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Statistical Physics of Information in Open Many-Body Systems
Get PDFIn recent years, concepts and techniques derived from classical and quantum statistical physics have proven invaluable in addressing key problems in the storage, protection, and manipulation of quantum information in near-term devices. A key challenge in this pursuit is the unavoidable presence of an external environment, which can lead to the loss of information encoded within the system. Although these open-system processes are typically detrimental to performing nontrivial quantum computations, they also serve as an invitation to critically investigate the universal physics of many-body systems exposed to decoherence and measurements. This dissertation investigates several different examples of phase transitions and collective phenomena in the flow of information into or out of a system, which arise from its interaction with an external environment. A unifying theme is the importance of nonlinear information-theoretic observables, which are necessary tools for detecting nontrivial critical phenomena in each example studied.
The first part of this dissertation studies the dynamics of quantum information in random unitary circuits which exchange information with an environment. Chapter 3 focuses on the revival of mixed-state entanglement in a one-dimensional monitored random circuit with decoherence at its boundaries. Although the system relaxes to a trivial infinite-temperature state in the absence of monitoring, a nonzero rate of projective measurements performed throughout the system can stabilize an entanglement negativity which scales as a nontrivial power of the system size. From a statistical physics perspective, this power-law scaling of the negativity can be understood as the Kardar-Parisi-Zhang fluctuations of entanglement domain walls due to the random measurement locations. Chapter 4 investigates operator and information spreading in a one-dimensional random circuit which "radiates" qubits into an environment. This circuit exhibits a competition between the scrambling of operators within the system and their leakage into the environment, resulting in a directed percolation phase transition at a critical rate of radiation. From an information-theoretic perspective, this transition is best understood in terms of an observer's ability to reconstruct information initially encoded within the system from the environment's radiated qubits.
The second part of this dissertation studies collective phenomena which arise from performing measurements throughout a critical quantum many-body system. Local measurements can exhibit highly nonlocal effects on entangled states, and so it is natural to ask whether a finite density of local measurements performed on a many-body system can collectively alter the long-range structure of a many-body wavefunction. Critical ground states in one spatial dimension offer a natural setting to explore this question, since their long-wavelength description as (1+1)-dimensional conformal field theories affords a high degree of theoretical control. Chapter 6 focuses on weak measurements performed on Luttinger liquids, a paradigmatic family of critical ground states with continuously tunable power-law correlations. In this setting, both postselected and ensemble-averaged weak measurements of the particle density can lead to transitions in the long-distance power-law scaling of density and phase correlations. Chapter 7 specializes to the critical one-dimensional transverse-field Ising model, where a careful correspondence can be established between randomly distributed projective measurements on the lattice and weak measurements in the continuum. This chapter additionally extends the preceding formalism to study the effect of measurements on the scaling of entanglement entropy, and carefully verifies its analytical predictions using exact free-fermion numerics.
The third and final part of this dissertation studies two further examples of criticality in mixed states which are diagnosed by rather unconventional observables. Chapter 9 investigates a new class of symmetry-breaking phases and transitions which can only arise in mixed quantum states, recently dubbed strong-to-weak spontaneous symmetry breaking (SWSSB). Specifically, this chapter introduces a new diagnostic for SWSSB called the Rényi-1 correlator, which provides a concrete operational definition for SWSSB in a mixed quantum state via conventional symmetry-breaking in its canonical purification. The Rényi-1 correlator additionally exhibits several useful information-theoretic properties, and provides a natural mechanism by which a large class of SWSSB transitions can be efficiently observed in quantum devices. Chapter 10 discusses the classical defect-mediated melting of a two-dimensional solid with strong Ising antiferromagnetic interactions, and the curious role played by "computational" observables in properly determining the model's phase diagram. Computational observables are observables which can only be observed with the assistance of a nontrivial classical computation, and were previously introduced in the study of measurement-induced phenomena and mixed-state phases of matter. Surprisingly, the notion of computational observables and computational phase transitions are shown to play a crucial role in explaining large-scale numerical observations and in the proper theoretical definition of an "antiferromagnetic tetratic" phase
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Anisotropy and Disorder in Fractionalized Phases
Get PDFIn this dissertation we will describe aspects of the interplay of anisotropy and disorder with fractionalized phases of matter through three studies. The first study concerns a material, -RuCl, which has been suggested to be proximate to a fractionalized phase called the Kitaev spin liquid. Despite the presence of traditional magnetic order at low temperatures, ab-initio predictions, and an observed continuum of magnetic excitations at high energies has led to excitement that the material is close to the spin liquid phase. In this study, we describe the magnetic excitations of -RuCl as observed by time-domain terahertz spectroscopy. In the presence of a small (T) magnetic field, a discontinuity in the spectra of magnetic excitations as well as a continuum of magnetic absorption is observed. These observations are suggestive of a field induced transition or proximity to the Kitaev spin liquid. However, with the assumption of random bond anisotropy, we show that a conventional magnetic order is sufficient to explain all observed features. While we find that the experiment can be qualitatively fit to a Hamiltonian with large Kitaev coupling, all aspects of the experiment are shown to be well described by non-fractionalized excitations.In the second study we consider the impact of lattice vacancies in the Kitaev spin liquid, which represents an expected form of disorder in any physical realization of the phase. In Kitaev's exactly solvable honeycomb model, it has been shown that introducing a lattice vacancy binds an emergent flux. This offers a feasible route to creating and trapping this fractionalized excitation. However, it is unclear if this would hold generally for Kitaev spin liquids or only for Kitaev's integrable model. To address this, we introduce a universal low-energy effective theory for the spin liquid with vacancies and fluxes. Using this low-energy theory in the gapless phase we find that the binding energy can be attributed to the suppression of a scattering resonance caused by the vacancy. In the non-abelian phase, where fluxes are Ising anyons, we find that the binding energy has a topological origin. Identifying the doubled spin liquid as a quantum Hall state allows us to argue that spectral flow as flux is threaded through the vacancy induces the binding energy. Our results show that lattice vacancies offer a robust method of creating and trapping Ising anyons in realistic instances of the Kitaev spin liquid. Additionally, this finding indicates that in the presence of vacancy disorder, the Kitaev spin liquid should be expected to have a ground state with fluxes pinned to the vacancies.In the final chapter we introduce exactly solvable models of the phase transition between a Fermi Liquid and a fractionalized Fermi Liquid (FL) defined by the emergence of a gauge field. We compare the cases where the interactions of this model are spatially disordered or translationally invariant. Unlike previous attempts to analytically describe this phase transition, the approach that we introduce allows for the description of strongly coupled fixed points. In particular, we find that it can describe the ubiquitous linear in temperature strange metal resistivity observed near many metallic critical points. For spatially disordered couplings this strange metal phenomenology only appears if the spin liquid deconfines anisotropically into two-dimensional planes of the three-dimensional material. In the limit of strong damping of the critical boson, the model describes a Planckian strange metal in which quasiparticle lifetimes are set only by fundamental constants and the temperature
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Many-Body Quantum Dynamics and Non-Equilibrium Phases of Matter
Get PDFIsolated, many-body quantum systems, evolving under their intrinsic dynamics, exhibit a multitude of exotic phenomena and raise foundational questions about statistical mechanics. A flurry of theoretical work has been devoted to understanding how these systems reach thermal equilibrium in the absence of coupling to an external bath and, when thermalization does not occur, investigating the emergent non-equilibrium phases of matter. With the advent of synthetic quantum systems, such as ultra-cold atoms in optical lattices or trapped ions, these questions are no longer academic and can be directly studied in the laboratory. This dissertation explores the non-equilibrium phenomena that stem from the interplay between interactions, disorder, symmetry, topology, and external driving. First, we study how strong disorder, leading to many-body localization, can arrest the heating of a Floquet system and stabilize symmetry-protected topological order that does not have a static analogue. We analyze its dynamical and entanglement properties, highlight its duality to a discrete time crystal, and propose an experimental implementation in a cold-atom setting.Quenched disorder and the many-body localized state are crucial ingredients in protecting macroscopic quantum coherence. We explore the stability of many-body localization in two and higher dimensions and analyze its robustness to rare regions of weak disorder.We then study a second example of non-thermal behavior, namely integrability. We show that a class of random spin models, realizable in systems of atoms coupled to an optical cavity, gives rise to a rich dynamical phase diagram, which includes regions of integrability, classical chaos, and of a novel integrable structure whose conservation laws are reminiscent of the integrals of motion found in a many-body localized phase.The third group of disordered, non-ergodic systems we consider, spin glasses, have fascinating connections to complexity theory and the hardness of constraint satisfaction. We define a statistical ensemble that interpolates between the classical and quantum limits of such a problem and show that there exists a sharp boundary separating satisfiable and unsatisfiable phases
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Phases of information encoding in many-body quantum states
Get PDFIntermediate-scale quantum devices operate controllably and can maintain quantum entanglement in systems of up to a few hundred qubits. From a many-body perspective, these devices exhibit a novel interplay of entangling unitary evolution, measurements, and decoherence, which is expected to give rise to new emergent phenomena. In this dissertation, we study the collective phenomena associated with information encoding and focus on two broad classes of systems: (i) monitored quantum circuits that consist of unitary evolution and measurements; (ii) topologically ordered states subject to local decoherence. Monitored random quantum circuits have been shown to undergo a measurement-induced phase transition in the steady state when increasing the measurement rate. In the first part of the dissertation, we develop a theoretical framework that maps the quantum information dynamics in monitored circuits to equilibrium statistical mechanics models. We show that the measurement-induced transition can be formulated as a transition in the capacity of the circuit to encode quantum information and further as symmetry-breaking transitions in statistical-mechanical models. Within this framework, we also identify new phases of information flow in monitored circuits, both when symmetry is imposed on circuit elements and when the circuit is at finite times.Topologically ordered states in quantum codes can store quantum information in the presence of local decoherence up to a finite threshold. In the second part of this dissertation, we study the effect of decoherence on general quantum ground states with topological order. We develop a theoretical framework based on effective field theory to identify the possible phases induced by decoherence and characterize their capacity to encode quantum information. We further propose information-theoretical quantities to define topological order in the ensuing decoherence-induced mixed states
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Analytical Studies of Non-Fermi Liquid Metals
Get PDFA wide range of strongly correlated materials – including cuprates, pnictides, heavy fermion compounds, and moiré systems – exhibit linear-in-temperature resistivity, signaling a breakdown of Landau’s Fermi liquid theory. Despite substantial progress, a controlled theoretical understanding of this non-Fermi liquid metallicity remains elusive.In this dissertation, we develop a class of analytically tractable large N models that offer controlled access to strongly coupled non-Fermi liquid metallic critical points. These models retain strong correlations while enabling exact computations of key observables such as transport coefficients and out-of-time-order correlators (OTOCs) that quantify quantum chaos.In the second part of the dissertation, we turn to the phenomenon of linear magnetoresistance (LMR), another common feature of strange metals that defy standard semiclassical theory. We explain this phenomenon through a simple theory of a metal coupled to fluctuating density wave or nematic order, both of which are ubiquitously found in strange metal materials
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From Physical-Level Performance to Logical-Level Robustness: A Dual Approach to Practical Quantum Computing
No full textQuantum computing has witnessed exciting breakthroughs in recent years, achieving remarkable progress at every level of the computing stack. Despite these significant advances, errors remain the primary barrier to making quantum computers practical. A dual approach has emerged to tackle this challenge: one strategy focuses on suppressing errors at the physical level through innovative designs and improved control systems, while the other embraces the inevitability of noise by constructing robust logical qubits from many noisy physical ones. This dissertation explores both avenues. The first part examines the use of machine learning, renowned for its powerful pattern recognition capabilities, to enhance qubit performance by learning directly from simulation and experimental data for superconducting qubits. It demonstrates the effectiveness of reinforcement learning in discovering novel control pulses that achieve higher fidelity with shorter durations when implementing two-qubit entangling gates, and develops a neural network approach for real-time qubit state discrimination, enabling fast and accurate mid-circuit measurements. The second part delves into various aspects of quantum error correction: it compares the performance of a recurrent neural network in correcting errors on continuously measured logical states against a traditional double threshold scheme and a discrete Bayesian classifier, benchmarks several fault-tolerant correction-ready encoding methods for the Steane code on a 2D grid topology, and explores an entropy-based cost function for adapting compass codes to specific noise profiles. By bridging advancements at both the physical and logical levels, this dissertation contributes to the ongoing effort to bring about practical quantum computing
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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