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Daniel K. Mark

Publications and source records attributed to Daniel K. Mark.

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Observation of ballistic plasma and memory in high-energy gauge theory dynamics

Gauge theories describe the fundamental forces of nature. However, high-energy dynamics, such as the formation of quark-gluon plasmas, is notoriously difficult to model with classical methods. Quantum simulation offers a promising alternative in this regime, yet experiments have mainly probed low energies. Here, we observe the formation of a ballistic plasma and long-time memory effects in high-energy gauge theory dynamics on a high-precision quantum simulator. Both observations are unexpected, as the initial state - fully filled with particle-antiparticle pairs - was thought to rapidly thermalize. Instead, we find correlations spreading ballistically to long distances and a memory of charge clusters. Our observations cannot be explained by many-body scars, but are captured by a new theory of plasma oscillations between electric field and current operators, persisting all the way to the continuum limit of the (1+1)D Schwinger model, of which we simulate a lattice version. Adapting techniques from quantum optics, we visualize plasma oscillations as rotations of Wigner distributions, leading to a novel set of predictions which we test in experiment and numerics. The new framework encompasses both our scenario and scars, which show up as coherent states of the plasma. The experimental surprises we observe in the high-energy dynamics of a simple gauge theory point to the potential of high-precision quantum simulations of gauge theories for general scientific discovery.

quant-ph

How much can we learn from quantum random circuit sampling?

Benchmarking quantum devices is a foundational task for the sustained development of quantum technologies. However, accurate in situ characterization of large-scale quantum devices remains a formidable challenge: such systems experience many different sources of errors, and cannot be simulated on classical computers. Here, we introduce new benchmarking methods based on random circuit sampling (RCS), that substantially extend the scope of conventional approaches. Unlike existing benchmarks that report only a single quantity--the circuit fidelity--our framework extracts rich diagnostic information, including spatiotemporal error profiles, correlated and contextual errors, and biased readout errors, without requiring any modifications of the experiment. Furthermore, we develop techniques that achieve this task without classically intractable simulations of the quantum circuit, by leveraging side information, in the form of bitstring samples obtained from reference quantum devices. Our approach is based on advanced high-dimensional statistical modeling of RCS data. We sharply characterize the information-theoretic limits of error estimation, deriving matching upper and lower bounds on the sample complexity across all regimes of side information. We identify surprising phase transitions in learnability as the amount of side information varies. We demonstrate our methods using publicly available RCS data from a state-of-the-art superconducting processor, obtaining in situ characterizations that are qualitatively consistent yet quantitatively distinct from component-level calibrations. Our results establish both practical benchmarking protocols for current and future quantum computers and fundamental information-theoretic limits on how much can be learned from RCS data.

quant-ph

Efficiently measuring $d$-wave pairing and beyond in quantum gas microscopes

Understanding the mechanism of high-temperature superconductivity is among the most important problems in physics, for which quantum simulation can provide new insights. However, it remains challenging to characterize superconductivity in existing cold-atom quantum simulation platforms. Here, we introduce a protocol for measuring a broad class of observables in fermionic quantum gas microscopes, including long-range superconducting pairing correlations (after a repulsive-to-attractive mapping). The protocol only requires global controls followed by site-resolved particle number measurements -- capabilities that have been already demonstrated in multiple experiments -- and is designed by analyzing the Hilbert-space structure of dimers of two sites. The protocol is sample efficient and we further optimize our pulses for robustness to experimental imperfections such as lattice inhomogeneity. Our work introduces a general tool for manipulating quantum states on optical lattices, enhancing their ability to tackle problems such as that of high-temperature superconductivity.

cond-mat.quant-gas

Experimental signatures of Hilbert-space ergodicity: Universal bitstring distributions and applications in noise learning

Systems reaching thermal equilibrium are ubiquitous. For classical systems, this phenomenon is typically understood statistically through ergodicity in phase space, but translating this to quantum systems is a long-standing problem of interest. Recently a strong notion of quantum ergodicity has been proposed, namely that isolated, global quantum states uniformly explore their available state space, dubbed Hilbert-space ergodicity. Here we observe signatures of this process with an experimental Rydberg quantum simulator and various numerical models, before generalizing to the case of a local quantum system interacting with its environment. For a closed system, where the environment is a complementary subsystem, we predict and observe a smooth quantum-to-classical transition in that observables progress from large, quantum fluctuations to small, Gaussian fluctuations as the bath size grows. This transition exhibits universal properties on a quantitative level amongst a wide range of systems, including those at finite temperature, those with itinerant particles, and random circuits. For an open system, where the environment is uncontrolled, we predict the statistics of observables under largely arbitrary noise channels including those with correlated errors, allowing us to discriminate between candidate error models both for continuous Hamiltonian time evolution and for digital random circuits. This allows for computationally efficient experimental noise learning, and more broadly is a new avenue for quantitatively classifying the behavior of noisy quantum systems. Ultimately our results clarify the role of ergodicity in quantum dynamics, with fundamental and practical consequences.

quant-ph

A Maximum Entropy Principle in Deep Thermalization and in Hilbert-Space Ergodicity

We report universal statistical properties displayed by ensembles of pure states that naturally emerge in quantum many-body systems. Specifically, two classes of state ensembles are considered: those formed by i) the temporal trajectory of a quantum state under unitary evolution or ii) the quantum states of small subsystems obtained by partial, local projective measurements performed on their complements. These cases respectively exemplify the phenomena of "Hilbert-space ergodicity" and "deep thermalization." In both cases, the resultant ensembles are defined by a simple principle: the distributions of pure states have maximum entropy, subject to constraints such as energy conservation, and effective constraints imposed by thermalization. We present and numerically verify quantifiable signatures of this principle by deriving explicit formulae for all statistical moments of the ensembles; proving the necessary and sufficient conditions for such universality under widely-accepted assumptions; and describing their measurable consequences in experiments. We further discuss information-theoretic implications of the universality: our ensembles have maximal information content while being maximally difficult to interrogate, establishing that generic quantum state ensembles that occur in nature hide (scramble) information as strongly as possible. Our results generalize the notions of Hilbert-space ergodicity to time-independent Hamiltonian dynamics and deep thermalization from infinite to finite effective temperature. Our work presents new perspectives to characterize and understand universal behaviors of quantum dynamics using statistical and information theoretic tools.

quant-ph

Benchmarking highly entangled states on a 60-atom analog quantum simulator

Quantum systems have entered a competitive regime where classical computers must make approximations to represent highly entangled quantum states. However, in this beyond-classically-exact regime, fidelity comparisons between quantum and classical systems have so far been limited to digital quantum devices, and it remains unsolved how to estimate the actual entanglement content of experiments. Here we perform fidelity benchmarking and mixed-state entanglement estimation with a 60-atom analog Rydberg quantum simulator, reaching a high entanglement entropy regime where exact classical simulation becomes impractical. Our benchmarking protocol involves extrapolation from comparisons against an approximate classical algorithm, introduced here, with varying entanglement limits. We then develop and demonstrate an estimator of the experimental mixed-state entanglement, finding our experiment is competitive with state-of-the-art digital quantum devices performing random circuit evolution. Finally, we compare the experimental fidelity against that achieved by various approximate classical algorithms, and find that only the algorithm we introduce is able to keep pace with the experiment on the classical hardware we employ. Our results enable a new paradigm for evaluating the ability of both analog and digital quantum devices to generate entanglement in the beyond-classically-exact regime, and highlight the evolving divide between quantum and classical systems.

quant-ph

Benchmarking Quantum Simulators using Ergodic Quantum Dynamics

We propose and analyze a sample-efficient protocol to estimate the fidelity between an experimentally prepared state and an ideal target state, applicable to a wide class of analog quantum simulators without advanced sophisticated spatiotemporal control. Our approach utilizes newly discovered universal fluctuations emerging from generic Hamiltonian dynamics, and it does not require any fine-tuned control over state preparation, quantum evolution, or readout capability. It only needs a small number of experimental measurements, achieving near optimal sample complexity: in ideal cases, a percent-level precision is obtained with $\sim 10^3$ measurements independent of system size. Furthermore, the accuracy of our fidelity estimation improves with increasing system size. We numerically demonstrate our protocol for a variety of quantum simulator platforms such as itinerant particles on optical lattices, trapped ions, and Rydberg atoms. We discuss further applications of our method for advanced tasks such as multi-parameter estimation of quantum states and processes.

quant-ph

Preparing random states and benchmarking with many-body quantum chaos

Producing quantum states at random has become increasingly important in modern quantum science, with applications both theoretical and practical. In particular, ensembles of such randomly-distributed, but pure, quantum states underly our understanding of complexity in quantum circuits and black holes, and have been used for benchmarking quantum devices in tests of quantum advantage. However, creating random ensembles has necessitated a high degree of spatio-temporal control, placing such studies out of reach for a wide class of quantum systems. Here we solve this problem by predicting and experimentally observing the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics, which we use to implement an efficient, widely applicable benchmarking protocol. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system, offering new insights into quantum thermalization. Predicated on this discovery, we develop a fidelity estimation scheme, which we demonstrate for a Rydberg quantum simulator with up to 25 atoms using fewer than 10^4 experimental samples. This method has broad applicability, as we show for Hamiltonian parameter estimation, target-state generation benchmarking, and comparison of analog and digital quantum devices. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a much wider context.

quant-ph

Measuring Arbitrary Physical Properties in Analog Quantum Simulation

A central challenge in analog quantum simulation is to characterize desirable physical properties of quantum states produced in experiments. However, in conventional approaches, the extraction of arbitrary information requires performing measurements in many different bases, which necessitates a high level of control that present-day quantum devices may not have. Here, we propose and analyze a scalable protocol that leverages the ergodic nature of generic quantum dynamics, enabling the efficient extraction of many physical properties. The protocol does not require sophisticated controls and can be generically implemented in analog quantum simulation platforms today. Our protocol involves introducing ancillary degrees of freedom in a predetermined state to a system of interest, quenching the joint system under Hamiltonian dynamics native to the particular experimental platform, and then measuring globally in a single, fixed basis. We show that arbitrary information of the original quantum state is contained within such measurement data, and can be extracted using a classical data-processing procedure. We numerically demonstrate our approach with a number of examples, including the measurements of entanglement entropy, many-body Chern number, and various superconducting orders in systems of neutral atom arrays, bosonic and fermionic particles on optical lattices, respectively, only assuming existing technological capabilities. Our protocol excitingly promises to overcome limited controllability and, thus, enhance the versatility and utility of near-term quantum technologies.

quant-ph

A scalable superconducting quantum simulator with long-range connectivity based on a photonic bandgap metamaterial

Synthesis of many-body quantum systems in the laboratory can help provide further insight into the emergent behavior of quantum materials, whose properties may provide improved methods for energy conversion, signal transport, or information processing. While the majority of engineerable many-body systems, or quantum simulators, consist of particles on a lattice with local interactions, quantum systems featuring long-range interactions are particularly challenging to model and interesting to study due to the rapid spatio-temporal growth of quantum entanglement and correlations. Here, we present a scalable quantum simulator architecture based on a linear array of superconducting qubits locally connected to an extensible photonic-bandgap metamaterial. The metamaterial acts both as a quantum bus mediating qubit-qubit interactions, and as a readout channel for multiplexed qubit-state measurement. As an initial demonstration, we realize a 10-qubit simulator of the one-dimensional Bose-Hubbard model with in situ tunability of both the hopping range and the on-site interaction. We characterize the Hamiltonian of the system using a measurement-efficient protocol based on quantum many-body chaos. Further, we study the many-body quench dynamics of the system, revealing through global bit-string statistics the predicted crossover from integrability to ergodicity as the hopping range increases. The metamaterial quantum bus architecture presented here can be extended to two-dimensional lattice systems and used to generate a wide range of qubit interactions, expanding the accessible Hamiltonians for analog quantum simulation and increasing the flexibility in implementing quantum circuits for gate-based computations

quant-ph

Emergent quantum state designs from individual many-body wavefunctions

Quantum chaos in many-body systems provides a bridge between statistical and quantum physics with strong predictive power. This framework is valuable for analyzing properties of complex quantum systems such as energy spectra and the dynamics of thermalization. While contemporary methods in quantum chaos often rely on random ensembles of quantum states and Hamiltonians, this is not reflective of most real-world systems. In this paper, we introduce a new perspective: across a wide range of examples, a single non-random quantum state is shown to encode universal and highly random quantum state ensembles. We characterize these ensembles using the notion of quantum state $k$-designs from quantum information theory and investigate their universality using a combination of analytic and numerical techniques. In particular, we establish that $k$-designs arise naturally from generic states as well as individual states associated with strongly interacting, time-independent Hamiltonian dynamics. Our results offer a new approach for studying quantum chaos and provide a practical method for sampling approximately uniformly random states; the latter has wide-ranging applications in quantum information science from tomography to benchmarking.

quant-ph

Eta-pairing states as true scars in an extended Hubbard Model

The eta-pairing states are a set of exactly known eigenstates of the Hubbard model on hypercubic lattices, first discovered by Yang [Phys. Rev. Lett. 63, 2144 (1989)]. These states are not many-body scar states in the Hubbard model because they occupy unique symmetry sectors defined by the so-called "eta-pairing SU(2)" symmetry. We study an extended Hubbard model with bond-charge interactions, popularized by Hirsch [Physica C 158, 326 (1989)], where the eta-pairing states survive without the eta-pairing symmetry and become true scar states. We also discuss similarities between the eta-pairing states and exact scar towers in the spin-1 XY model found by Schecter and Iadecola [Phys. Rev. Lett. 123, 147201 (2019)], and systematically arrive at all nearest-neighbor terms that preserve such scar towers in 1D. We also generalize these terms to arbitrary bipartite lattices. Our study of the spin-1 XY model also leads us to several new scarred models, including a spin-1/2 $J_1-J_2$ model with Dzyaloshinkskii-Moriya interaction, in realistic quantum magnet settings in 1D and 2D.

cond-mat.str-el

New exact eigenstates in the Lesanovsky model, proximity to integrability and the PXP model, and approximate scar states

We study a model of Rydberg atoms in a nearest-neighbor Rydberg blockaded regime, introduced by Lesanovsky in Phys. Rev. Lett. 108, 105301 (2012). This many-body model (which has one parameter $z$) has an exactly known gapped liquid ground state, and two exactly known low-lying excitations. We discover two new exact low-lying eigenstates. We also discuss behavior of the model at small parameter $z$ and its proximity to an integrable model. Lastly, we discuss connections between the Lesanovsky model at intermediate $z$ and so-called PXP model. The PXP model describes a recent experiment that observed unusual revivals from a charge density wave initial state, which are attributed to a set of many-body "scar states" which do not obey the eigenstate thermalization hypothesis. We discuss the possibility of scar states in the Lesanovsky model and present two approximations for them.

cond-mat.quant-gas

Unified structure for exact towers of scar states in the AKLT and other models

Quantum many-body scar states are many-body states with finite energy density in non-integrable models that do not obey the eigenstate thermalization hypothesis. Recent works have revealed "towers" of scar states that are exactly known and are equally spaced in energy, specifically in the AKLT model, the spin-1 XY model, and a spin-1/2 model that conserves number of domain walls. We provide a common framework to understand and prove known exact towers of scars in these systems, by evaluating the commutator of the Hamiltonian and a ladder operator. In particular we provide a simple proof of the scar towers in the integer-spin 1d AKLT models by studying two-site spin projectors. Through this picture we deduce a family of Hamiltonians that share the scar tower with the AKLT model, and also find common parent Hamiltonians for the AKLT and XY model scars. We also introduce new towers of exact states, organized in a "pyramid" structure, in the spin-1/2 model through successive application of a non-local ladder operator.

cond-mat.str-el