arXiv subjects

Utkarsh Agrawal

Publications and source records attributed to Utkarsh Agrawal.

18 recordsLinked to original sources

arXiv2024

Information dynamics in decohered quantum memory with repeated syndrome measurements: a dual approach

Measurements can detect errors in a decohered quantum memory allowing active error correction to increase the memory time. Previous understanding of this mechanism has focused on evaluating the performance of error correction algorithms based on measurement results. In this work, we instead intrinsically characterize the information dynamics in a quantum memory under repeated measurements, using coherent information and relative entropy. We consider the dynamics of a $d$-dimensional stabilizer code subject to Pauli errors and noisy stabilizer measurements and develop a $(d+1)$-dimensional statistical mechanics model for the information-theoretic diagnostics. Our model is dual to the model previously obtained for the optimal decoding algorithm, and the potential decoding transition in the quantum memory again manifests as a thermal phase transition in the statistical mechanics model. We explicitly derive the model and study the phase transition in information encoding in three examples: surface codes, repetition codes, and the XZZX code.

quant-ph↗

arXiv2024

Quantum Communication and Mixed-State Order in Decohered Symmetry-Protected Topological States

Certain pure-state symmetry-protected topological orders (SPT) can be used as a resource for transmitting quantum information. Here, we investigate the ability to transmit quantum information using decohered SPT states, and relate this property to the "strange correlation functions" which diagnose quantum many-body orders in these mixed-states. This perspective leads to the identification of a class of quantum channels -- termed symmetry-decoupling channels -- which do not necessarily preserve any weak or strong symmetries of the SPT state, but nevertheless protect quantum many-body order in the decohered mixed-state. We quantify the ability to transmit quantum information in decohered SPT states through the coherent quantum information, whose behavior is generally related to a decoding problem, whereby local measurements in the system are used to attempt to "learn" the symmetry charge of the SPT state before decoherence.

quant-ph↗

arXiv2023

Observing quantum measurement collapse as a learnability phase transition

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.

quant-ph↗

arXiv2023

Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits

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.

quant-ph↗

arXiv2023

Quantum Coding Transitions in the Presence of Boundary Dissipation

We investigate phase transitions in the encoding of quantum information in a quantum many-body system due to the competing effects of unitary scrambling and boundary dissipation. Specifically, we study the fate of quantum information in a one-dimensional qudit chain, subject to local unitary quantum circuit evolution in the presence of depolarizating noise at the boundary. If the qudit chain initially contains a finite amount of locally-accessible quantum information, unitary evolution in the presence of boundary dissipation allows this information to remain partially protected when the dissipation is sufficiently weak, and up to time-scales growing linearly in system size $L$. In contrast, for strong enough dissipation, this information is completely lost to the dissipative environment. We analytically investigate this ``quantum coding transition" by considering dynamics involving Haar-random, local unitary gates, and confirm our predictions in numerical simulations of Clifford quantum circuits. We demonstrate that scrambling the quantum information in the qudit chain with a unitary circuit of depth $ \mathcal{O}(\log L)$ before the onset of dissipation can perfectly protect the information until late times. The nature of the coding transition changes when the dynamics extend for times much longer than $L$. We further show that at weak dissipation, it is possible to code at a finite rate, i.e. a fraction of the many-body Hilbert space of the qudit chain can be used to encode quantum information.

quant-ph↗

arXiv2022

Transitions in the learnability of global charges from local measurements

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.

quant-ph↗

arXiv2022

A note on the quasiperiodic many-body localization transition in dimension $d>1$

The nature of the many-body localization (MBL) transition and even the existence of the MBL phase in random many-body quantum systems have been actively debated in recent years. In spatial dimension $d>1$, there is some consensus that the MBL phase is unstable to rare thermal inclusions that can lead to an avalanche that thermalizes the whole system. In this note, we explore the possibility of MBL in quasiperiodic systems in dimension $d>1$. We argue that (i) the MBL phase is stable at strong enough quasiperiodic modulations for $d = 2$, and (ii) the possibility of an avalanche strongly constrains the finite-size scaling behavior of the MBL transition. We present a suggestive construction that MBL is unstable for $d \geq 3$.

cond-mat.dis-nn↗

arXiv2022

Contextual Intelligent Decisions: Expert Moderation of Machine Outputs for Fair Assessment of Commercial Driving

Commercial driving is a complex multifaceted task influenced by personal traits and external contextual factors, such as weather, traffic, road conditions, etc. Previous intelligent commercial driver-assessment systems do not consider these factors when analysing the impact of driving behaviours on road safety, potentially producing biased, inaccurate, and unfair assessments. In this paper, we introduce a methodology (Expert-centered Driver Assessment) towards a fairer automatic road safety assessment of drivers' behaviours, taking into consideration behaviours as a response to contextual factors. The contextual moderation embedded within the intelligent decision-making process is underpinned by expert input, comprising of a range of associated stakeholders in the industry. Guided by the literature and expert input, we identify critical factors affecting driving and develop an interval-valued response-format questionnaire to capture the uncertainty of the influence of factors and variance amongst experts' views. Questionnaire data are modelled and analysed using fuzzy sets, as they provide a suitable computational approach to be incorporated into decision-making systems with uncertainty. The methodology has allowed us to identify the factors that need to be considered when moderating driver sensor data, and to effectively capture experts' opinions about the effects of the factors. An example of our methodology using Heavy Goods Vehicles professionals input is provided to demonstrate how the expert-centred moderation can be embedded in intelligent driver assessment systems.

cs.HC↗

arXiv2021

Field theory of charge sharpening in symmetric monitored quantum circuits

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.

quant-ph↗

arXiv2021

Central Values of Degree Six L-functions: The Case of Hilbert Modular Forms

In this paper we give a formula for the central value of the completed $L$-function $L(s,Sym^{2} g\times f)$, where $f$ and $g$ are Hilbert newforms, by explicitly computing the local integrals appearing in the refined Gan-Gross-Prasad conjecture for $SL_{2}\times\tilde{SL_{2}}$. We also work out the rationality of this value in some special cases and give a conjecture for the general case.

math.NT↗

arXiv2021

Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits

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.

cond-mat.dis-nn↗

arXiv2020

Pristine annotations-based multi-modal trained artificial intelligence solution to triage chest X-ray for COVID-19

The COVID-19 pandemic continues to spread and impact the well-being of the global population. The front-line modalities including computed tomography (CT) and X-ray play an important role for triaging COVID patients. Considering the limited access of resources (both hardware and trained personnel) and decontamination considerations, CT may not be ideal for triaging suspected subjects. Artificial intelligence (AI) assisted X-ray based applications for triaging and monitoring require experienced radiologists to identify COVID patients in a timely manner and to further delineate the disease region boundary are seen as a promising solution. Our proposed solution differs from existing solutions by industry and academic communities, and demonstrates a functional AI model to triage by inferencing using a single x-ray image, while the deep-learning model is trained using both X-ray and CT data. We report on how such a multi-modal training improves the solution compared to X-ray only training. The multi-modal solution increases the AUC (area under the receiver operating characteristic curve) from 0.89 to 0.93 and also positively impacts the Dice coefficient (0.59 to 0.62) for localizing the pathology. To the best our knowledge, it is the first X-ray solution by leveraging multi-modal information for the development.

eess.IV↗

arXiv2020

A Note on the Stochastic Ruler Method for Discrete Simulation Optimization

In this paper, we propose a relaxation to the stochastic ruler method originally described by Yan and Mukai in 1992 for asymptotically determining the global optima of discrete simulation optimization problems. The `original' version of the stochastic ruler and its variants require that a candidate for the next estimate of the optimal solution pass a certain number of tests with respect to the stochastic ruler to be selected as the next estimate of the optimal solution. This requirement - that all tests need to be passed - can lead to promising candidate solutions being rejected and can slow down the convergence of the algorithm. Our proposed modification to the stochastic ruler algorithm relaxes this requirement, and we show analytically that our proposed variant of the stochastic ruler method incurs lesser computational overhead when a new solution in the neighborhood of the current solution is a `successful' candidate for the next estimate of the current solution. We then show numerically that this can yield accelerated convergence to the optimal solution via multiple numerical examples. We also provide the theoretical grounding for the asymptotic convergence in probability of the variant to the global optimal solution under the same set of assumptions as those underlying the original stochastic ruler method.

math.OC↗

arXiv2020

Quantum criticality in the 2d quasiperiodic Potts model

Quantum critical points in quasiperiodic magnets can realize new universality classes, with critical properties distinct from those of clean or disordered systems. Here, we study quantum phase transitions separating ferromagnetic and paramagnetic phases in the quasiperiodic $q$-state Potts model in $2+1d$. Using a controlled real-space renormalization group approach, we find that the critical behavior is largely independent of $q$, and is controlled by an infinite-quasiperiodicity fixed point. The correlation length exponent is found to be $\nu=1$, saturating a modified version of the Harris-Luck criterion.

cond-mat.dis-nn↗

arXiv2019

Anomalous low-frequency conductivity in easy-plane XXZ spin chains

In the easy-plane regime of XXZ spin chains, spin transport is ballistic, with a Drude weight that has a discontinuous fractal dependence on the value of the anisotropy $Δ= \cos πλ$ at nonzero temperatures. We show that this structure necessarily implies the divergence of the low-frequency conductivity for generic irrational values of $λ$. Within the framework of generalized hydrodynamics, we show that in the high-temperature limit the low-frequency conductivity at a generic anisotropy scales as $σ(ω) \sim 1/\sqrtω$; anomalous response occurs because quasiparticles undergo Lévy flights. For rational values of $λ$, the divergence is cut off at low frequencies and the corrections to ballistic spin transport are diffusive. We also use our approach to recover that at the isotropic point $Δ=1$, spin transport is superdiffusive with $σ(ω) \sim ω^{-1/3}$. We support our results with extensive numerical studies using matrix-product operator methods.

cond-mat.stat-mech↗

arXiv2019

Universality and Quantum Criticality in Quasiperiodic Spin Chains

Quasiperiodic systems are aperiodic but deterministic, so their critical behavior differs from that of clean systems as well as disordered ones. Quasiperiodic criticality was previously understood only in the special limit where the couplings follow discrete quasiperiodic sequences. Here we consider generic quasiperiodic modulations; we find, remarkably, that for a wide class of spin chains, generic quasiperiodic modulations flow to discrete sequences under a real-space renormalization group transformation. These discrete sequences are therefore fixed points of a \emph{functional} renormalization group. This observation allows for an asymptotically exact treatment of the critical points. We use this approach to analyze the quasiperiodic Heisenberg, Ising, and Potts spin chains, as well as a phenomenological model for the quasiperiodic many-body localization transition.

cond-mat.dis-nn↗

arXiv2019

Generalized hydrodynamics, quasiparticle diffusion, and anomalous local relaxation in random integrable spin chains

We study the nonequilibrium dynamics of random spin chains that remain integrable (i.e., solvable via Bethe ansatz): because of correlations in the disorder, these systems escape localization and feature ballistically spreading quasiparticles. We derive a generalized hydrodynamic theory for dynamics in such random integrable systems, including diffusive corrections due to disorder, and use it to study non-equilibrium energy and spin transport. We show that diffusive corrections to the ballistic propagation of quasiparticles can arise even in noninteracting settings, in sharp contrast with clean integrable systems. This implies that operator fronts broaden diffusively in random integrable systems. By tuning parameters in the disorder distribution, one can drive this model through an unusual phase transition, between a phase where all wavefunctions are delocalized and a phase in which low-energy wavefunctions are quasi-localized (in a sense we specify). Both phases have ballistic transport; however, in the quasi-localized phase, local autocorrelation functions decay with an anomalous power law, and the density of states diverges at low energy.

cond-mat.dis-nn↗

arXiv2017

Noninteger-spin magnonic excitations in untextured magnets

Interactions are responsible for intriguing physics, e.g. emergence of exotic ground states and excitations, in a wide range of systems. Here we theoretically demonstrate that dipole-dipole interaction leads to bosonic eigen-excitations with average spin ranging from zero to above $\hbar$ in magnets with uniformly magnetized ground states. These exotic excitations can be interpreted as quantum coherent conglomerates of spin $\hbar$ magnons, the eigen-excitations when the dipolar interactions are disregarded. We further find that the eigenmodes in an easy-axis antiferromagnet are spin-zero quasiparticles instead of the widely believed spin $\pm \hbar$ magnons. The latter re-emerge when the symmetry is broken by a sufficiently large applied magnetic field. The average spin greater than $\hbar$ is accompanied by vacuum fluctuations and may be considered to be a weak form of frustration.

cond-mat.mes-hall↗