We analyze a readout scheme for Majorana qubits based on dispersive coupling to a resonator. We consider two variants of Majorana qubits: the Majorana transmon and the Majorana box qubit. In both cases, the qubit-resonator interaction can produce sizeable dispersive shifts in the megahertz range for reasonable system parameters, allowing for submicrosecond readout with high fidelity. For Majorana transmons, the light-matter interaction used for readout manifestly conserves Majorana parity, which leads to a notion of quantum nondemolition (QND) readout that is stronger than for conventional charge qubits. In contrast, Majorana box qubits only recover an approximately QND readout mechanism in the dispersive limit where the resonator detuning is large. We also compare dispersive readout to longitudinal readout for the Majorana box qubit. We show that the latter gives faster and higher fidelity readout for reasonable parameters, while having the additional advantage of being manifestly QND, and so may prove to be a better readout mechanism for these systems.

Here we explore which heuristic quantum algorithms for combinatorial optimization might be most practical to try out on a small fault-tolerant quantum computer. We compile circuits for several variants of quantum-accelerated simulated annealing including those using qubitization or Szegedy walks to quantize classical Markov chains and those simulating spectral-gap-amplified Hamiltonians encoding a Gibbs state. We also optimize fault-tolerant realizations of the adiabatic algorithm, quantum-enhanced population transfer, the quantum approximate optimization algorithm, and other approaches. Many of these methods are bottlenecked by calls to the same subroutines; thus, optimized circuits for those primitives should be of interest regardless of which heuristic is most effective in practice. We compile these bottlenecks for several families of optimization problems and report for how long and for what size systems one can perform these heuristics in the surface code given a range of resource budgets. Our results discourage the notion that any quantum optimization heuristic realizing only a quadratic speedup achieves an advantage over classical algorithms on modest superconducting qubit surface code processors without significant improvements in the implementation of the surface code. For instance, under quantum-favorable assumptions (e.g., that the quantum algorithm requires exactly quadratically fewer steps), our analysis suggests that quantum-accelerated simulated annealing requires roughly a day and a million physical qubits to optimize spin glasses that could be solved by classical simulated annealing in about 4 CPU-minutes.

Quantum annealing aims at solving optimization problems efficiently by preparing the ground state of an Ising spin-Hamiltonian quantum mechanically. A prerequisite of building a quantum annealer is the implementation of programmable long-range two-, three-, or multispin Ising interactions. We discuss an architecture, where the required spin interactions are implemented via two-port or in general multiport quantum Ising wires connecting the spins of interest. This quantum annealing architecture of spins connected by Ising quantum wires can be realized by exploiting the three-dimensional (3D) character of atomic platforms, including atoms in optical lattices and Rydberg tweezer arrays. The realization only requires engineering on-site terms and two-body interactions between nearest neighboring qubits. The locally coupled spin model on a 3D cubic lattice is sufficient to effectively produce arbitrary all-to-all coupled Ising Hamiltonians. We illustrate the approach for few-spin devices solving Max-Cut and prime factorization problems, and discuss the potential scaling to large atom-based systems.

Tools of quantum information theory offer a new perspective to characterize phases and phase transitions in interacting many-body quantum systems. The Hubbard model is the archetypal model of such systems and can explain rich phenomena of quantum matter with minimal assumptions. Recent measurements of entanglement-related properties of this model using ultracold atoms in optical lattices hint that entanglement could provide the key to understanding open questions of the doped Hubbard model, including the remarkable properties of the pseudogap phase. These experimental findings call for a theoretical framework and new predictions. Here we approach the doped Hubbard model in two dimensions from the perspective of quantum information theory. We study the local entropy and the total mutual information across the doping-driven Mott transition within plaquette cellular dynamical mean-field theory. We find that upon varying doping these two entanglement-related properties detect the Mott insulating phase, the strongly correlated pseudogap phase, and the metallic phase. Imprinted in the entanglement-related properties we also find the pseudogap to correlated metal first-order transition, its finite-temperature critical endpoint, and its supercritical crossovers. Through this footprint we reveal an unexpected interplay of quantum and classical correlations. Our work shows that sharp variation in the entanglement-related properties and not broken symmetry phases characterizes the onset of the pseudogap phase at finite temperature.

Here, we present an efficient quantum algorithm to generate a many-body state equivalent to Laughlin’s $\nu =1/3$ fractional quantum Hall state on a digitized quantum computer. Our algorithm only uses quantum gates acting on neighboring qubits in a quasi-one-dimensional (1D) setting and its circuit depth is linear in the number of qubits, i.e., the number of Landau orbitals in the second quantized picture. We identify correlation functions that serve as signatures of the Laughlin state and discuss how to obtain them on a quantum computer. We also discuss a generalization of the algorithm for creating quasiparticles in the Laughlin state. This paves the way for several important studies, including quantum simulation of nonequilibrium dynamics and braiding of quasiparticles in quantum Hall states.

Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. However, it remains unclear to what extent a noisy device can output reliable results in the presence of unavoidable imperfections. Here we propose a framework to characterize the performance of quantum simulators by linking the robustness of measured quantum expectation values to the spectral properties of the output observable, which in turn can be associated with its macroscopic or microscopic character. We show that, under general assumptions and on average over all states, imperfect devices are able to reproduce the dynamics of macroscopic observables accurately, while the relative error in the expectation value of microscopic observables is much larger on average. We experimentally demonstrate the universality of these features in a state-of-the-art quantum simulator and show that the predicted behavior is generic for a highly accurate device, without assuming any detailed knowledge about the nature of the imperfections.

We introduce a reliable compressive procedure to uniquely characterize any given low-rank quantum measurement using a minimal set of probe states that is based solely on data collected from the unknown measurement itself. The procedure is most compressive when the measurement constitutes pure detection outcomes, requiring only an informationally complete number of probe states that scales linearly with the system dimension. We argue and provide numerical evidence showing that the minimal number of probe states needed is even generally below the numbers known in the closely related classical phase-retrieval problem because of the quantum constraint. We also present affirmative results with polarization experiments that illustrate significant compressive behaviors for both two- and four-qubit detectors just by using random product probe states.

Quantum technologies are built on the power of coherent superposition. Atomic coherence is typically generated from optical coherence, most often via Rabi oscillations. However, canonical coherent states of light create imperfect resources; a fully quantized description of “$\pi /2$ pulses” shows that the atomic superpositions generated remain entangled with the light. We show that there are quantum states of light that generate coherent atomic states perfectly, with no residual atom-field entanglement. These states can be found for arbitrarily short times and approach slightly-number-squeezed $\pi /2$ pulses in the limit of large intensities; similar ideal states can be found for any $(2k+1)\pi /2$ pulses, requiring more number squeezing with increasing $k$. Moreover, these states can be repeatedly used as “quantum catalysts” to successfully generate coherent atomic states with high probability. From this perspective we identify states that are “more coherent” than coherent states.

We develop a general formalism, based on the Wigner function representation of continuous-variable quantum states, to describe the action of an arbitrary conditional operation on a multimode Gaussian state. We apply this formalism to several examples, thus showing its potential as an elegant analytical tool for simulating quantum optics experiments. Furthermore, we also use it to prove that Einstein-Podolsky-Rosen steering is a necessary requirement to remotely prepare a Wigner-negative state.

Variational quantum algorithms are believed to be promising for solving computationally hard problems on noisy intermediate-scale quantum (NISQ) systems. Gaining computational power from these algorithms critically relies on the mitigation of errors during their execution, which for coherence-limited operations is achievable by reducing the gate count. Here, we demonstrate an improvement of up to a factor of 3 in algorithmic performance for the quantum approximate optimization algorithm (QAOA) as measured by the success probability, by implementing a continuous hardware-efficient gate set using superconducting quantum circuits. This gate set allows us to perform the phase separation step in QAOA with a single physical gate for each pair of qubits instead of decomposing it into two $\mathrm{C}Z$ gates and single-qubit gates. With this reduced number of physical gates, which scales with the number of layers employed in the algorithm, we experimentally investigate the circuit-depth-dependent performance of QAOA applied to exact-cover problem instances mapped onto three and seven qubits, using up to a total of 399 operations and up to nine layers. Our results demonstrate that the use of continuous gate sets may be a key component in extending the impact of near-term quantum computers.

In recent years, arrays of atomic ions in a linear radio-frequency trap have proven to be a particularly successful platform for quantum simulation. However, a wide range of quantum models and phenomena have, so far, remained beyond the reach of such simulators. In this work we introduce a technique that can substantially extend this reach using an external field gradient along the ion chain and a global, uniform driving field. The technique can be used to generate both static and time-varying synthetic gauge fields in a linear chain of trapped ions, and enables continuous simulation of a variety of coupling geometries and topologies, including periodic boundary conditions and high-dimensional Hamiltonians. We describe the technique, derive the corresponding effective Hamiltonian, propose a number of variations, and discuss the possibility of scaling to quantum-advantage-sized simulators. Additionally, we suggest several possible implementations and briefly examine two: the Aharonov-Bohm ring and the frustrated triangular ladder.

We discuss monitoring the time evolution of an analog quantum simulator via a quantum nondemolition (QND) coupling to an auxiliary “clock” qubit. The QND variable of interest is the “energy” of the quantum many-body system, represented by the Hamiltonian of the quantum simulator. We describe a physical implementation of the underlying QND Hamiltonian for Rydberg atoms trapped in tweezer arrays using laser-dressing schemes for a broad class of spin models. As an application, we discuss a quantum protocol for measuring the spectral form factor of quantum many-body systems, where the aim is to identify signatures of ergodic versus nonergodic dynamics, which we illustrate for disordered one-dimensional Heisenberg and Floquet spin models on Rydberg platforms. Our results also provide the physical ingredients for running quantum phase estimation protocols for measurement of energies and preparation of energy eigenstates for a specified spectral resolution on an analog quantum simulator.

Long-distance entanglement distribution is a vital capability for quantum technologies. An outstanding practical milestone towards this aim is the identification of a suitable matter-photon interface that possesses, simultaneously, long coherence lifetimes and efficient telecommunication-band optical access. In this work we report upon the $T$ center, a silicon defect with long-lived spins and spin-selective bound exciton optical transitions at 1326 nm in the telecommunications $O$-band. In this first study of $T$ centers in ${}^{28}\mathrm{Si}$, we present the temperature dependence of the zero-phonon line, report ensemble zero-phonon linewidths as narrow as 33(2) MHz, and elucidate the excited state spectrum of the bound exciton. Magnetophotoluminescence, in conjunction with magnetic resonance, is used to observe twelve distinct orientational subsets of the $T$ center, which are independently addressable due to the anisotropic $g$ factor of the bound exciton’s hole spin. Here we show that the $T$ center in ${}^{28}\mathrm{Si}$ offers electron and nuclear spin lifetimes beyond a millisecond and second, respectively, as well as optical lifetimes of 0.94(1) $\mu \mathrm{s}$ and a Debye-Waller factor of 0.23(1). This work represents a significant step towards coherent photonic interconnects between long-lived silicon spins, spin-entangled telecom single-photon emitters, and spin-dependent silicon-integrated photonic nonlinearities for future global quantum technologies.

The standard approach to deriving fluctuation theorems fails to capture the effect of quantum correlation and coherence in the initial state of the system. Here, we overcome this difficulty and derive the heat-exchange-fluctuation theorem in the full quantum regime by showing that the energy exchange between two locally thermal states in the presence of initial quantum correlations is faithfully captured by a quasiprobability distribution. Its negativities, being associated with proofs of contextuality, are proxies of nonclassicality. We discuss the thermodynamic interpretation of negative probabilities and provide heat-flow inequalities that can only be violated in their presence. Remarkably, testing these fully quantum inequalities, at an arbitrary dimension, is no more difficult than testing traditional fluctuation theorems. We test these results on data collected in a recent experiment studying the heat transfer between two qubits and give examples for the capability of witnessing negative probabilities at higher dimensions.

Information exchange requires a measurement of physical states. Because quantum measurements enable accuracy beyond the classical shot-noise limit, they are successfully used to develop measurement tools and applications. In particular, quantum-measurement-enhanced strategies are used for the discrimination of nonorthogonal coherent states. The efficient discrimination of these states is crucial for optical communication networks, that are now approaching the classical limits of the underlying physical systems. However, quantum-enhanced discrimination strategies demonstrated to date are based on legacy communication protocols designed for classical measurements and thus provide only a limited advantage. In our work, we use photon detection times readily available in quantum measurement, but not accessible by classical means. We measure and use these times to maximize our knowledge about faint nonorthogonal coherent states. We employ communication strategies designed to benefit most from this knowledge. This holistic approach in our experiment has resulted in the record low error rates in discrimination of multiple faint nonorthogonal coherent states carrying energy corresponding to just one photon per bit of transmitted information. We demonstrate successful discrimination of large alphabets of optical states ($4\le M\le 16$) beyond the ideal classical shot-noise limit, showing the scalability of quantum-measurement-enabled communication. This experimental work explores unforeseen advantages of quantum measurement on one hand, and may help address the capacity crunch in modern optical networks caused by the exponential growth of data exchange on the other.

We develop and characterize a symmetry-protected superconducting qubit that offers simultaneous exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise. The qubit consists of a Cooper-pair box (CPB) shunted by a superinductor, forming a superconducting loop. Provided the offset charge on the CPB island is an odd number of electrons, the qubit potential corresponds to that of a $\cos \left(\varphi /2\right)$ Josephson element, preserving the parity of fluxons in the loop via Aharonov-Casher interference. In this regime, the logical-state wavefunctions reside in disjoint regions of Hilbert space, thereby ensuring protection against energy decay. By switching the protection on, we observe a tenfold increase of the decay time, reaching up to $100\mu \mathrm{s}$. Though the qubit is sensitive to charge noise, the sensitivity is much reduced in comparison with the charge qubit, and the charge-noise-induced dephasing time of the current device exceeds $1\mu \mathrm{s}$. Implementation of full dephasing protection can be achieved in the next-generation devices by combining several $\cos (\varphi /2)$ Josephson elements in a small array.

Recent progress in generating entangled spin states of neutral atoms provides opportunities to advance quantum sensing technology. In particular, entanglement can enhance the performance of accelerometers and gravimeters based on light-pulse atom interferometry. We study the effects of error sources that may limit the sensitivity of such devices, including errors in the preparation of the initial entangled state, imperfections in the laser pulses, momentum spread of the initial atomic wave packet, measurement errors, spontaneous emission, and atom loss. We determine that, for each of these errors, the expectation value of the parity operator $\mathrm{\Pi }$ has the general form $\overline{⟨\mathrm{\Pi }⟩}={\mathrm{\Pi }}_0\cos (N\varphi )$, where $\varphi$ is the interferometer phase and $N$ is the number of atoms prepared in the maximally entangled Greenberger-Horne-Zeilinger state. Correspondingly, the minimum phase uncertainty has the general form $\mathrm{\Delta }\varphi =({\mathrm{\Pi }}_{0}N{)}^{-1}$. Each error manifests itself through a reduction of the amplitude of the parity oscillations, ${\mathrm{\Pi }}_0$, below the ideal value of ${\mathrm{\Pi }}_0=1$. For each of the errors, we derive an analytic result that expresses the dependence of ${\mathrm{\Pi }}_0$ on error parameter(s) and $N$, and also obtain a simplified approximate expression valid when the error is small. Based on the performed analysis, entanglement-enhanced atom interferometry appears to be feasible with existing experimental capabilities.

Noise that exhibits significant temporal and spatial correlations across multiple qubits can be especially harmful to both fault-tolerant quantum computation and quantum-enhanced metrology. However, a complete spectral characterization of the noise environment of even a two-qubit system has not been reported thus far. We propose and experimentally demonstrate a protocol for two-qubit dephasing noise spectroscopy based on continuous-control modulation. By combining ideas from spin-locking relaxometry with a statistically motivated robust estimation approach, our protocol allows for the simultaneous reconstruction of all the single-qubit and two-qubit cross-correlation spectra, including access to their distinctive nonclassical features. Only single-qubit control manipulations and state-tomography measurements are employed, with no need for entangled-state preparation or readout of two-qubit observables. While our experimental demonstration uses two superconducting qubits coupled to a shared, colored engineered noise source, our methodology is portable to a variety of dephasing-dominated qubit architectures. By pushing quantum noise spectroscopy beyond the single-qubit setting, our work heralds the characterization of spatiotemporal correlations in both engineered and naturally occurring noise environments.

Matrix product states form a powerful ansatz for the simulation of a wide range of one-dimensional quantum systems that are in a pure state. Their power stems from the fact that they faithfully approximate states with a low amount of entanglement, the “area law.” However, in order to accurately capture the physics of realistic systems, one generally needs to apply a mixed-state description. In this work, we establish the mixed-state analog of this characterization. We show that one-dimensional mixed states with a low amount of entanglement, quantified by the entanglement of purification, can be efficiently approximated by matrix product density operators.

The Lieb-Robinson (LR) bound rigorously shows that in quantum systems with short-range interactions, the maximum amount of information that travels beyond an effective “light cone” decays exponentially with distance from the light-cone front, which expands at finite velocity. Despite being a fundamental result, existing bounds are often extremely loose, limiting their applications. We introduce a method that dramatically and qualitatively improves LR bounds in models with finite-range interactions. Most prominently, in systems with a large local Hilbert space dimension $D$, our method gives a LR velocity that grows much slower than previous bounds with $D$ as $D\to \mathrm{\infty }$. For example, in the Heisenberg model with spin $S$, we find $v\le \mathrm{const}$. compared to the previous $v\propto S$, which diverges at large $S$, and in multiorbital Hubbard models with $N$ orbitals, we find $v\propto \sqrt{N}$ instead of previous $v\propto N$, and similarly in the $N$-state truncated Bose-Hubbard model and Wen’s quantum rotor model. Our bounds also scale qualitatively better in some systems when the spatial dimension or certain model parameters become large, for example in the $d$-dimensional quantum Ising model and perturbed toric code models. Even in spin-1/2 Ising and Fermi-Hubbard models, our method improves the LR velocity by an order of magnitude with typical model parameters, and significantly improves the LR bound at large distance and early time.