basis and the entanglement structure of the state (before measurement), and has operational significance for whether the state is a resource for measurement-based quantum computing, as well as for the computational complexity of simulating the state using quantum or classical computers. In this work, we examine entropic measures of measurement-induced entanglement (MIE) and information (MII) for the ground-states of quantum many-body systems in one- and two- spatial dimensions. From numerical and analytic analysis of a variety of models encompassing critical points, quantum Hall states, string-net topological orders, and Fermi liquids, we identify universal features of the long-distance structure of MIE and MII that depend only on the underlying phase or critical universality class of the state. We argue that, whereas in $1d$ the leading contributions to long-range MIE and MII are universal, in $2d$, the existence of a teleportation transition for finite-depth circuits implies that trivial $2d$ states can exhibit long-range MIE, and the universal features lie in sub-leading corrections. We introduce modified MIE measures that directly extract these universal contributions. As a corollary, we show that the leading contributions to strange-correlators, used to numerically identify topological phases, are in fact non-universal in two or more dimensions, and explain how our modified constructions enable one to isolate universal components. We discuss the implications of these results for classical- and quantum- computational simulation of quantum materials., Comment: 14+2 pages, 10+1 figures; v2: published version, added DMRG simulation for the XXZ model

The mechanism by which an effective macroscopic description of quantum measurement in terms of discrete, probabilistic collapse events emerges from the reversible microscopic dynamics remains an enduring open question. Emerging quantum computers offer a promising platform to explore how measurement processes evolve across a range of system sizes while retaining coherence. Here, we report the experimental observation of evidence for an observable-sharpening measurement-induced phase transition in a chain of trapped ions in Quantinuum H1-1 system model quantum processor. This transition manifests as a sharp, concomitant change in both the quantum uncertainty of an observable and the amount of information an observer can (in principle) learn from the measurement record, upon increasing the strength of measurements. We leverage insights from statistical mechanical models and machine learning to design efficiently-computable algorithms to observe this transition (without non-scalable post-selection on measurement outcomes) and to mitigate the effects on errors in noisy hardware.

Symmetry topological field theory (SymTFT) gives a holographic correspondence between systems with a global symmetry and a higher-dimensional topological field theory. In this framework, classification of gapped phases of matter in spacetime dimension 1+1D correspond to classifications of mechanisms to confine the SymTFT by condensing anyons. In this work, we extend these results to characterize gapless symmetry-protected topological states: symmetry-enriched gapless phases or critical points that exhibit edge modes protected by symmetry and topology. We establish a one-to-one correspondence between 1+1D bosonic gSPTs, and partially-confined boundaries of 2+1D SymTFTs. From general physical considerations, we determine the set of data and consistency conditions required to define a 1+1D gSPT, and show that this data precisely matches that of symmetry-preserving partial confinement (or partially gapped boundaries) of 2+1D quantum double models. We illustrate this correspondence through a dimensional reduction (thin-slab) construction, which enables a physically-intuitive derivation of how properties of the gSPT such as edge modes, emergent anomalies, and stability to perturbations arise from the SymTFT perspective.ditions required to define a 1+1D gSPT and show that they fully determine the physics of the gSPT including edge modes and emergent anomaly., Comment: 21 pages, 7 figures

Quantum simulation of many-body systems in materials science and chemistry are promising application areas for quantum computers. However, the limited scale and coherence of near-term quantum processors pose a significant obstacle to realizing this potential. Here, we theoretically outline how a single-circuit quantum electrodynamics (cQED) device, consisting of a transmon qubit coupled to a long-lived cavity mode, can be used to simulate the ground state of a highly-entangled quantum many-body spin chain. We exploit recently developed methods for implementing quantum operations to sequentially build up a matrix product state (MPS) representation of a many-body state. This approach re-uses the transmon qubit to read out the state of each spin in the chain and exploits the large state space of the cavity as a quantum memory encoding inter-site correlations and entanglement. We show, through simulation, that analog (pulse-level) control schemes can accurately prepare a known MPS representation of a quantum critical spin chain in significantly less time than digital (gate-based) methods, thereby reducing the exposure to decoherence. We then explore this analog-control approach for the variational preparation of an unknown ground state. We demonstrate that the large state space of the cavity can be used to replace multiple qubits in a qubit-only architecture, and could therefore simplify the design of quantum processors for materials simulation. We explore the practical limitations of realistic noise and decoherence and discuss avenues for scaling this approach to more complex problems that challenge classical computational methods., Comment: 9 pages, 4 figures

We propose a novel qubit architecture based on a planar $c$-axis Josephson junction between a thin flake $d$-wave superconductor ($d$SC), such as a high-$T_c$ cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$, and a conventional $s$-wave superconductor. When operated in the transmon regime the device -- that we call "$d$-mon" -- becomes insensitive to offset charge fluctuations and, importantly, exhibits at the same time energy level spectrum with strong anharmonicity that is widely tunable through the device geometry and applied magnetic flux. Crucially, unlike previous qubit designs based on $d$-wave superconductors the proposed device operates in a regime where quasiparticles are fully gapped and can be therefore expected to achieve long coherence times., Comment: 4 pages main text + 6 pages SM; V2: corrected typos and updated references

Projected entangled pair states (PEPS) offer memory-efficient representations of some quantum many-body states that obey an entanglement area law, and are the basis for classical simulations of ground states in two-dimensional (2d) condensed matter systems. However, rigorous results show that exactly computing observables from a 2d PEPS state is generically a computationally hard problem. Yet approximation schemes for computing properties of 2d PEPS are regularly used, and empirically seen to succeed, for a large subclass of (not too entangled) condensed matter ground states. Adopting the philosophy of random matrix theory, in this work we analyze the complexity of approximately contracting a 2d random PEPS by exploiting an analytic mapping to an effective replicated statistical mechanics model that permits a controlled analysis at large bond dimension. Through this statistical-mechanics lens, we argue that: i) although approximately sampling wave-function amplitudes of random PEPS faces a computational-complexity phase transition above a critical bond dimension, ii) one can generically efficiently estimate the norm and correlation functions for any finite bond dimension. These results are supported numerically for various bond-dimension regimes. It is an important open question whether the above results for random PEPS apply more generally also to PEPS representing physically relevant ground states

Monitored quantum circuits exhibit entanglement transitions at certain measurement rates. Such a transition separates phases characterized by how much information an observer can learn from the measurement outcomes. We study SU(2)-symmetric monitored quantum circuits, using exact numerics and a mapping onto an effective statistical-mechanics model. Due to the symmetry's non-Abelian nature, measuring qubit pairs allows for nontrivial entanglement scaling even in the measurement-only limit. We find a transition between a volume-law entangled phase and a critical phase whose diffusive purification dynamics emerge from the non-Abelian symmetry. Additionally, we numerically identify a "spin-sharpening transition." On one side is a phase in which the measurements can efficiently identify the system's total spin quantum number; on the other side is a phase in which measurements cannot., Comment: 8 pages (6 figures) + appendices (11.5 pages)

We introduce a class of models, dubbed paired twist-defect networks, that generalize the structure of Kitaev's honeycomb model for which there is a direct equivalence between: i) Floquet codes (FCs), ii) adiabatic loops of gapped Hamiltonians, and iii) unitary loops or Floquet-enriched topological orders (FETs) many-body localized phases. This formalism allows one to apply well-characterized topological index theorems for FETs to understand the dynamics of FCs, and to rapidly assess the code properties of many FC models. As an application, we show that the Honeycomb Floquet code of Haah and Hastings is governed by an irrational value of the chiral Floquet index, which implies a topological obstruction to forming a simple, logical boundary with the same periodicity as the bulk measurement schedule. In addition, we construct generalizations of the Honeycomb Floquet code exhibiting arbitrary anyon-automorphism dynamics for general types of Abelian topological order., Comment: 17+5 pages, 10 figures

At transitions between phases of matter, physical systems can exhibit universal behavior independent of their microscopic details. Probing such behavior in quantum many-body systems is a challenging and practically important problem that can be solved by quantum computers, potentially exponentially faster than by classical computers. In this work, we use the Quantinuum H1-1 quantum computer to realize a quantum extension of a simple classical disease spreading process that is known to exhibit a non-equilibrium phase transition between an active and absorbing state. Using techniques such as qubit-reuse and error avoidance based on real-time conditional logic (utilized extensively in quantum error correction), we are able to implement large instances of the model with $73$ sites and up to $72$ circuit layers, and quantitatively determine the model's critical properties. This work demonstrates how quantum computers capable of mid-circuit resets, measurements, and conditional logic enable the study of difficult problems in quantum many-body physics: the simulation of open quantum system dynamics and non-equilibrium phase transitions., Comment: 7 pages, 4 figures; supplement 18 pages, 19 figures, 1 table; Updated acknowledgements

Intrinsically gapless symmetry protected topological phases (igSPT) are gapless systems with SPT edge states with properties that could not arise in a gapped system with the same symmetry and dimensionality. igSPT states arise from gapless systems in which an anomaly in the low-energy (IR) symmetry group emerges from an extended anomaly-free microscopic (UV) symmetry We construct a general framework for constructing lattice models for igSPT phases with emergent anomalies classified by group cohomology, and establish a direct connection between the emergent anomaly, group-extension, and topological edge states by gauging the extending symmetry. In many examples, the edge-state protection has a physically transparent mechanism: the extending UV symmetry operations pump lower dimensional SPTs onto the igSPT edge, tuning the edge to a (multi)critical point between different SPTs protected by the IR symmetry. In two- and three- dimensional systems, an additional possibility is that the emergent anomaly can be satisfied by an anomalous symmetry-enriched topological order, which we call a quotient-symmetry enriched topological order (QSET) that is sharply distinguished from the non-anomalous UV SETs by an edge phase transition. We construct exactly solvable lattice models with QSET order., Comment: 37 pages, 9 figures

We consider monitored quantum systems with a global conserved charge, and ask how efficiently an observer ("eavesdropper") can learn the global charge of such systems from local projective measurements. We find phase transitions as a function of the measurement rate, depending on how much information about the quantum dynamics the eavesdropper has access to. For random unitary circuits with U(1) symmetry, we present an optimal classical classifier to reconstruct the global charge from local measurement outcomes only. We demonstrate the existence of phase transitions in the performance of this classifier in the thermodynamic limit. We also study numerically improved classifiers by including some knowledge about the unitary gates pattern.

We present a numerical method to simulate non-equilibrium Floquet steady states of one-dimensional periodically-driven (Floquet) many-body systems coupled to a dissipative bath, called open-system Floquet DMRG (OFDMRG). This method is based on a matrix product operator ansatz for the Floquet density matrix in frequency-space, and enables access to large systems beyond the reach of exact master-equation or quantum trajectory simulations, while retaining information about the periodic micro-motion in Floquet steady states. An excited-state extension of this technique also allows computation of the dynamical approach to the steady state on asymptotically long timescales. We benchmark the OFDMRG approach with a driven-dissipative Ising model, and apply it to study the possibility of dissipatively stabilizing pre-thermal discrete time-crystalline order by coupling to a cold bath., Comment: 6+7 pages, 3+1 figures

We present a holographic quantum simulation algorithm to variationally prepare thermal states of $d$-dimensional interacting quantum many-body systems, using only enough hardware qubits to represent a ($d$-1)-dimensional cross-section. This technique implements the thermal state by approximately unraveling the quantum matrix-product density operator (qMPDO) into a stochastic mixture of quantum matrix product states (sto-qMPS). The parameters of the quantum circuits generating the qMPS and of the probability distribution generating the stochastic mixture are determined through a variational optimization procedure. We demonstrate a small-scale proof of principle demonstration of this technique on Quantinuum's trapped-ion quantum processor to simulate thermal properties of correlated spin-chains over a wide temperature range using only a single pair of hardware qubits. Then, through classical simulations, we explore the representational power of two versions of sto-qMPS ansatzes for larger and deeper circuits and establish empirical relationships between the circuit resources and the accuracy of the variational free-energy., Comment: 13 pages, 7 figures

While standard approaches to quantum simulation require a number of qubits proportional to the number of simulated particles, current noisy quantum computers are limited to tens of qubits. With the technique of holographic quantum simulation, a $D$-dimensional system can be simulated with a $D{\rm -}1$-dimensional subset of qubits, enabling the study of systems significantly larger than current quantum computers. Using circuits derived from the multiscale entanglement renormalization ansatz (MERA), we accurately prepare the ground state of an $L=32$ critical, non-integrable perturbed Ising model and measure long-range correlations on the 10 qubit Quantinuum trapped ion computer. We introduce generalized MERA (gMERA) networks that interpolate between MERA and matrix product state networks and demonstrate that gMERA can capture far longer correlations than a MERA with the same number of qubits, at the expense of greater circuit depth. Finally, we perform noisy simulations of these two network ans\"atze and find that the optimal choice of network depends on noise level, available qubits, and the state to be represented.

We develop holographic quantum simulation techniques to prepare correlated electronic ground states in quantum matrix product state (qMPS) form, using far fewer qubits than the number of orbitals represented. Our approach starts with a holographic technique to prepare a compressed approximation to electronic mean-field ground-states, known as fermionic Gaussian matrix product states (GMPS), with a polynomial reduction in qubit- and (in select cases gate-) resources compared to existing techniques. Correlations are then introduced by augmenting the GMPS circuits in a variational technique which we denote GMPS+X. We demonstrate this approach on Quantinuum's System Model H1 trapped-ion quantum processor for 1$d$ models of correlated metal and Mott insulating states. Focusing on the $1d$ Fermi-Hubbard chain as a benchmark, we show that GMPS+X methods faithfully capture the physics of correlated electron states, including Mott insulators and correlated Luttinger liquid metals, using considerably fewer parameters than problem-agnostic variational circuits., Comment: 16 pages, 10 figures

Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp phase in which measurements collapse quantum fluctuations of charge without destroying the volume-law entanglement of neutral degrees of freedom. By taking a continuous-time, weak-measurement limit, we construct a controlled replica field theory description of these phases and their intervening charge-sharpening transition in one spatial dimension. We find that the charge fuzzy phase is a critical phase with continuously evolving critical exponents that terminates in a modified Kosterlitz-Thouless transition to the short-range correlated charge-sharp phase. We numerically corroborate these scaling predictions also hold for discrete-time projective-measurement circuit models using large-scale matrix-product state simulations, and discuss generalizations to higher dimensions., Comment: 5+8 pages, 3 figures

The central philosophy of statistical mechanics (stat-mech) and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple universal "laws". This same philosophy promises powerful methods for studying the dynamics of quantum information in ideal and noisy quantum circuits -- for which classical description of individual circuits is expected to be generically intractable. Here, we review recent progress in understanding the dynamics of quantum information in ensembles of random quantum circuits, through a stat-mech lens. We begin by reviewing discoveries of universal features of entanglement growth, operator spreading, thermalization, and chaos in unitary random quantum circuits, and their relation to stat-mech problems of random surface growth and noisy hydrodynamics. We then explore the dynamics of monitored random circuits, which can loosely be thought of as noisy dynamics arising from an environment monitoring the system, and exhibit new types of measurement-induced phases and criticality. Throughout, we attempt to give a pedagogical introduction to various technical methods, and to highlight emerging connections between concepts in stat-mech, quantum information and quantum communication theory., Comment: v2: various updated sections, new figures. Chapter in "Springer volume: Entanglement in Spin Chains -- Theory and Quantum Technology Applications"

We propose a realization of Kondo-lattice physics in moir\'e superlattices at the interface between a WX$_2$ homobilayer and MoX$_2$ monolayer (where X=S,Se). Under appropriate gating conditions, the interface-WX$_2$-layer forms a triangular lattice of local moments that couple to itinerant electrons in the other WX$_2$-layer via a gate-tunable Kondo exchange interaction. Using a parton mean-field approach we identify a range of twist-angles which support a gate-tuned quantum phase transition between a heavy-fermion liquid with large anomalous Hall conductance and a fractionalized chiral spin-liquid coexisting with a light Fermi liquid, and describe experimental signatures to distinguish among competing theoretical scenarios., Comment: 4+7 pages, 2+5 figures

This is a reply to the comment from Khemani, Moessner and Sondhi (KMS) [arXiv:2109.00551] on our manuscript [Phys. Rev. Lett. 118, 030401 (2017)]. The main new claim in KMS is that the short-ranged model does not support an MBL DTC phase. We show that, even for the parameter values they consider and the system sizes they study, the claim is an artifact of an unusual choice of range for the crucial plots. Conducting a standard finite-size scaling analysis on the same data strongly suggests that the system is in fact a many-body localized (MBL) discrete time crystal (DTC). Furthermore, we have carried out additional simulations at larger scales, and provide an analytic argument, which fully support the conclusions of our original paper. We also show that the effect of boundary conditions, described as essential by KMS, is exactly what one would expect, with boundary effects decreasing with increasing system size. The other points in KMS are either a rehashing of points already in the literature (for the long-ranged model) or are refuted by a proper finite-size scaling analysis., Comment: 7 pages, 4 figures

This chapter provides an overview of research in computer-based writing instruction (CBWI). CBWI may entail any type of writing instruction with computers and may refer specifically to technologies that provide computer-generated feedback and instruction. The purpose of CBWI is to support students in improving their written products and writing processes, and to also optimize teacher labor regarding instruction and feedback. We argue in this chapter that the benefits afforded by CBWI are enhanced within the context of writing instruction that emphasizes principles of evidence-based writing practices and is situated within authentic writing communities. We conclude with a discussion about potential affordances and threats to writing instruction practices and communities from generative artificial intelligence tools. Future research directions for CBWI are discussed. [This chapter was published in: "Handbook of Writing Research (3rd Ed.)," Guilford, 2023.]

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 find that while R\'enyi entropies grow sub-ballistically as $\sqrt{t}$ in the absence of measurement, for even an infinitesimal rate of measurements, all average R\'enyi entropies grow ballistically with time $\sim t$. 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, and offers a general framework for studying dissipatively-stabilized symmetry-breaking and topological orders., Comment: Updated some statements and a figure. 29 pages, 17 figures

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in (approximately) isolated systems. Here, achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work suggests that these capabilities can enable dynamical phases and critical phenomena that exhibit topologically-robust methods to create, protect, and manipulate quantum entanglement that self-correct against large classes of errors. However, to date, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders. In this work, we demonstrate an emergent dynamical symmetry protected topological phase (EDSPT), in a quasiperiodically-driven array of ten $^{171}\text{Yb}^+$ hyperfine qubits in Honeywell's System Model H1 trapped-ion quantum processor. This phase exhibits edge qubits that are dynamically protected from control errors, cross-talk, and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. This property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit-array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders that would enable error-resilient techniques to manipulate quantum information., Comment: 6+12 pages; 3+7 figures

We characterize the variational power of quantum circuit tensor networks in the representation of physical many-body ground-states. Such tensor networks are formed by replacing the dense block unitaries and isometries in standard tensor networks by local quantum circuits. We explore both quantum circuit matrix product states and the quantum circuit multi-scale entanglement renormalization ansatz, and introduce an adaptive method to optimize the resulting circuits to high fidelity with more than $10^4$ parameters. We benchmark their expressiveness against standard tensor networks, as well as other common circuit architectures, for the 1D/2D Heisenberg and 1D Fermi-Hubbard models. We find quantum circuit tensor networks to be substantially more expressive than other quantum circuits for these problems, and that they can even be more compact than standard tensor networks. Extrapolating to circuit depths which can no longer be emulated classically, this suggests a region of advantage in quantum expressiveness in the representation of physical ground-states., Comment: 13 pages, 13 figures

Quantum computers have the potential to efficiently simulate the dynamics of many interacting quantum particles, a classically intractable task of central importance to fields ranging from chemistry to high-energy physics. However, precision and memory limitations of existing hardware severely limit the size and complexity of models that can be simulated with conventional methods. Here, we demonstrate and benchmark a new scalable quantum simulation paradigm--holographic quantum dynamics simulation--which uses efficient quantum data compression afforded by quantum tensor networks along with opportunistic mid-circuit measurement and qubit reuse to simulate physical systems that have far more quantum degrees of freedom than can be captured by the available number of qubits. Using a Honeywell trapped ion quantum processor, we simulate the non-integrable (chaotic) dynamics of the self-dual kicked Ising model starting from an entangled state of $32$ spins using at most $9$ trapped ion qubits, obtaining excellent quantitative agreement when benchmarking against dynamics computed directly in the thermodynamic limit via recently developed exact analytical techniques. These results suggest that quantum tensor network methods, together with state-of-the-art quantum processor capabilities, enable a viable path to practical quantum advantage in the near term., Comment: 8 pages, 6 figures, 1 table

The ability to selectively measure, initialize, and reuse qubits during a quantum circuit enables a mapping of the spatial structure of certain tensor-network states onto the dynamics of quantum circuits, thereby achieving dramatic resource savings when using a quantum computer to simulate many-body systems with limited entanglement. We experimentally demonstrate a significant benefit of this approach to quantum simulation: In addition to all correlation functions, the entanglement structure of an infinite system -- specifically the half-chain entanglement spectrum -- is conveniently encoded within a small register of "bond qubits" and can be extracted with relative ease. Using a trapped-ion QCCD quantum computer equipped with selective mid-circuit measurement and reset, we quantitatively determine the near-critical entanglement entropy of a correlated spin chain directly in the thermodynamic limit and show that its phase transition becomes quickly resolved upon expanding the bond-qubit register., Comment: 5 pages + supplemental material

We construct an example of a 1$d$ quasiperiodically driven spin chain whose edge states can coherently store quantum information, protected by a combination of localization, dynamics, and topology. Unlike analogous behavior in static and periodically driven (Floquet) spin chains, this model does not rely upon microscopic symmetry protection: Instead, the edge states are protected purely by emergent dynamical symmetries. We explore the dynamical signatures of this Emergent Dynamical Symmetry-Protected Topological (EDSPT) order through exact numerics, time evolving block decimation, and analytic high-frequency expansion, finding evidence that the EDSPT is a stable dynamical phase protected by bulk many-body localization up to (at least) stretched-exponentially long time scales, and possibly beyond. We argue that EDSPTs are special to the quasiperiodically driven setting, and cannot arise in Floquet systems. Moreover, we find evidence of a new type of boundary criticality, in which the edge spin dynamics transition from quasiperiodic to chaotic, leading to bulk thermalization., Comment: 7+8 pages, 5 figures

We investigate the effects of quenched randomness on topological quantum phase transitions in strongly interacting two-dimensional systems. We focus first on transitions driven by the condensation of a subset of fractionalized quasiparticles (`anyons') identified with `electric charge' excitations of a phase with intrinsic topological order. All other anyons have nontrivial mutual statistics with the condensed subset and hence become confined at the anyon condensation transition. Using a combination of microscopically exact duality transformations and asymptotically exact real-space renormalization group techniques applied to these two-dimensional disordered gauge theories, we argue that the resulting critical scaling behavior is `superuniversal' across a wide range of such condensation transitions, and is controlled by the same infinite-randomness fixed point as that of the 2D random transverse-field Ising model. We validate this claim using large-scale quantum Monte Carlo simulations that allow us to extract zero-temperature critical exponents and correlation functions in (2+1)D disordered interacting systems. We discuss generalizations of these results to a large class of ground-state and excited-state topological transitions in systems with intrinsic topological order as well as those where topological order is either protected or enriched by global symmetries. When the underlying topological order and the symmetry group are Abelian, our results provide prototypes for topological phase transitions between distinct many-body localized phases., Comment: 33 pages, 35 figures; published version