Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this Letter, we propose quantum algorithms capable of testing whether a Hamiltonian exhibits symmetry with respect to a group. We demonstrate that familiar expressions of Hamiltonian symmetry in quantum mechanics correspond directly with the acceptance probabilities of our algorithms. We execute one of our symmetry-testing algorithms on existing quantum computers for simple examples of both symmetric and asymmetric cases.

Non-Abelian gauge theories underlie our understanding of fundamental forces in nature, and developing tailored quantum hardware and algorithms to simulate them is an outstanding challenge in the rapidly evolving field of quantum simulation. Here we take an approach where gauge fields, discretized in spacetime, are represented by qudits and are time evolved in Trotter steps with multiqudit quantum gates. This maps naturally and hardware efficiently to an architecture based on Rydberg tweezer arrays, where long-lived internal atomic states represent qudits, and the required quantum gates are performed as holonomic operations supported by a Rydberg blockade mechanism. We illustrate our proposal for a minimal digitization of SU(2) gauge fields, demonstrating a significant reduction in circuit depth and gate errors in comparison to a traditional qubit-based approach, which puts simulations of non-Abelian gauge theories within reach of NISQ devices.

We investigate the effect of kinetic constraints on classical many-body chaos in a translationally invariant Heisenberg spin chain using a classical counterpart of the out-of-time-ordered correlator (OTOC). The strength of the constraint drives a “dynamical phase transition” separating a delocalized phase, where the classical OTOC propagates ballistically, from a localized phase, where the OTOC does not propagate at all and the entire system freezes. This is unexpected given that all spin configurations are dynamically connected to each other. We show that localization arises due to the dynamical formation of frozen islands, contiguous segments of spins immobile due to the constraints, dominating over the melting of such islands.

The scalable production of multipartite entangled states in ensembles of qubits is a crucial function of quantum devices, as such states are an essential resource both for fundamental studies on entanglement, as well as for applied tasks. Here we focus on the U(1) symmetric Hamiltonians for qubits with dipolar interactions—a model realized in several state-of-the-art quantum simulation platforms for lattice spin models, including Rydberg-atom arrays with resonant interactions. Making use of exact and variational simulations, we theoretically show that the nonequilibrium dynamics generated by this Hamiltonian shares fundamental features with that of the one-axis-twisting model, namely, the simplest interacting collective-spin model with U(1) symmetry. The evolution governed by the dipolar Hamiltonian generates a cascade of multipartite entangled states—spin-squeezed states, Schrödinger’s cat states, and multicomponent superpositions of coherent spin states. Investigating systems with up to $N=144$ qubits, we observe full scalability of the entanglement features of these states directly related to metrology, namely, scalable spin squeezing at an evolution time $\mathcal{O}(N^{1/3})$ and Heisenberg scaling of sensitivity of the spin parity to global rotations for cat states reached at times $\mathcal{O}(N)$. Our results suggest that the native Hamiltonian dynamics of state-of-the-art quantum simulation platforms, such as Rydberg-atom arrays, can act as a robust source of multipartite entanglement.

Quantum information processing is in real systems often limited by dissipation, stemming from remaining uncontrolled interaction with microscopic degrees of freedom. Given recent experimental progress, we consider weak dissipation, resulting in a small error probability per operation. Here, we find a simple formula for the fidelity reduction of any desired quantum operation, where the ideal evolution is confined to the computational subspace. Interestingly, this reduction is independent of the specific operation; it depends only on the operation time and the dissipation. Using our formula, we investigate the situation where dissipation in different parts of the system has correlations, which is detrimental for the successful application of quantum error correction. Surprisingly, we find that a large class of correlations gives the same fidelity reduction as uncorrelated dissipation of similar strength.

We classify phases of a bosonic lattice model based on the computational complexity of classically simulating the system. We show that the system transitions from being classically simulable to classically hard to simulate as it evolves in time, extending previous results to include on-site number-conserving interactions and long-range hopping. Specifically, we construct a complexity phase diagram with easy and hard “phases” and derive analytic bounds on the location of the phase boundary with respect to the evolution time and the degree of locality. We find that the location of the phase transition is intimately related to upper bounds on the spread of quantum correlations and protocols to transfer quantum information. Remarkably, although the location of the transition point is unchanged by on-site interactions, the nature of the transition point does change. Specifically, we find that there are two kinds of transitions, sharp and coarse, broadly corresponding to interacting and noninteracting bosons, respectively. Our Letter motivates future studies of complexity in many-body systems and its interplay with the associated physical phenomena.

The performance of quantum gates is often assessed using some form of randomized benchmarking. However, the existing methods become infeasible for more than approximately five qubits. Here we show how to use a simple and customizable class of circuits—randomized mirror circuits—to perform scalable, robust, and flexible randomized benchmarking of Clifford gates. We show that this technique approximately estimates the infidelity of an average many-qubit logic layer, and we use simulations of up to 225 qubits with physically realistic error rates in the range 0.1%–1% to demonstrate its scalability. We then use up to 16 physical qubits of a cloud quantum computing platform to demonstrate that our technique can reveal and quantify crosstalk errors in many-qubit circuits.

Two parties sharing entangled quantum systems can generate correlations that cannot be produced using only shared classical resources. These nonlocal correlations are a fundamental feature of quantum theory but also have practical applications. For instance, they can be used for device-independent random number generation, whose security is certified independently of the operations performed inside the devices. The amount of certifiable randomness that can be generated from some given nonlocal correlations is a key quantity of interest. Here, we derive tight analytic bounds on the maximum certifiable randomness as a function of the nonlocality as expressed using the Clauser-Horne-Shimony-Holt (CHSH) value. We show that for every CHSH value greater than the local value (2) and up to $3\sqrt{3}/2\approx 2.598$ there exist quantum correlations with that CHSH value that certify a maximal two bits of global randomness. Beyond this CHSH value the maximum certifiable randomness drops. We give a second family of Bell inequalities for CHSH values above $3\sqrt{3}/2$, and show that they certify the maximum possible randomness for the given CHSH value. Our work hence provides an achievable upper bound on the amount of randomness that can be certified for any CHSH value. We illustrate the robustness of our results, and how they could be used to improve randomness generation rates in practice, using a Werner state noise model.

While Bell nonlocality of a bipartite system is counterintuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here, we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrations that both four-photon GHZ state and generalized four-photon GHZ state significantly violate the inequality, i.e., the observed four-partite correlations resist explanations involving three-way nonlocal resources subject to local operations and common shared randomness, hence confirming that nature is boundless multipartite nonlocal.

Quantum theory predicts the existence of genuinely tripartite-entangled states, which cannot be obtained from local operations over any bipartite-entangled states and unlimited shared randomness. Some of us recently proved that this feature is a fundamental signature of quantum theory. The state $|{\mathrm{GHZ}}_3⟩=(|000⟩+|111⟩)/\sqrt{2}$ gives rise to tripartite quantum correlations that cannot be explained by any causal theory limited to bipartite nonclassical common causes of any kind (generalizing entanglement) assisted with unlimited shared randomness. Hence, any conceivable physical theory that would reproduce quantum predictions will necessarily include genuinely tripartite resources. In this Letter, we verify that such tripartite correlations are experimentally achievable. We derive a new device-independent witness capable of falsifying causal theories wherein nonclassical resources are merely bipartite. Using a high-performance photonic $|{\mathrm{GHZ}}_3⟩$ state with fidelities of $0.9741\pm 0.002$, we provide a clear experimental violation of that witness by more than 26.3 standard deviations, under the locality and fair sampling assumption. We generalize our Letter to the $|{\mathrm{GHZ}}_4⟩$ state, obtaining correlations that cannot be explained by any causal theory limited to tripartite nonclassical common causes assisted with unlimited shared randomness.

Exchange operator formalism describes many-body integrable systems using phase-space variables involving an exchange operator that acts on any pair of particles. We establish an equivalence between models described by exchange operator formalism and the complete infinite family of parent Hamiltonians describing quantum many-body models with ground states of Jastrow form. This makes it possible to identify the invariants of motion for any model in the family and establish its integrability, even in the presence of an external potential. Using this construction we establish the integrability of the long-range Lieb-Liniger model, describing bosons in a harmonic trap and subject to contact and Coulomb interactions in one dimension. We further identify a variety of models exemplifying the integrability of Hamiltonians in this family.

The third law of thermodynamics, also known as the Nernst unattainability principle, puts a fundamental bound on how close a system, whether classical or quantum, can be cooled to a temperature near to absolute zero. On the other hand, a fundamental assumption of quantum computing is to start each computation from a register of qubits initialized in a pure state, i.e., at zero temperature. These conflicting aspects, at the interface between quantum computing and thermodynamics, are often overlooked or, at best, addressed only at a single-qubit level. In this Letter, we argue how the existence of a small but finite effective temperature, which makes the initial state a mixed state, poses a real challenge to the fidelity constraints required for the scaling of quantum computers. Our theoretical results, carried out for a generic quantum circuit with $N$-qubit input states, are validated by test runs performed on a real quantum processor.

We present an effective field theory for the nonlinear fluctuating hydrodynamics of a single conserved charge with or without time-reversal symmetry, based on the Martin-Siggia-Rose formalism. Applying this formalism to fluids with only charge and multipole conservation, and with broken time-reversal symmetry, we predict infinitely many new dynamical universality classes, including some with arbitrarily large upper critical dimensions. Using large scale simulations of classical Markov chains, we find numerical evidence for a breakdown of hydrodynamics in quadrupole-conserving models with broken time-reversal symmetry in one spatial dimension. Our framework can be applied to the hydrodynamics around stationary states of open systems, broadening the applicability of previously developed ideas and methods to a wide range of systems in driven and active matter.

We study the growth of entanglement between two adjacent regions in a tripartite, one-dimensional many-body system after a quantum quench. Combining a replica trick with a space-time duality transformation, we derive an exact, universal relation between the entanglement negativity and Rényi-$1/2$ mutual information that holds at times shorter than the sizes of all subsystems. Our proof is directly applicable to any local quantum circuit, i.e., any lattice system in discrete time characterized by local interactions, irrespective of the nature of its dynamics. Our derivation indicates that such a relation can be directly extended to any system where information spreads with a finite maximal velocity.

We derive a universal, exact asymptotic form of the splitting probability for symmetric continuous jump processes, which quantifies the probability ${\pi }_{0,\underset{\_}{x}}(x_0)$ that the process crosses $x$ before 0 starting from a given position $x_0\in [0,x]$ in the regime $x_0\ll x$. This analysis provides in particular a fully explicit determination of the transmission probability ($x_0=0$), in striking contrast with the trivial prediction ${\pi }_{0,\underset{\_}{x}}(0)=0$ obtained by taking the continuous limit of the process, which reveals the importance of the microscopic properties of the dynamics. These results are illustrated with paradigmatic models of jump processes with applications to light scattering in heterogeneous media in realistic 3D slab geometries. In this context, our explicit predictions of the transmission probability, which can be directly measured experimentally, provide a quantitative characterization of the effective random process describing light scattering in the medium.

We exploit the properties of chain mapping transformations of bosonic environments to identify a finite collection of modes able to capture the characteristic features, or fingerprint, of the environment. Moreover we show that the countable infinity of residual bath modes can be replaced by a universal Markovian closure, namely, a small collection of damped modes undergoing a Lindblad-type dynamics whose parametrization is independent of the spectral density under consideration. We show that the Markovian closure provides a quadratic speedup with respect to standard chain mapping techniques and makes the memory requirement independent of the simulation time, while preserving all the information on the fingerprint modes. We illustrate the application of the Markovian closure to the computation of linear spectra but also to nonlinear spectral response, a relevant experimentally accessible many body coherence witness for which efficient numerically exact calculations in realistic environments are currently lacking.

Quantum speed limits set the maximal pace of state evolution. Two well-known limits exist for a unitary time-independent Hamiltonian: the Mandelstam-Tamm and Margolus-Levitin bounds. The former restricts the rate according to the state energy uncertainty, while the latter depends on the mean energy relative to the ground state. Here we report on an additional bound that exists for states with a bounded energy spectrum. This bound is dual to the Margolus-Levitin one in the sense that it depends on the difference between the state’s mean energy and the energy of the highest occupied eigenstate. Each of the three bounds can become the most restrictive one, depending on the spread and mean of the energy, forming three dynamical regimes which are accessible in a multilevel system. The new bound is relevant for quantum information applications, since in most of them, information is stored and manipulated in a Hilbert space with a bounded energy spectrum.

We present general results on fluctuations and spatial correlations of the coarse-grained empirical density and current of Markovian diffusion in equilibrium or nonequilibrium steady states on all timescales. We unravel a deep connection between current fluctuations and generalized time-reversal symmetry, providing new insight into time-averaged observables. We highlight the essential role of coarse graining in space from mathematical, thermodynamical, and experimental points of view. Spatial coarse graining is required to uncover salient features of currents that break detailed balance, and a thermodynamically “optimal” coarse graining ensures the most precise inference of dissipation. Defined without coarse graining, the fluctuations of empirical density and current are proven to diverge on all timescales in dimensions higher than one, which has far-reaching consequences for the central-limit regime in continuous space. We apply the results to examples of irreversible diffusion. Our findings provide new intuition about time-averaged observables and allow for a more efficient analysis of single-molecule experiments.