Modulating the frequency of a harmonic oscillator at nearly twice its natural frequency leads to amplification and self-oscillation. Above the oscillation threshold and in the presence of a nonlinearity, the field settles into a coherent oscillating state with a well-defined phase of either 0 or $\pi$. We demonstrate a quantum parametric oscillator operating at microwave frequencies and drive it into oscillating states containing only a few photons. The small number of photons present in the system and the coherent nature of the nonlinearity prevent the environment from learning the randomly chosen phase of the oscillator. This result allows the system to oscillate briefly in a quantum superposition of both phases at once, effectively generating a nonclassical Schrödinger’s cat state. We characterize the dynamics and states of the system by analyzing the output field emitted by the oscillator and implementing quantum state tomography suited for nonlinear resonators. By demonstrating a quantum parametric oscillator and the requisite techniques for characterizing its quantum state, we set the groundwork for new schemes of quantum and classical information processing and extend the reach of these ubiquitous devices deep into the quantum regime.

With the help of quantum key distribution (QKD), two distant peers are able to share information-theoretical secure key bits. Increasing the key rate is ultimately significant for the applications of QKD in the lossy channel. However, it has been proven that there is a fundamental rate-distance limit, called the linear bound, which restricts the performance of all existing repeaterless protocols and realizations. Surprisingly, a recently proposed protocol, called twin-field (TF) QKD, can beat the linear bound with no need for quantum repeaters. Here, we present one of the first implementations of the TF-QKD protocol and demonstrate its advantage of beating the linear bound at a channel distance of 300 km. In our experiment, a modified TF-QKD protocol that does not assume phase postselection is considered, and thus a higher key rate than the original one is expected. After controlling the phase evolution of the twin fields traveling through hundreds of kilometers of optical fibers, the implemented system achieves high-visibility single-photon interference and allows stable and high-rate measurement-device-independent QKD. Our experimental demonstration and results confirm the feasibility of the TF-QKD protocol and its prominent superiority in long-distance key distribution services.

Gates in error-prone quantum information processors are often modeled using sets of one- and two-qubit process matrices, the standard model of quantum errors. However, the results of quantum circuits on real processors often depend on additional external “context” variables. Such contexts may include the state of a spectator qubit, the time of data collection, or the temperature of control electronics. In this article, we demonstrate a suite of simple, widely applicable, and statistically rigorous methods for detecting context dependence in quantum-circuit experiments. They can be used on any data that comprise two or more “pools” of measurement results obtained by repeating the same set of quantum circuits in different contexts. These tools may be integrated seamlessly into standard quantum device characterization techniques, like randomized benchmarking or tomography. We experimentally demonstrate these methods by detecting and quantifying crosstalk and drift on the publicly accessible 16-qubit ibmqx3.

The compass model on a square lattice provides a natural template for building subsystem stabilizer codes. The surface code and the Bacon-Shor code represent two extremes of possible codes depending on how many gauge qubits are fixed. We explore threshold behavior in this broad class of local codes by trading locality for asymmetry and gauge degrees of freedom for stabilizer syndrome information. We analyze these codes with asymmetric and spatially inhomogeneous Pauli noise in the code capacity and phenomenological models. In these idealized settings, we observe considerably higher thresholds against asymmetric noise. At the circuit level, these codes inherit the bare-ancilla fault tolerance of the Bacon-Shor code.

The spreading of entanglement in out-of-equilibrium quantum systems is currently at the center of intense interdisciplinary research efforts involving communities with interests ranging from holography to quantum information. Here we provide a constructive and mathematically rigorous method to compute the entanglement dynamics in a class of “maximally chaotic,” periodically driven, quantum spin chains. Specifically, we consider the so-called “self-dual” kicked Ising chains initialized in a class of separable states and devise a method to compute exactly the time evolution of the entanglement entropies of finite blocks of spins in the thermodynamic limit. Remarkably, these exact results are obtained despite the maximally chaotic models considered: Their spectral correlations are described by the circular orthogonal ensemble of random matrices on all scales. Our results saturate the so-called “minimal cut” bound and are in agreement with those found in the contexts of random unitary circuits with infinite-dimensional local Hilbert space and conformal field theory. In particular, they agree with the expectations from both the quasiparticle picture, which accounts for the entanglement spreading in integrable models, and the minimal membrane picture, recently proposed to describe the entanglement growth in generic systems. Based on a novel “duality-based” numerical method, we argue that our results describe the entanglement spreading from any product state at the leading order in time when the model is nonintegrable.

Many experiments that interrogate fundamental theories require detectors whose sensitivities are limited by the laws of quantum mechanics. In cavity-based searches for axionic dark matter, vacuum fluctuations in the two quadratures of the cavity electromagnetic field limit the sensitivity to an axion-induced field. In an apparatus designed to partially mimic existing axion detectors, we demonstrate experimentally that such quantum limits can be overcome through the use of squeezed states. By preparing a microwave cavity in a squeezed state and measuring just the squeezed quadrature, we enhance the spectral scan rate by a factor of $2.12\pm 0.08$. This enhancement is in excellent quantitative agreement with a theoretical model accounting for both imperfect squeezing and measurement.

We report the first complete characterization of single-qubit and two-qubit gate fidelities in silicon-based spin qubits, including cross talk and error correlations between the two qubits. To do so, we use a combination of standard randomized benchmarking and a recently introduced method called character randomized benchmarking, which allows for more reliable estimates of the two-qubit fidelity in this system, here giving a 92% fidelity estimate for the controlled-$Z$ gate. Interestingly, with character randomized benchmarking, the two-qubit gate fidelity can be obtained by studying the additional decay induced by interleaving the two-qubit gate in a reference sequence of single-qubit gates only. This work sets the stage for further improvements in all the relevant gate fidelities in silicon spin qubits beyond the error threshold for fault-tolerant quantum computation.

To isolate individual neutral atoms in microtraps, experimenters have long harnessed molecular photoassociation to make atom distributions sub-Poissonian. While a variety of approaches have used a combination of attractive (red-detuned) and repulsive (blue-detuned) molecular states, to date all experiments have been predicated on red-detuned cooling. In our work, we present a shifted perspective—namely, the efficient way to capture single atoms is to eliminate red-detuned light in the loading stage and use blue-detuned light that both cools the atoms and precisely controls trap loss through the amount of energy released during atom-atom collisions in the photoassociation process. Subsequent application of red-detuned light then assures the preparation of maximally one atom in the trap. Using $\mathrm{\Lambda }$-enhanced gray-molasses for loading, we study and model the molecular processes and find we can trap single atoms with 90% probability even in a very shallow optical tweezer. Using 100 traps loaded with 80% probability, we demonstrate one example of the power of enhanced loading by assembling a grid of 36 atoms using only a single move of rows and columns in 2D. Our insight is key in scaling the number of particles in a bottom-up quantum simulation and computation with atoms, or even molecules.

Qubits strongly coupled to a photonic crystal give rise to qubit-photon dressed bound states. These bound states, comprising the qubits and spatially localized photonic modes induced around the qubits, are the basis for many exotic physical scenarios. The localization of these states changes with qubit detuning from the photonic crystal band edge, offering an avenue of in situ control of bound-state interaction. Here, we present experimental results from a device with two transmon qubits coupled to a superconducting microwave photonic crystal and realize tunable on-site and interbound state interactions. We observe a fourth-order two-photon virtual process between bound states indicating strong coupling between the photonic crystal and transmon qubits. Because of their localization-dependent interaction, these states offer the ability to realize one-dimensional chains of bound states with tunable and potentially long-range interactions that preserve the qubits’ spatial organization. The widely tunable, strong, and robust interactions demonstrated with this system are promising benchmarks towards realizing larger, more complex systems that use bound states to build and study quantum spin models.

The difficulty of validating large-scale quantum devices, such as boson samplers, poses a major challenge for any research program that aims to show quantum advantages over classical hardware. Towards this aim, we propose a novel data-driven approach, wherein models are trained to identify common pathologies using unsupervised machine-learning methods. We illustrate this idea by training a classifier that exploits $K$-means clustering to distinguish between boson samplers that use indistinguishable photons from those that do not. We tune the model on numerical simulations of small-scale boson samplers and then validate the pattern-recognition technique on larger numerical simulations as well as on photonic chips in both traditional boson-sampling and scatter-shot experiments. The effectiveness of such a method relies on particle-type-dependent internal correlations present in the output distributions. This approach performs substantially better on the test data than previous methods and underscores the ability to further generalize its operation beyond the scope of the examples that it was trained on.

Out-of-time-order correlation (OTOC) functions provide a powerful theoretical tool for diagnosing chaos and the scrambling of information in strongly interacting, quantum systems. However, their direct and unambiguous experimental measurement remains an essential challenge. At its core, this challenge arises from the fact that the effects of both decoherence and experimental noise can mimic that of information scrambling, leading to decay of OTOCs. Here, we analyze a quantum teleportation protocol that explicitly enables one to differentiate between scrambling and decoherence. Moreover, we demonstrate that within this protocol, one can extract a precise “noise” parameter which quantitatively captures the nonscrambling-induced decay of OTOCs. Using this parameter, we prove explicit bounds on the true value of the OTOC. Our results open the door to experimentally measuring quantum scrambling with built-in verifiability.

A crucial limit to measurement efficiencies of superconducting circuits comes from losses involved when coupling to an external quantum amplifier. Here, we realize a device circumventing this problem by directly embedding an artificial atom, comprised of a transmon qubit, within a flux-pumped Josephson parametric amplifier. This configuration is able to enhance dispersive measurement without exposing the qubit to appreciable excess backaction. Near-optimal backaction is obtained by engineering the circuit to permit high-power operation that reduces information loss to unmonitored channels associated with the amplification and squeezing of quantum noise. By mitigating the effects of off-chip losses downstream, the on-chip gain of this device produces end-to-end measurement efficiencies of up to 80%. Our theoretical model accurately describes the observed interplay of gain and measurement backaction and delineates the parameter space for future improvement. The device is compatible with standard fabrication and measurement techniques and, thus, provides a route for definitive investigations of fundamental quantum effects and quantum control protocols.

We demonstrate single-shot imaging and narrow-line cooling of individual alkaline-earth atoms in optical tweezers; specifically, strontium trapped in $515.2\text{−}\mathrm{nm}$ light. Our approach enables high-fidelity detection of single atoms by imaging photons from the broad singlet transition while cooling on the narrow intercombination line, and we extend this technique to highly uniform two-dimensional tweezer arrays with 121 sites. Cooling during imaging is based on a previously unobserved narrow-line Sisyphus mechanism, which we predict to be applicable in a wide variety of experimental situations. Further, we demonstrate optically resolved sideband cooling of a single atom to near the motional ground state of a tweezer, which is tuned to a magic-trapping configuration achieved by elliptical polarization. Finally, we present calculations, in agreement with our experimental results, that predict a linear-polarization and polarization-independent magic crossing at 520(2) nm and 500.65(50) nm, respectively. Our results pave the way for a wide range of novel experimental avenues based on individually controlled alkaline-earth atoms in tweezers—from fundamental experiments in atomic physics to quantum computing, simulation, and metrology.

Optical tweezers provide a versatile platform for the manipulation and detection of single atoms. Here, we use optical tweezers to demonstrate a set of tools for the microscopic control of atomic strontium, which has two valence electrons. Compared to the single-valence-electron atoms typically used with tweezers, strontium has a more complex internal state structure with a variety of transition wavelengths and linewidths. We report single-atom loading into an array of subwavelength scale optical tweezers and light-shift-free control of a narrow-linewidth optical transition. We use this transition to perform three-dimensional ground-state cooling and to enable high-fidelity nondestructive imaging of single atoms on subwavelength spatial scales. These capabilities, combined with the rich internal structure of strontium, open new possibilities including tweezer-based metrology, new quantum computing architectures, and new paths to low-entropy many-body physics.

Thermodynamics at the nanoscale is known to differ significantly from its familiar macroscopic counterpart: The possibility of state transitions is not determined by free energy alone but by an infinite family of free-energy-like quantities; strong fluctuations (possibly of quantum origin) allow one to extract less work reliably than what is expected from computing the free-energy difference. However, these known results rely crucially on the assumption that the thermal machine is not only exactly preserved in every cycle but also kept uncorrelated from the quantum systems on which it acts. Here, we lift this restriction: We allow the machine to become correlated with the microscopic systems on which it acts while still exactly preserving its own state. Surprisingly, we show that this possibility restores the second law in its original form: Free energy alone determines the possible state transitions, and the corresponding amount of work can be invested or extracted from single systems exactly and without any fluctuations. At the same time, the work reservoir remains uncorrelated from all other systems and parts of the machine. Thus, microscopic machines can increase their efficiency via clever “correlation engineering” in a perfectly cyclic manner, which is achieved by a catalytic system that can sometimes be as small as a single qubit (though some setups require very large catalysts). Our results also solve some open mathematical problems on majorization which may lead to further applications in entanglement theory.

Quantum dots are arguably the best interface between matter spin qubits and flying photonic qubits. Using quantum dot devices to produce joint spin-photonic states requires the electronic spin qubits to be stored for extended times. Therefore, the study of the coherence of spins of various quantum dot confined charge carriers is important both scientifically and technologically. In this study we report on spin-relaxation measurements performed on five different forms of electronic spin qubits confined in the very same quantum dot. In particular, we use all optical techniques to measure the spin relaxation of the confined heavy hole and that of the dark exciton—a long-lived electron-heavy-hole pair with parallel spins. Our measured results for the spin relaxation of the electron, the heavy hole, the dark exciton, the negative and the positive trions, in the absence of externally applied magnetic field, are in agreement with a central spin theory which attributes the dephasing of the carriers’ spin to their hyperfine interactions with the nuclear spins of the atoms forming the quantum dots. We demonstrate that the heavy hole dephases much slower than the electron. We also show, both experimentally and theoretically, that the dark exciton dephases slower than the heavy hole, due to the electron-hole exchange interaction, which partially protects its spin state from dephasing.

Recent work using tools from quantum information theory has shown that for small systems where quantum effects become prevalent, there is not one thermodynamical second law but many. Derivations of these laws assume that an experimenter has very precise control of the system and heat bath. Here we show that these multitude of laws can be saturated using two very simple operations: changing the energy levels of the system and thermalizing over any two system energy levels. Using these two operations, one can distill the optimal amount of work from a system, as well as perform the reverse formation process. What is more, using only these two operations and one ancilla qubit in a thermal state, one can transform any state into any other state allowable by the second laws. We thus have the result that the second laws hold for fine-grained manipulation of system and bath, but can be achieved using very coarse control. This brings the full array of thermal operations towards a regime accessible by experiment, and establishes the physical relevance of these second laws, potentially opening a new direction of studies.

Genuinely quantum states of a harmonic oscillator may be distinguished from their classical counterparts by the Glauber-Sudarshan $P$ representation—a state lacking a positive $P$ function is said to be nonclassical. In this paper, we propose a general operational framework for studying nonclassicality as a resource in networks of passive linear elements and measurements with feed forward. Within this setting, we define new measures of nonclassicality based on the quantum fluctuations of quadratures, as well as the quantum Fisher information of quadrature displacements. These measures lead to fundamental constraints on the manipulation of nonclassicality, especially its concentration into subsystems, that apply to generic multimode non-Gaussian states. Special cases of our framework include no-go results in the concentration of squeezing and a complete hierarchy of nonclassicality for single-mode Gaussian states.

For solid-state spin qubits, single-gate rf readout can minimize the number of gates required for scale-up since the readout sensor can integrate into the existing gates used to manipulate the qubits. However, state-of-the-art topological error correction codes benefit from the ability to resolve the qubit state within a single shot, that is, without repeated measurements. Here, we demonstrate single-gate, single-shot readout of a singlet-triplet spin state in silicon, with an average readout fidelity of 82.9% at 3.3 kHz measurement bandwidth. We use this technique to measure a triplet $T_{-}$ to singlet $S_0$ relaxation time of 0.62 ms in precision donor quantum dots in silicon. We also show that the use of rf readout does not impact the spin lifetimes ($S_0$ to $T_{-}$ decay remained approximately 2 ms at zero detuning). This establishes single-gate sensing as a viable readout method for spin qubits.

We study a 1D chain of noninteracting bosonic cavities which are subject to nearest-neighbor parametric driving, thus realizing a bosonic Hamiltonian whose form is reminiscent of the celebrated Kitaev model of a 1D $p$-wave superconductor. For a suitable choice of drive phases, the model exhibits a number of remarkable properties. This includes phase-dependent chirality: Photons propagate and are amplified in a direction determined by the phase of the initial drive or excitation. It also exhibits a drastic sensitivity to boundary conditions: For a range of parameters, the boundaryless system has only delocalized, dynamically unstable modes, while a finite open chain is described by localized, dynamically stable modes. While our model is described by a Hermitian Hamiltonian, we show that it has a surprising connection to non-Hermitian asymmetric hopping models. In addition to being of fundamental interest as a new kind of topological bosonic system, our system also has potential practical utility as a quantum amplifier and a source of multimode entangled photons.