We present general guidelines for finding solid-state systems that could serve as coherent electron-spin–photon interfaces even at relatively high temperatures, where phonons are abundant but cooling is easier, and show that transition-metal ions in various crystals could comply with these guidelines. As an illustrative example, we focus on divalent nickel ions in magnesium oxide. We perform electron-spin-resonance spectroscopy and polarization-sensitive magneto-optical fluorescence spectroscopy of a dense ensemble of these ions and find that (i) the ground-state electron spin stays coherent at liquid-helium temperatures for several microseconds and (ii) there exist energetically well-isolated excited states that can couple to two ground-state spin sublevels via optical transitions of orthogonal polarizations. The latter implies that fast coherent optical control over the electron spin is possible. We then propose schemes for optical initialization and control of the ground-state electron spin using polarized optical pulses, as well as two schemes for implementing a noise-free broadband quantum optical memory at near-telecom wavelengths in this material system.

We develop a theory of symmetry in open quantum systems. Using the operator-state mapping, we characterize symmetry of Liouvillian superoperators for the open quantum dynamics by symmetry of operators in the double Hilbert space and apply the 38-fold internal-symmetry classification of non-Hermitian operators. We find rich symmetry classification due to the interplay between symmetry in the corresponding closed quantum systems and symmetry inherent in the construction of the Liouvillian superoperators. As an illustrative example of open quantum bosonic systems, we study symmetry classes of dissipative quantum spin models. For open quantum fermionic systems, we develop the ${\mathbb{Z}}_4$ classification of fermion parity symmetry and antiunitary symmetry in the double Hilbert space, which contrasts with the ${\mathbb{Z}}_8$ classification in closed quantum systems. We also develop the symmetry classification of open quantum fermionic many-body systems—a dissipative generalization of the Sachdev-Ye-Kitaev (SYK) model described by the Lindblad master equation. We establish the periodic tables of the SYK Lindbladians and elucidate the difference from the SYK Hamiltonians. Furthermore, from extensive numerical calculations, we study its complex-spectral statistics and demonstrate dissipative quantum chaos enriched by symmetry.

Gate-based quantum computers typically encode and process information in two-dimensional units called qubits. Using $d$-dimensional qudits instead may offer intrinsic advantages, including more efficient circuit synthesis, problem-tailored encodings and embedded error correction. In this work, we design a superconducting qudit-based quantum processor wherein the logical space of transmon qubits is extended to higher-excited levels. We propose a universal gate set featuring a two-qudit cross-resonance entangling gate, for which we predict fidelities beyond $99\mathrm{\%}$ in the $d=4$ case of ququarts with realistic experimental parameters. Furthermore, we present a decomposition routine that compiles general qudit unitaries into these elementary gates, requiring fewer entangling gates than qubit alternatives. As proof-of-concept applications, we numerically demonstrate the synthesis of $\mathrm{SU}(16)$ gates for noisy quantum hardware and an embedded error-correction sequence that encodes a qubit memory in a transmon ququart to protect against pure dephasing noise. We conclude that universal qudit control—a valuable extension to the operational toolbox of superconducting quantum information processing—is within reach of current transmon-based architectures and has applications to near-term and long-term hardware.

Quadratic light-matter interactions are nonlinear couplings such that quantum emitters interact with photonic or phononic modes exclusively via the exchange of excitation pairs. Implementable with atomic and solid-state systems, these couplings lead to a plethora of phenomena that have been characterized in the context of cavity QED, where quantum emitters interact with localized bosonic modes. Here, we explore quadratic interactions in a waveguide QED setting, where quantum emitters interact with propagating fields confined in a one-dimensional environment. We develop a general scattering theory under the Markov approximation and discuss paradigmatic examples for spontaneous emission and scattering of biphoton states. Our analytical and semianalytical results unveil fundamental differences with respect to conventional waveguide QED systems, such as the spontaneous emission frequency-entangled photon pairs or the full transparency of the emitter to single-photon inputs. This unlocks new opportunities in quantum information processing with propagating photons. As a striking example, we show that a single quadratically coupled emitter can implement a two-photon logic gate with unit fidelity, circumventing a no-go theorem derived for conventional waveguide-QED interactions.

In a fast-scrambling many-body quantum system, information is spread and entanglement is built up on a time scale that grows logarithmically with the system size. This is of fundamental interest in understanding the dynamics of many-body systems, as well as in efficiently producing entangled resource states and error-correcting codes. In this work, we identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity. In particular, we show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse around a critical point between two clearly defined regimes of different dynamical behavior. We study this transition analytically in a related long-range Brownian-circuit model and show how the transition can be mapped onto the statistical mechanics of a long-range Ising model in a particular region of parameter space. This mapping predicts mean-field critical exponents $\nu =-1/(1+s_c)$, which are consistent with the critical exponents extracted from Clifford-circuit numerics. In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic sparse circuits that can be realized in experiments with neutral-atom arrays.

Flux-biased loops including one or more Josephson junctions are ubiquitous elements in quantum information experiments based on superconducting circuits. These quantum circuits can be tuned to implement a variety of Hamiltonians, with applications ranging from decoherence-protected qubits to quantum limited converters and amplifiers. The extrema of the Hamiltonian of these circuits are of special interest because they govern their low-energy dynamics. However, the theory of superconducting quantum circuits so far lacks a systematic method to find these extrema and compute the series expansion of the Hamiltonian in their vicinity for an arbitrary nonlinear superconducting circuit. We present such a method, which can aid the synthesis of new functionalities in quantum devices.

Strongly coupled gauge theories far from equilibrium may exhibit unique features that could illuminate the physics of the early universe and of hadron and ion colliders. Studying real-time phenomena has proven challenging with classical-simulation methods, but is a natural application of quantum simulation. To demonstrate this prospect, we quantum compute nonequal-time correlation functions and perform entanglement tomography of nonequilibrium states of a simple lattice gauge theory, the Schwinger model, using a trapped-ion quantum computer by IonQ Inc. As an ideal target for near-term devices, a recently predicted [Zache et al., Phys. Rev. Lett. 122, 050403 (2019)] dynamical quantum phase transition in this model is studied by preparing, quenching, and tracking the subsequent nonequilibrium dynamics in three ways: (i) overlap echos signaling dynamical transitions, (ii) nonequal-time correlation functions with an underlying topological nature, and (iii) the entanglement structure of nonequilibrium states, including entanglement Hamiltonians. These results constitute the first observation of a dynamical quantum phase transition in a lattice gauge theory on a quantum computer, and are a first step toward investigating topological phenomena in nuclear and high-energy physics using quantum technologies.

Quantum thermalization in a many-body system is defined by the approach of local subsystems toward a universal form, describable as an ensemble of quantum states wherein observables acquire thermal expectation values. Recently, it has been demonstrated that the distribution of these quantum states can also exhibit universal statistics, upon associating each state with the outcome of a local projective measurement of the complementary subsystem. Specifically, this collection of pure quantum states—called the projected ensemble—can, under certain conditions, mimic the behavior of a maximally entropic uniformly random ensemble, i.e., form a quantum state design, representing a “deeper” form of quantum thermalization. In this work, we investigate the dynamical process underlying this novel emergent universality. Leveraging a space-time duality mapping for one-dimensional quantum circuits, we argue that the physics of dynamical purification, which arises in the context of monitored quantum systems, constrains the approach of the projected ensemble toward the uniform distribution. We prove that the absence of dynamical purification in the space-time dual dynamics (a condition realized in dual-unitary quantum circuits with appropriate initial states and final measurement bases) generically yields exact state designs for all moments $k$ at the same time, extending previous rigorous results [Ho and Choi, Phys. Rev. Lett. 128, 060601 (2022)]. Conversely, we show that, departing from these conditions, dynamical purification can lead to a separation of time scales between the formation of a quantum state design for moment $k=1$ (regular thermalization) and for high moments $k\gg 1$ (deep thermalization). Our results suggest that the projected ensemble can probe nuanced features of quantum dynamics inaccessible to regular thermalization, such as quantum information scrambling.

When two initially thermal many-body systems start to interact strongly, their transient states quickly become non-Gibbsian, even if the systems eventually equilibrate. To see beyond this apparent lack of structure during the transient regime, we use a refined notion of thermality, which we call g-local. A system is g-locally thermal if the states of all its small subsystems are marginals of global thermal states. We numerically demonstrate for two harmonic lattices that whenever the total system equilibrates in the long run, each lattice remains g-locally thermal at all times, including the transient regime. This is true even when the lattices have long-range interactions within them. In all cases, we find that the equilibrium is described by the generalized Gibbs ensemble, with three-dimensional lattices requiring special treatment due to their extended set of conserved charges. We compare our findings with the well-known two-temperature model. While its standard form is not valid beyond weak coupling, we show that at strong coupling it can be partially salvaged by adopting the concept of a g-local temperature.

Quantum simulation is one of the most promising scientific applications of quantum computers. Due to decoherence and noise in current devices, it is however challenging to perform digital quantum simulation in a regime that is intractable with classical computers. In this work, we propose an experimental protocol for probing dynamics and equilibrium properties on near-term digital quantum computers. As a key ingredient of our work, we show that it is possible to study thermalization even with a relatively coarse Trotter decomposition of the Hamiltonian evolution of interest. Even though the step size is too large to permit a rigorous bound on the Trotter error, we observe that the system prethermalizes in accordance with previous results for Floquet systems. The dynamics closely resemble the thermalization of the model underlying the Trotterization up to long times. We make our approach resilient to noise by developing an error mitigation scheme based on measurement and rescaling of survival probabilities, which is applicable to time-evolution problems in general. We demonstrate the effectiveness of the entire protocol by applying it to the two-dimensional $XY$ model and we numerically verify its performance with realistic noise parameters for superconducting quantum devices. Our proposal thus provides a route to achieving quantum advantage for relevant problems in condensed-matter physics.

Simulation of continuous-time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision but it inevitably leads to increased computational efforts. This is particularly costly for today’s noisy intermediate-scale quantum computers, where notable gate imperfections limit the circuit depth that can be executed at a given accuracy. Classical adaptive solvers are well developed to save numerical computation times. However, it remains an outstanding challenge to make optimal usage of the available quantum resources by means of adaptive time steps. Here, we introduce a quantum algorithm to solve this problem, providing a controlled solution of the quantum many-body dynamics of local observables. The key conceptual element of our algorithm is a feedback loop that self-corrects the simulation errors by adapting time steps, thereby significantly outperforming conventional Trotter schemes on a fundamental level and reducing the circuit depth. It even allows for a controlled asymptotic long-time error, where the usual Trotterized dynamics faces difficulties. Another key advantage of our quantum algorithm is that any desired conservation law can be included in the self-correcting feedback loop, which has a potentially wide range of applicability. We demonstrate the capabilities by enforcing gauge invariance, which is crucial for a faithful and long-sought-after quantum simulation of lattice gauge theories. Our algorithm can potentially be useful on a more general level whenever time discretization is involved also concerning, e.g., numerical approaches based on time-evolving block-decimation methods.

We propose a general framework for using local measurements, local unitaries, and nonlocal classical communication to construct quantum channels, which can efficiently prepare mixed states with long-range quantum order or quantum criticality. As an illustration, symmetry-protected topological phases can be universally converted into mixed states with long-range entanglement, which can undergo phase transitions with quantum critical correlations of local operators and a logarithmic scaling of the entanglement negativity, despite coexisting with volume-law entropy. Within the same framework, we present two applications using fermion occupation-number measurement to convert (i) spinful free fermions in one dimension into a quantum critical mixed state with enhanced algebraic correlations between spins and (ii) Chern insulators into a mixed state with critical quantum correlations in the bulk. The latter is an example where mixed-state quantum criticality can emerge from a gapped state of matter in constant depth using local quantum operations and nonlocal classical communication.

Decoherence inevitably happens when a quantum state is exposed to its environment, which can affect quantum critical points (QCPs) in a nontrivial way. As was pointed out in the recent literature on $(1+1)d$ conformal field theory (CFT) [Garratt et al. Measurements conspire nonlocally to restructure critical quantum states, arXiv:2207.09476 (2022)], the effect of weak measurement can be mathematically mapped to the problem of boundary CFT. In this work, we focus on the $(2+1)d$ QCPs, whose boundary and defect effects have attracted enormous theoretical and numerical interests very recently. We focus on decoherence caused by weak measurements with and without postselecting the measurement outcomes. Our main results are as follows: (1) for an $\mathrm{O}(N)$ Wilson-Fisher QCP under weak measurement with postselection, an observer would, in general, observe two different types of boundary and defect criticality with very different behaviors from the well-known Wilson-Fisher fixed points; in particular, it is possible to observe the recently proposed exotic “extraordinary-log” correlation. (2) An extra quantum phase transition can be driven by decoherence, if we consider quantities nonlinear with the decohered density matrix, such as the Renyi entropy. We demonstrate the connection between this transition to the information-theoretic transition driven by an error in the toric code model. (3) When there is no postselection, though correlation functions between local operators remain the same as the undecohered pure state, nonlocal operators such as the “disorder operator” would have qualitatively distinct behaviors; and we also show that the decoherence can lead to confinement.

We show that the effect of a Gaussian bosonic environment linearly coupled to a quantum system can be simulated by a stochastic Lindblad master equation characterized by a set of ancillary bosonic modes initially at zero temperature and classical stochastic fields. We test the method for Ohmic environments with exponential and polynomial cut-offs against, respectively, the hierarchical equations of motion and the deterministic pseudomode model, with respect to which the number of ancillary quantum degrees of freedom is reduced. For a subset of rational spectral densities, all parameters are explicitly specified without the need for any fitting procedure, thereby simplifying the modeling strategy. Interestingly, the classical fields in this decomposition must sometimes be imaginary valued, which can have counterintuitive effects on the system properties, which we demonstrate by showing that they can decrease the entropy of the system, in contrast to real-valued fields.

Non-Hermitian band theory distinguishes between line gaps and point gaps. While point gaps can give rise to intrinsic non-Hermitian band topology without Hermitian counterparts, line-gapped systems can always be adiabatically deformed to a Hermitian limit. Here, we show that line-gap topology and point-gap topology can be intricately connected: topological line-gapped systems in $d$ dimensions induce nontrivial point-gap topology on their $(d-1)$-dimensional boundaries when suitable internal and spatial symmetries are present. Since line-gapped systems essentially realize Hermitian topological phases, this establishes a correspondence between Hermitian bulk topology and intrinsic non-Hermitian boundary topology. For the correspondence to hold, no non-Hermitian perturbations are required in the bulk itself, so that the bulk can be purely Hermitian. Concomitantly, the presence of non-Hermitian perturbations in the bulk does not affect any results as long as they do not close the bulk line gap. On the other hand, non-Hermitian perturbations are essential on the boundary to open a point gap. The non-Hermitian boundary topology then further leads to higher-order skin modes, as well as chiral and helical hinge modes, that are protected by point gaps and hence unique to non-Hermitian systems. We identify all the internal symmetry classes where bulk line-gap topology induces boundary point-gap topology as long as an additional spatial symmetry is present and establish the correspondence between their topological invariants. There also exist some symmetry classes where the Hermitian edge states remain stable, in the sense that even a point gap cannot open on the boundary.

Fermion-to-qubit mappings are used to represent fermionic modes on quantum computers, an essential first step in many quantum algorithms for electronic structure calculations. In this work, we present a formalism to design flexible fermion-to-qubit mappings from ternary trees. We intuitively discuss the connection between the structure of the generating trees and certain properties of the resulting mapping, such as the Pauli weight and the delocalization of mode occupation. Moreover, we introduce a recipe that guarantees that Fock basis states are mapped to computational basis states in qubit space, a desirable property for many applications in quantum computing. Based on this formalism, we introduce the Bonsai algorithm, which takes as input the potentially limited topology of the qubit connectivity of a quantum device and returns a tailored fermion-to-qubit mapping that reduces the swap overhead compared to other paradigmatic mappings. We illustrate the algorithm by producing mappings for the heavy-hexagon topology widely used in IBM quantum computers. The resulting mappings have a favorable Pauli-weight scaling $\mathcal{O}(\sqrt{N})$ on this connectivity while ensuring that no swap gates are necessary for single-excitation operations.

Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in deterministic circuits with similar applications, we construct classes of nonrandom unitary Clifford circuits by imposing translation invariance in both time and space. Further imposing dual unitarity, our circuits effectively become crystalline spacetime lattices whose vertices are swap or iswap two-qubit gates and whose edges may contain one-qubit gates. One can then require invariance under (subgroups of) the crystal’s point group. Working on the square and kagome lattices, we use the formalism of Clifford quantum cellular automata to describe operator spreading, entanglement generation, and recurrence times of these circuits. A full classification on the square lattice reveals, of particular interest, a “nonfractal good scrambling class” with dense operator spreading that generates codes with linear contiguous code distance and high performance under erasure errors at the end of the circuit. We also break unitarity by adding spacetime translation-invariant measurements and find a class of such circuits with fractal dynamics.

Three-level $\mathrm{\Lambda }$ systems appear in various quantum information processing platforms. In several control schemes, the excited level serves as an auxiliary state for implementing gate operations between the lower qubit states. However, extra excited levels give rise to unwanted transitions that cause leakage and other errors, degrading the gate fidelity. We focus on a coherent-population-trapping scheme for gates and design protocols that reduce the effects of the unwanted off-resonant couplings and improve the gate performance up to several orders of magnitude. For a particular setup of unwanted couplings, we find an exact solution, which leads to error-free gate operations via only a static detuning modification. In the general case, we improve gate operations by adding corrective modulations to the pulses, thereby generalizing the derivative removal by adiabatic gates protocol to $\mathrm{\Lambda }$ systems. Our techniques enable fast and high-fidelity gates and apply to a wide range of optically driven platforms, such as quantum dots, color centers, and trapped ions.

Trapped atomic ion qubits or effective spins are a powerful quantum platform for quantum computation and simulation, featuring densely connected and efficiently programmable interactions between the spins. While native interactions between trapped-ion spins are typically pairwise, many quantum algorithms and quantum spin models naturally feature couplings between triplets, quartets, or higher orders of spins. Here, we formulate and analyze a mechanism that extends the standard Mølmer-Sørensen pairwise entangling gate and generates a controllable and programmable coupling between $N$ spins of trapped ions. We show that spin-dependent optical parametric drives applied at twice the motional frequency generate a coordinate transformation of the collective ion motion in phase space, rendering displacement forces that are nonlinear in the spin operators. We formulate a simple framework that enables a systematic and faithful construction of high-order spin Hamiltonians and gates, including the effect of multiple modes of motion, and characterize the performance of such operations under realistic conditions.

Single flux quantum (SFQ) digital logic has been proposed for the scalable control of next-generation superconducting-qubit arrays. In the initial implementation, SFQ-based gate fidelity was limited by quasiparticle (QP) poisoning induced by the dissipative on-chip SFQ driver circuit. In this work, we introduce a multichip-module architecture to suppress phonon-mediated QP poisoning. Here, the SFQ elements and qubits are fabricated on separate chips that are joined with $\mathrm{In}$-bump bonds. We use interleaved randomized benchmarking to characterize the fidelity of SFQ-based gates and we demonstrate an error per Clifford gate of 1.2(1)%, an order-of-magnitude reduction over the gate error achieved in the initial realization of SFQ-based qubit control. We use purity benchmarking to quantify the contribution of incoherent error at 0.96(2)%; we attribute this error to photon-mediated QP poisoning mediated by the resonant millimeter-wave antenna modes of the qubit and SFQ-qubit coupler. We anticipate that a straightforward redesign of the SFQ driver circuit to limit the bandwidth of the SFQ pulses will eliminate this source of infidelity, allowing SFQ-based gates with error approaching approximate known theoretical limits, of order 0.1% for resonant sequences and 0.01% for more complex pulse sequences involving variable pulse-to-pulse separation.