Quantum Many-body Dynamics Research Articles

Noncommuting charges can remove non-stationary quantum many-body dynamics

Studying noncommuting conserved quantities, or ‘charges,’ has revealed a conceptual puzzle: noncommuting charges hinder thermalization in some ways yet promote it in others. While many quantum systems thermalize according to the Eigenstate Thermalization Hypothesis (ETH), systems with ‘dynamical symmetries’ violate the ETH and exhibit non-stationary dynamics, preventing them from equilibrating, much less thermalizing. We demonstrate that each pair of dynamical symmetries corresponds to a specific charge. We find that introducing new charges that do not commute with existing ones disrupts these symmetries, thereby eliminating non-stationary dynamics and facilitating thermalization. We illustrate this behavior across various models, including the Hubbard model and Heisenberg spin chains. Our findings demonstrate that noncommuting charges can enhance thermalization by reducing the number of local observables that thermalize according to the ETH.

Quantum Walks and Correlated Dynamics in an Interacting Synthetic Rydberg Lattice.

Coherent dynamics of interacting quantum particles plays a central role in the study of strongly correlated quantum matter and the pursuit of quantum information processors. Here, we present the state space of interacting Rydberg atoms as a synthetic landscape on which to control and observe coherent and correlated dynamics. With full control of the coupling strengths and energy offsets between the pairs of sites in a nine-site synthetic lattice, we realize quantum walks, Bloch oscillations, and dynamics in an Escher-type "continuous staircase." In the interacting regime, we observe correlated quantum walks, Bloch oscillations, and confinement of particle pairs. Additionally, we simultaneously tilt our lattice both up and down to achieve coherent pair oscillations. When combined with a few straightforward upgrades, this work establishes synthetic Rydberg lattices of interacting atom arrays as a promising platform for programmable quantum many-body dynamics with access to features that are difficult to realize in real-space lattices.

Quantum next generation reservoir computing: an efficient quantum algorithm for forecasting quantum dynamics

Next Generation Reservoir Computing (NG-RC) is a modern class of model-free machine learning that enables an accurate forecasting of time series data generated by dynamical systems. We demonstrate that NG-RC can accurately predict full many-body quantum dynamics in both integrable and chaotic systems. This is in contrast to the conventional application of reservoir computing that concentrates on the prediction of the dynamics of observables. In addition, we apply a technique which we refer to as skipping ahead to predict far future states accurately without the need to extract information about the intermediate states. However, adopting a classical NG-RC for many-body quantum dynamics prediction is computationally prohibitive due to the large Hilbert space of sample input data. In this work, we propose an end-to-end quantum algorithm for many-body quantum dynamics forecasting with a quantum computational speedup via the block-encoding technique. This proposal presents an efficient model-free quantum scheme to forecast quantum dynamics coherently, bypassing inductive biases incurred in a model-based approach.

Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains.

Entanglement propagation provides a key routine to understand quantum many-body dynamics in and out of equilibrium. Entanglement entropy (EE) usually approaches to a subsaturation known as the Page value S[over ˜]_{P}=S[over ˜]-dS (with S[over ˜] the maximum of EE and dS the Page correction) in, e.g., the random unitary evolutions. The ballistic spreading of EE usually appears in the early time and will be deviated far before the Page value is reached. In this work, we uncover that the magnetic field that maximizes the EE robustly induces persistent ballistic spreading of entanglement in quantum spin chains. The linear growth of EE is demonstrated to persist until the maximal S[over ˜] (along with a flat entanglement spectrum) is reached. The robustness of ballistic spreading and the enhancement of EE under such an optimal control are demonstrated, considering particularly perturbing the initial state by random pure states (RPSs). These are argued as the results from the endomorphism of the time evolution under such an entanglement-enhancing optimal control for the RPSs.

From dual-unitary to biunitary: a 2-categorical model for exactly-solvable many-body quantum dynamics

Dual-unitary brickwork circuits are an exactly-solvable model for many-body chaotic quantum systems, based on 2-site gates which are unitary in both the time and space directions. Prosen has recently described an alternative model called dual-unitary interactions round-a-face, which we here call clockwork, based on 2-controlled 1-site unitaries composed in a non-brickwork structure, yet with many of the same attractive global properties. We present a 2-categorical framework that simultaneously generalizes these two existing models, and use it to show that brickwork and clockwork circuits can interact richly, yielding new types of generalized heterogeneous circuits. We show that these interactions are governed by quantum combinatorial data, which we precisely characterize. These generalized circuits remain exactly-solvable and we show that they retain the attractive features of the original models such as single-site correlation functions vanishing everywhere except on the causal light-cone. Our framework allows us to directly extend the notion of solvable initial states to these biunitary circuits, and we show these circuits demonstrate maximal entanglement growth and exact thermalization after finitely many time steps.

Prolonging a discrete time crystal by quantum-classical feedback

Nonequilibrium phases of quantum matter featuring time crystalline eigenstate order have been realized recently on noisy intermediate-scale quantum (NISQ) devices. While ideal quantum time crystals exhibit collective subharmonic oscillations and spatiotemporal long-range order persisting for infinite times, the decoherence time of current NISQ devices sets a natural limit to the survival of these phases, restricting their observation to a shallow quantum circuit. Here we propose a time-periodic scheme that leverages quantum-classical feedback protocols in subregions of the system to enhance a time crystal signal significantly exceeding the decoherence time of the device. As a case of study, we demonstrate the survival of the many-body localized discrete time crystal phase in the one-dimensional periodically kicked Ising model, accounting for decoherence of the system with an environment. Based on classical simulation of quantum circuit realizations we find that this approach is suitable for implementation on existing quantum hardware and presents a prospective path to simulate complex quantum many-body dynamics that transcend the low depth limit of current digital quantum computers. Published by the American Physical Society 2024

Superconducting Quantum Simulation for Many-Body Physics beyond Equilibrium.

Quantum computing is an exciting field that uses quantum principles, such as quantum superposition and entanglement, to tackle complex computational problems. Superconducting quantum circuits, based on Josephson junctions, is one of the most promising physical realizations to achieve the long-term goal of building fault-tolerant quantum computers. The past decade has witnessed the rapid development of this field, where many intermediate-scale multi-qubit experiments emerged to simulate nonequilibrium quantum many-body dynamics that are challenging for classical computers. Here, we review the basic concepts of superconducting quantum simulation and their recent experimental progress in exploring exotic nonequilibrium quantum phenomena emerging in strongly interacting many-body systems, e.g., many-body localization, quantum many-body scars, and discrete time crystals. We further discuss the prospects of quantum simulation experiments to truly solve open problems in nonequilibrium many-body systems.

Unravelling quantum dynamics using flow equations

The study of many-body quantum dynamics in strongly correlated systems is extremely challenging. To date, few numerical methods exist that are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, which is partly due to complexity theoretic obstructions. In this work, we present a technique able to overcome this obstacle, by combining continuous unitary flow techniques with the newly developed method of scrambling transforms. We overcome the assumption that approximately diagonalizing the Hamiltonian cannot lead to reliable predictions for relatively long times. Rather, we show that the method achieves good accuracy in both localized and delocalized phases and makes reliable predictions for a number of quantities including infinite-temperature autocorrelation functions. We complement our findings with rigorous incremental bounds on the truncation error. Our approach shows that, in practice, the exploration of intermediate-scale time evolution may be more feasible than is commonly assumed, challenging near-term quantum simulators.

Non-Markovian character and irreversibility of real-time quantum many-body dynamics

Non-Markovian character and irreversibility of real-time quantum many-body dynamics

Universal Measurement-Based Quantum Computation in a One-Dimensional Architecture Enabled by Dual-Unitary Circuits.

A powerful tool emerging from the study of many-body quantum dynamics is that of dual-unitary circuits, which are unitary even when read "sideways," i.e., along the spatial direction. Here, we show that this provides the ideal framework to understand and expand on the notion of measurement-based quantum computation (MBQC). In particular, applying a dual-unitary circuit to a many-body state followed by appropriate measurements effectively implements quantum computation in the spatial direction. We show how the dual-unitary dynamics generated by the dynamics of the paradigmatic one-dimensional kicked Ising chain with certain parameter choices generate resource states for universal deterministic MBQC. Specifically, after k time steps, equivalent to a depth-k quantum circuit, we obtain a resource state for universal MBQC on ∼3k/4 encoded qubits. Our protocol allows generic quantum circuits to be "rotated" in space-time and gives new ways to exchange between resources like qubit number and coherence time in quantum computers. Beyond the practical advantages, we also interpret the dual-unitary evolution as generating an infinite sequence of new symmetry-protected topological phases with spatially modulated symmetries, which gives a vast generalization of the well-studied one-dimensional cluster state and shows that our protocol is robust to symmetry-respecting deformations.

Blue-Detuned Magneto-optical Trap of CaF Molecules.

A key method to produce trapped and laser-cooled molecules is the magneto-optical trap (MOT), which is conventionally created using light red detuned from an optical transition. In this work, we report a MOT for CaF molecules created using blue-detuned light. The blue-detuned MOT (BDM) achieves temperatures well below the Doppler limit and provides the highest densities and phase-space densities reported to date in CaF MOTs. Our results suggest that BDMs are likely achievable in many relatively light molecules including polyatomic ones, but our measurements suggest that BDMs will be challenging to realize in substantially heavier molecules due to sub-mK trap depths. In addition to record temperatures and densities, we find that the BDM substantially simplifies and enhances the loading of molecules into optical tweezer arrays, which are a promising platform for quantum simulation and quantum information processing. Notably, the BDM reduces molecular number requirements ninefold compared to a conventional red-detuned MOT, while not requiring additional hardware. Our work therefore substantially simplifies preparing large-scale molecular tweezer arrays, which are a novel platform for simulation of quantum many-body dynamics and quantum information processing with molecular qubits.

Many-body quantum dynamics of spin-orbit coupled Andreev states in a Zeeman field

Many-body quantum dynamics of spin-orbit coupled Andreev states in a Zeeman field

Efficient Large-Scale Many-Body Quantum Dynamics via Local-Information Time Evolution

During time evolution of many-body systems entanglement grows rapidly, limiting exact simulations to small-scale systems or small timescales. Quantum information tends, however, to flow towards larger scales without returning to local scales, such that its detailed large-scale structure does not directly affect local observables. This allows for the removal of large-scale quantum information in a way that preserves all local observables and gives access to large-scale and large-time quantum dynamics. To this end, we use the recently introduced to organize quantum information into different scales, allowing us to define and that we employ to systematically discard long-range quantum correlations in a controlled way. Our approach relies on decomposing the system into subsystems up to a maximum scale and time evolving the subsystem density matrices by solving the subsystem von Neumann equations in parallel. Importantly, the information flow needs to be preserved during the discarding of large-scale information. To achieve this without the need to make assumptions about the microscopic details of the information current, we introduce a second scale at which information is discarded, while using the state at the maximum scale to accurately obtain the information flow. The resulting algorithm, which we call local-information time evolution, is highly versatile and suitable for investigating many-body quantum dynamics in both closed and open quantum systems with diverse hydrodynamic behaviors. We present results for the energy transport in the mixed-field Ising model and the magnetization transport in the XX spin chain with onsite dephasing where we accurately determine the power-law exponent and the diffusion coefficients. Furthermore, the information lattice framework employed here promises to offer insightful results about the spatial and temporal behavior of entanglement in many-body systems. Published by the American Physical Society 2024

From many-body quantum dynamics to the Hartree–Fock and Vlasov equations with singular potentials

In a combined mean-field and semiclassical regime, we consider the time evolution of N fermions interacting through singular pair interaction potentials of the form \pm |x-y|^{-a} , which includes the Coulomb and gravitational interactions. We prove that the many-body dynamics of mixed states are well approximated by solutions of the Hartree–Fock and Vlasov equations in terms of Schatten norms. The errors in these approximations are expressed in terms of the expected number of particles, N , and the Planck constant, h . For cases where a\in(0,1/2) , we obtain local-in-time results when N^{-1/2}\ll h \leq N^{-1/3} . Notably, this leads to the derivation of the Vlasov equation with singular potentials. For cases where a\in[1/2,1] , our results hold only within a small time scale or require an N -dependent cut-off. A fundamental ingredient in our analysis is the propagation of regularity for solutions to the Hartree–Fock equation uniformly in the Planck constant, which holds for a\in(0,1] .

Information scrambling —A quantum thermodynamic perspective

Recent advances in quantum information science have shed light on the intricate dynamics of quantum many-body systems, for which quantum information scrambling is a perfect example. Motivated by considerations of the thermodynamics of quantum information, this perspective aims at synthesizing key findings from several pivotal studies and exploring various aspects of quantum scrambling. We consider quantifiers such as the out-of-time-ordered correlator (OTOC) and the quantum mutual information, their connections to thermodynamics, and their role in understanding chaotic vs. integrable quantum systems. With a focus on representative examples, we cover a range of topics, including the thermodynamics of quantum information scrambling, and the scrambling dynamics in quantum gravity models such as the Sachdev-Ye-Kitaev (SYK) model. Examining these diverse approaches enables us to highlight the multifaceted nature of quantum information scrambling and its significance in understanding the fundamental aspects of quantum many-body dynamics at the intersection of quantum mechanics and thermodynamics.

Quantum simulation of the bosonic Kitaev chain

Superconducting quantum circuits are a natural platform for quantum simulations of a wide variety of important lattice models describing topological phenomena, spanning condensed matter and high-energy physics. One such model is the bosonic analog of the well-known fermionic Kitaev chain, a 1D tight-binding model with both nearest-neighbor hopping and pairing terms. Despite being fully Hermitian, the bosonic Kitaev chain exhibits a number of striking features associated with non-Hermitian systems, including chiral transport and a dramatic sensitivity to boundary conditions known as the non-Hermitian skin effect. Here, using a multimode superconducting parametric cavity, we implement the bosonic Kitaev chain in synthetic dimensions. The lattice sites are mapped to frequency modes of the cavity, and the in situ tunable complex hopping and pairing terms are created by parametric pumping at the mode-difference and mode-sum frequencies, respectively. We experimentally demonstrate important precursors of nontrivial topology and the non-Hermitian skin effect in the bosonic Kitaev chain, including chiral transport, quadrature wavefunction localization, and sensitivity to boundary conditions. Our experiment is an important first step towards exploring genuine many-body non-Hermitian quantum dynamics.

Numerical simulation of long-range open quantum many-body dynamics with tree tensor networks

Numerical simulation of long-range open quantum many-body dynamics with tree tensor networks

Approaching a fully-polarized state of nuclear spins in a solid

Magnetic noise of atomic nuclear spins is a major source of decoherence in solid-state spin qubits. In theory, near-unity nuclear spin polarization can eliminate decoherence of the electron spin qubit, while turning the nuclei into a useful quantum information resource. However, achieving sufficiently high nuclear polarizations has remained an evasive goal. Here we implement a nuclear spin polarization protocol which combines strong optical pumping and fast electron tunneling. Nuclear polarizations well above 95% are generated in GaAs semiconductor quantum dots on a timescale of 1 minute. The technique is compatible with standard quantum dot device designs, where highly-polarized nuclear spins can simplify implementations of qubits and quantum memories, as well as offer a testbed for studies of many-body quantum dynamics and magnetism.

Multiple-quantum-coherence dynamics of spin-1 Bose–Einstein condensate during quantum phase transitions

Multiple quantum coherences are often employed to describe quantum many-body dynamics in nuclear spin systems and recently, to characterize quantum phase transitions in trapped ions. Here we investigate the multiple-quantum-coherence dynamics of a spin-1 Bose–Einstein condensate. By adjusting the quadratic Zeeman shift, the condensate exhibits three quantum phases. Our numerical results show that the spectrum of multiple quantum coherence does indeed catch the quantum critical points. More importantly, with only a few low-order multiple quantum coherences, the spin-1 condensate exhibits rich signals of the many-body dynamics, beyond conventional observables. The experimental implementation of such multiple quantum coherence protocol is also discussed.

Speed limits and locality in many-body quantum dynamics.

We review the mathematical speed limits on quantum information processing in many-body systems. After the proof of the Lieb-Robinson Theorem in 1972, the past two decades have seen substantial developments in its application to other questions, such as the simulatability of quantum systems on classical or quantum computers, the generation of entanglement, and even the properties of ground states of gapped systems. Moreover, Lieb-Robinson bounds have been extended in non-trivial ways, to demonstrate speed limits in systems with power-law interactions or interacting bosons, and even to prove notions of locality that arise in cartoon models for quantum gravity with all-to-all interactions. We overview the progress which has occurred, highlight the most promising results and techniques, and discuss some central outstanding questions which remain open. To help bring newcomers to the field up to speed, we provide self-contained proofs of the field's most essential results.