arXiv subjects

Vadim Oganesyan

Publications and source records attributed to Vadim Oganesyan.

At least 37 records · Page 2Linked to original sources

arXiv2023

Embedding quantum optimization problems using AC driven quantum ferromagnets

Analog quantum optimization methods, such as quantum annealing, are promising and at least partially noise tolerant ways to solve hard optimization and sampling problems with quantum hardware. However, they have thus far failed to demonstrate broadly applicable quantum speedups, and an important contributing factor to this is slowdowns from embedding, the process of mapping logical variables to long chains of physical qubits, enabling arbitrary connectivity on the short-ranged 2d hardware grid. Beyond the spatial overhead in qubit count, embedding can lead to severe time overhead, arising from processes where individual chains ``freeze" into ferromagnetic states at different times during evolution, and once frozen the tunneling rate of this single logical variable decays exponentially in chain length. We show that this effect can be substantially mitigated by local AC variation of the qubit parameters as in the RFQA protocol (Kapit and Oganesyan, Quant. Sci. Tech. \textbf{6}, 025013 (2021)), through a mechanism we call Symphonic Tunneling. We provide general arguments and substantial numerical evidence to show that AC-driven multi-qubit tunneling is dramatically faster than its DC counterpart, and since ST is not a 1d-specific mechanism, this enhancement should extend to clusters of coupled chains as well. And unlike a uniform transverse field, in higher dimensions this method cannot be efficiently simulated classically. We explore schemes to synchronize the AC tones within chains to further improve performance. Implemented at scale, these methods could significantly improve the prospects for achieving quantum scaling advantages in near-term hardware.

cond-mat.mes-hall↗

arXiv2022

Small logical qubit architecture based on strong interactions and many-body dynamical decoupling

We propose a novel superconducting logical qubit architecture, called the Cold Echo Qubit (CEQ), which is capable of preserving quantum information for much longer timescales than any of its component parts. The CEQ operates fully autonomously, requiring no measurement or feedback, and is compatible with relatively strong interaction elements, allowing for fast, high fidelity logical gates between multiple CEQ's. Its quantum state is protected by a combination of strong interactions and microwave driving, which implements a form of many-body dynamical decoupling to suppress phase noise. Estimates based on careful theoretical analysis and numerical simulations predict improvements in lifetimes and gate fidelities by an order of magnitude or more compared to the current state of the art, assuming no improvements in base coherence. Here, we consider the simplest possible implementation of the CEQ, using a pair of fluxonium qubits shunted through a shared mutual inductance. While not necessarily the best possible implementation, it is the easiest to test experimentally and should display coherence well past breakeven (as compared to the limiting coherence times of its components). A more complex three-node circuit is also presented; it is expected to roughly double the coherence of its two-fluxonium counterpart.

quant-ph↗

arXiv2022

Critical correlations of Ising and Yang-Lee critical points from Tensor RG

We examine feasibility of accurate estimations of universal critical data using tensor renormalization group (TRG) algorithm introduced by Levin and Nave. Specifically, we compute critical exponents $γ, γ/ν, δ, η$ and amplitude ratio $A$ for the magnetic susceptibility from one- and two-point correlation functions for three critical points in two dimensions -- isotropic and anisotropic Ising models and the Yang-Lee critical point at finite imaginary magnetic field. While TRG performs quantitaviely well in all three cases already at smaller bond dimension, $D=16$, the latter two appear to show more rapid improvement in bond dimension, e.g. we are able to reproduce exactly known results to better than one percent at bond dimension $D=24$. We are able to reproduce exactly known values to better than 1 percent with modest effort of bond dimension 28. We comment on the relationship between these results and earlier results on conformal dimensions, fixed points of tensor RG, and also compare computational costs of tensor renormalization vs. conventional Monte-Carlo sampling.

cond-mat.stat-mech↗

arXiv2021

Counting edge modes via dynamics of boundary spin impurities

We study dynamics of the one-dimensional Ising model in the presence of static symmetry-breaking boundary field via the two-time autocorrelation function of the boundary spin. We find that the correlations decay as a power law. We uncover a dynamical phase diagram where, upon tuning the strength of the boundary field, we observe distinct power laws that directly correspond to changes in the number of edge modes as the boundary and bulk magnetic field are varied. We suggest how the universal physics can be demonstrated in current experimental setups, such as Rydberg chains.

cond-mat.stat-mech↗

arXiv2021

Quantum percolation of monopole paths and the response of quantum spin ice

We consider quantum spin ice in a temperature regime in which its response is dominated by the coherent motion of a dilute gas of monopoles. The hopping amplitude of a monopole is sensitive to the configuration of its surrounding spins, taken to be quasi-static on the relevant timescales. This leads to well-known blocked directions in the monopole motion; we find that these are sufficient to reduce the coherent propagation of monopoles to quantum diffusion. This result is robust against disorder, as a direct consequence of the ground-state degeneracy, which disrupts the quantum interference processes needed for weak localization. Moreover, recent work [Tomasello et al., Phys. Rev. Lett. 123, 067204 (2019)] has shown that the monopole hopping amplitudes are roughly bimodal: for $\approx 1/3$ of the flippable spins surrounding a monopole, these amplitudes are extremely small. We exploit this structure to construct a theory of quantum monopole motion in spin ice. In the limit where the slow hopping terms are set to zero, the monopole wavefunctions appear to be fractal; we explain this observation via a mapping to quantum percolation on trees. The fractal, non-ergodic nature of monopole wavefunctions manifests itself in the low-frequency behavior of monopole spectral functions, and is consistent with experimental observations.

cond-mat.stat-mech↗

arXiv2021

Fisher zeros and persistent temporal oscillations in non-unitary quantum circuits

We present a quantum circuit with measurements and post-selection that exhibits a panoply of space- and/or time-ordered phases, from ferromagnetic order to spin-density waves to time crystals. Unlike the time crystals that have been found in unitary models, those that occur here are \emph{incommensurate} with the drive frequency. The period of the incommensurate time-crystal phase may be tuned by adjusting the circuit parameters. We demonstrate that the phases of our quantum circuit, including the inherently non-equilibrium dynamical ones, correspond to complex-temperature equilibrium phases of the exactly solvable square-lattice anisotropic Ising model.

cond-mat.stat-mech↗

arXiv2020

Dissipative failure of adiabatic quantum transport as a dynamical phase transition

Entanglement is the central resource in adiabatic quantum transport. Dephasing affects the availability of that resource by biasing trajectories, driving transitions between success and failure. This depletion of entanglement is important for the practical implementation of quantum technologies. We present a new perspective on the failure of adiabatic computation by understanding the failure of adiabatic transport as a dynamical phase transition. These ideas are demonstrated in a toy model of adiabatic quantum transport in a two spin system.

quant-ph↗

arXiv2020

Beyond Ohm's law -- Bernoulli effect and streaming in electron hydrodynamics

Recent observations of non-local transport in ultraclean 2D materials raised the tantalizing possibility of accessing hydrodynamic correlated transport of many-electron state. However, it has been pointed out that non-local transport can also arise from impurity scattering rather than interaction. At the crux of the ambiguity is the focus on linear effects, i.e. Ohm's law, which cannot easily differentiate among different modes of transport. Here we propose experiments that can reveal rich hydrodynamic features in the system by tapping into the non-linearity of the Navier-Stokes equation. Three experiments we propose will each manifest unique phenomenon well-known in classical fluids: the Bernoulli effect, Eckart streaming, and Rayleigh streaming. Analysis of known parameters confirms that the proposed experiments are feasible and the hydrodynamic signatures are within reach of graphene-based devices. Experimental realization of any one of the three phenomena will provide a stepping stone to formulating and exploring the notions of nonlinear electron fluid dynamics with an eye to celebrated examples from classical non-laminar flows, e.g. pattern formation and turbulence.

cond-mat.str-el↗

arXiv2020

Noise-tolerant quantum speedups in quantum annealing without fine tuning

Quantum annealing is a powerful alternative model for quantum computing, which can succeed in the presence of environmental noise even without error correction. However, despite great effort, no conclusive proof of a quantum speedup (relative to state of the art classical algorithms) has been shown for these systems, and rigorous theoretical proofs of a quantum advantage generally rely on exponential precision in at least some aspects of the system, an unphysical resource guaranteed to be scrambled by random noise. In this work, we propose a new variant of quantum annealing, called RFQA, which can maintain a scalable quantum speedup in the face of noise and modest control precision. Specifically, we consider a modification of flux qubit-based quantum annealing which includes random, but coherent, low-frequency oscillations in the directions of the transverse field terms as the system evolves. We show that this method produces a quantum speedup for finding ground states in the Grover problem and quantum random energy model, and thus should be widely applicable to other hard optimization problems which can be formulated as quantum spin glasses. Further, we show that this speedup should be resilient to two realistic noise channels ($1/f$-like local potential fluctuations and local heating from interaction with a finite temperature bath), and that another noise channel, bath-assisted quantum phase transitions, actually accelerates the algorithm and may outweigh the negative effects of the others. The modifications we consider have a straightforward experimental implementation and could be explored with current technology.

quant-ph↗

arXiv2020

Quantum aspects of "hydrodynamic" transport from weak electron-impurity scattering

Recent experimental observations of apparently hydrodynamic electronic transport have generated much excitement. However, the understanding of the observed non-local transport (whirlpool) effects and parabolic (Poiseuille-like) current profiles has largely been motivated by a phenomenological analogy to classical fluids. This is due to difficulty in incorporating strong correlations in quantum mechanical calculation of transport, which has been the primary angle for interpreting the apparently hydrodynamic transport. Here we demonstrate that even free fermion systems, in the presence of (inevitable) disorder, exhibit non-local conductivity effects such as those observed in experiment because of the fermionic system's long-range entangled nature. On the basis of explicit calculations of the conductivity at finite wavevector, $σ({\bf q})$, for selected weakly disordered free fermion systems, we propose experimental strategies for demonstrating distinctive quantum effects in non-local transport at odds with the expectations of classical kinetic theory. Our results imply that the observation of whirlpools or other "hydrodynamic" effects does not guarantee the dominance of electron-electron scattering over electron-impurity scattering.

cond-mat.str-el↗

arXiv2020

Dimensional crossover and the link between thermodynamics and dynamics: the case of Ising models at complex temperature

We study dimensional crossover in Ising systems at complex temperatures by comparing three types of system: the infinite isotropic 2D Ising model; the infinite anisotropic 2D Ising model; and Ising ladders with a finite number of legs. In particular we present evidence, from both tensor-network calculations and numerical evaluations based on the exact solution of the model, that the infinite anisotropic 2D Ising model exhibits long-range spatially modulated magnetization in certain regions of the complex-temperature plane. We discuss the physics of the special unitary points that exists in the complex-temperature plane, and their connections to the theory of quantum information processing.

cond-mat.stat-mech↗

arXiv2019

Spectral gaps and mid-gap states in random quantum master equations

We discuss the decay rates of chaotic quantum systems coupled to noise. We model both the Hamiltonian and the system-noise coupling by random $N \times N$ Hermitian matrices, and study the spectral properties of the resulting Lindblad superoperator. We consider various random-matrix ensembles, and find that for all of them the asymptotic decay rate remains nonzero in the thermodynamic limit, i.e., the spectrum of the superoperator is gapped as $N \rightarrow \infty$. A sharp spectral transition takes place as the dissipation strength is increased: for weak dissipation, the non-zero eigenvalues of the master equation form a continuum; whereas for strong dissipation, the asymptotic decay rate is an \emph{isolated eigenvalue}, i.e., a `mid-gap state' that is sharply separated from the continuous spectrum of the master equation. For finite $N$, the probability of finding a very small gap vanishes algebraically with a scaling exponent that is extensive in system size, and depends only on the symmetry class of the random matrices and the number of independent decay channels. We comment on experimental implications of our results.

quant-ph↗

arXiv2019

Length scales in the many-body localized phase and their spectral signatures

We compute and compare the decay lengths of several correlation functions and effective coupling constants in the many-body localized (MBL) phase. To this end, we consider the distribution of the logarithms of these couplings and correlators: in each case the log-coupling follows a normal distribution with mean and variance that grow linearly with separation. Thus, a localization length is asymptotically sharply defined for each of these quantities. These localization lengths differ numerically from one another, but all of them remain short up to the numerically observed MBL transition, indicating stability of the MBL phase against isolated ergodic inclusions. We also show how these broad distributions may be extracted using interferometric probes such as double electron-electron resonance (DEER) and the statistics of local spin precession frequencies.

cond-mat.str-el↗

arXiv2018

Anomalous and regular transport in spin 1/2 chains: AC conductivity

We study magnetization transport in anisotropic spin-$1/2$ chains governed by the integrable XXZ model with and without integrability-breaking perturbations at high temperatures ($T\to \infty$) using a hybrid approach that combines exact sum-rules with judiciously chosen Ansätze. In the integrable XXZ model we find (i) super-diffusion at the isotropic (Heisenberg) point, with frequency dependent conductivity $ σ'(ω\to 0) \sim |ω|^α$, where $α=-3/7$ in close numerical agreement with recent $t$-DMRG computations; (ii) a continuously drifting exponent from $α=-1^+$ in the XY limit of the model to $α>0$ within the Ising regime; and (iii) a diffusion constant saturating in the XY coupling deep in the Ising limit. We consider two kinds of integrability breaking perturbations --- a simple next-nearest-neighbor spin-flip term ($J_2$) and a three-spin assisted variant ($t_2$), natural in the fermion particle representation of the spin chain. In the first case we discover a remarkable sensitivity of $σ'(ω)$ to the sign of $J_2$, with enhanced low frequency spectral weight and a pronounced upward shift in the magnitude of $α$ for $J_2>0$. Perhaps even more surprising, we find sub-diffusion ($α>0$) over a range of $J_2<0$. By contrast, the effects of the \enquote{fermionic} three-spin perturbation are sign symmetric; this perturbation produces a clearly observable hydrodynamic relaxation. At large strength of the integrability breaking term $J_2\to \pm \infty$ the problem is effectively non-interacting (fermions hopping on odd and even sublattices) and we find $α\to -1$ behavior reminiscent of the XY limit of the XXZ chain. Exact diagonalization studies largely corroborate these findings at mid-frequencies.

cond-mat.str-el↗

arXiv2017

Magnetic noise spectroscopy as a probe of local electronic correlations in two-dimensional systems

We develop the theoretical framework for calculating magnetic noise from conducting two-dimensional (2D) materials. We describe how local measurements of this noise can directly probe the wave-vector dependent transport properties of the material over a broad range of length scales, thus providing new insight into a range of correlated phenomena in 2D electronic systems. As an example, we demonstrate how transport in the hydrodynamic regime in an electronic system exhibits a unique signature in the magnetic noise profile that distinguishes it from diffusive and ballistic transport and how this can be used to measure the viscosity of the electronic fluid. We employ a Boltzmann approach in a two-time relaxation-time approximation to compute the conductivity of graphene and quantitatively illustrate these transport regimes and the experimental feasibility of observing them. Next, we discuss signatures of isolated impurities lodged inside the conducting 2D material. The noise near an impurity is found to be suppressed compared to the background by an amount that is directly proportional to the cross-section of electrons/holes scattering off of the impurity. We use these results to outline an experimental proposal to measure the temperature dependent level-shift and line-width of the resonance associated with an Anderson impurity.

cond-mat.str-el↗

arXiv2016

Multipoint entanglement in disordered systems

We develop an approach to characterize excited states of disordered many-body systems using spatially resolved structures of entanglement. We show that the behavior of the mutual information (MI) between two parties of a many-body system can signal a qualitative difference between thermal and localized phases -- MI is finite in insulators while it approaches zero in the thermodynamic limit in the ergodic phase. Related quantities, such as the recently introduced Codification Volume (CV), are shown to be suitable to quantify the correlation length of the system. These ideas are illustrated using prototypical non-interacting wavefunctions of localized and extended particles and then applied to characterize states of strongly excited interacting spin chains. We especially focus on evolution of spatial structure of quantum information between high temperature diffusive and many-body localized phases believed to exist in these models. We study MI as a function of disorder strength both averaged over the eigenstates and in time-evolved product states drawn from continuously deformed family of initial states realizable experimentally. As expected, spectral and time-evolved averages coincide inside the ergodic phase and differ significantly outside. We also highlight dispersion among the initial states \emph{within} the localized phase -- some of these show considerable generation and delocalization of quantum information.

cond-mat.dis-nn↗

arXiv2016

Transverse Thermoelectric Response as a Probe for Existence of Quasiparticles

The electrical Hall conductivities of any anisotropic interacting system with reflection symmetry obey sigma_{xy} = - sigma_{yx}. In contrast, we show that the analogous relation between the transverse thermoelectric Peltier coefficients, alpha_{xy}= - alpha_{yx}, does not generally hold in the same system. This fact may be traced to interaction contributions to the heat current operator and the mixed nature of the thermoelectric response functions. Remarkably, however, it appears that emergence of quasiparticles at low temperatures forces alpha_{xy} = - alpha_{yx}. This suggests that quasiparticle-free groundstates (so-called non-Fermi liquids) may be detected by examining the relationship between alpha_{xy} and alpha_{yx} in the presence of reflection symmetry and microscopic anisotropy. These conclusions are based on the following results: (i) The relation between the Peltier coefficients is exact for elastically scattered noninteracting particles; (ii) It holds approximately within Boltzmann theory for interacting particles when elastic scattering dominates over inelastic processes. In a disordered Fermi liquid the latter lead to deviations that vanish as T^3. (iii) We calculate the thermoelectric response in a model of weakly-coupled spin-gapped Luttinger liquids and obtain strong breakdown of antisymmetry between the off-diagonal components of alpha. We also find that the Nernst signal in this model is enhanced by interactions and can change sign as function of magnetic field and temperature.

cond-mat.str-el↗

arXiv2016

Fixed points of Wegner-Wilson flows and many-body localization

Many-body localization (MBL) is a phase of matter that is characterized by the absence of thermalization. Dynamical generation of a large number of local quantum numbers has been identified as one key characteristic of this phase, quite possibly the microscopic mechanism of breakdown of thermalization and the phase transition itself. We formulate a robust algorithm, based on Wegner Wilson flow (WWF) renormalization, for computing these conserved quantities and their interactions. We present evidence for the existence of distinct fixed point distributions of the latter: a flat "white noise" distribution in the ergodic phase, a "1/f" law inside the MBL phase, and scale-free distributions in the transition regime.

cond-mat.dis-nn↗