Hosting nonclassical states of light in three-dimensional microwave cavities has emerged as a promising paradigm for continuous-variable quantum information processing. Here we experimentally demonstrate high-fidelity generation of a range of Wigner-negative states useful for quantum computation, such as Schrödinger-cat states, binomial states, Gottesman-Kitaev-Preskill states, as well as cubic phase states. The latter states have been long sought after in quantum optics and have never been achieved experimentally before. We use a sequence of interleaved selective number-dependent arbitrary phase (SNAP) gates and displacements. We optimize the state preparation in two steps. First we use a gradient-descent algorithm to optimize the parameters of the SNAP and displacement gates. Then we optimize the envelope of the pulses implementing the SNAP gates. Our results show that this way of creating highly nonclassical states in a harmonic oscillator is robust to fluctuations of the system parameters such as the qubit frequency and the dispersive shift.

We introduce operational quantum tasks based on betting with risk aversion—or quantum betting tasks for short—inspired by standard quantum state discrimination and classical horse betting with risk aversion and side information. In particular, we introduce the operational tasks of quantum state betting (QSB), noisy quantum state betting (NQSB), and quantum-channel betting (QCB) played by gamblers with different risk tendencies. We prove that the advantage that informative measurements (nonconstant channels) provide in QSB (NQSB) is exactly characterized by Arimoto’s $\alpha$-mutual information, with the order $\alpha$ determining the risk aversion of the gambler. More generally, we show that Arimoto-type information-theoretic quantities characterize the advantage that resourceful objects offer at playing quantum betting tasks when compared to resourceless objects, for general quantum resource theories (QRTs) of measurements, channels, states, and state-measurement pairs, with arbitrary resources. In limiting cases, we show that QSB (QCB) recovers the known tasks of quantum state (channel) discrimination when $\alpha \to \mathrm{\infty }$, and quantum state (channel) exclusion when $\alpha \to -\mathrm{\infty }$. Inspired by these connections, we also introduce new quantum Rényi divergences for measurements, and derive a new family of resource monotones for the QRT of measurement informativeness. This family of resource monotones recovers in the same limiting cases as above, the generalized robustness and the weight of informativeness. Altogether, these results establish a broad and continuous family of four-way correspondences between operational tasks, mutual information measures, quantum Rényi divergences, and resource monotones, that can be seen to generalize two limiting correspondences that were recently discovered for the QRT of measurement informativeness.

Variational quantum algorithms are promising algorithms for achieving quantum advantage on near-term devices. The quantum hardware is used to implement a variational wave function and measure observables, whereas the classical computer is used to store and update the variational parameters. The optimization landscape of expressive variational ansätze is however dominated by large regions in parameter space, known as barren plateaus, with vanishing gradients, which prevents efficient optimization. In this work we propose a general algorithm to avoid barren plateaus in the initialization and throughout the optimization. To this end we define a notion of weak barren plateaus (WBPs) based on the entropies of local reduced density matrices. The presence of WBPs can be efficiently quantified using recently introduced shadow tomography of the quantum state with a classical computer. We demonstrate that avoidance of WBPs suffices to ensure sizable gradients in the initialization. In addition, we demonstrate that decreasing the gradient step size, guided by the entropies allows WBPs to be avoided during the optimization process. This paves the way for efficient barren plateau-free optimization on near-term devices.

We devise a quasilinear quantum algorithm for generating an approximation for the ground state of a quantum field theory (QFT). Our quantum algorithm delivers a superquadratic speedup over the state-of-the-art quantum algorithm for ground-state generation, overcomes the ground-state-generation bottleneck of the prior approach and is optimal up to a polylogarithmic factor. Specifically, we establish two quantum algorithms—Fourier-based and wavelet-based—to generate the ground state of a free massive scalar bosonic QFT with gate complexity quasilinear in the number of discretized QFT modes. The Fourier-based algorithm is limited to translationally invariant QFTs. Numerical simulations show that the wavelet-based algorithm successfully yields the ground state for a QFT with broken translational invariance. Furthermore, the cost of preparing particle excitations in the wavelet approach is independent of the energy scale. Our algorithms require a routine for generating one-dimensional Gaussian (1DG) states. We replace the standard method for 1DG-state generation, which requires the quantum computer to perform lots of costly arithmetic, with a novel method based on inequality testing that significantly reduces the need for arithmetic. Our method for 1DG-state generation is generic and could be extended to preparing states whose amplitudes can be computed on the fly by a quantum computer.

Entanglement is the fuel of advanced quantum technology, enabling, e.g., measurement-based quantum computing and loss-tolerant encoding of quantum information. In photonics, entanglement has traditionally been generated probabilistically, requiring massive multiplexing for scaling up to many photons. An alternative approach utilizing quantum emitters in nanophotonic devices can realize deterministic generation of entangled photons. However, such sources generate polarization entanglement that is incompatible with spatial dual-rail qubit encoding employed in scalable photonic quantum-computing platforms utilizing integrated circuits. Here we propose and experimentally realize an on-demand source of dual-rail photon pairs using a quantum dot in a planar nanophotonic waveguide. The source exploits the cascaded decay of a biexciton state and chiral light-matter coupling to achieve deterministic generation of spatial dual-rail Bell pairs with the amount of entanglement determined by the chirality. The operational principle can readily be extended to multiphoton entanglement generation required for efficient preparation of resource states for photonic quantum computing.

It is well established that measurement-induced quantum back action (QBA) can be eliminated in composite systems by engineering so-called quantum-mechanics-free subspaces (QMFSs) of commuting variables, leading to a trajectory of a quantum system without quantum uncertainties. This situation can be realized in a composite system that includes a negative-mass subsystem, which can be implemented by, e.g., a polarized spin ensemble or a two-tone-driven optomechanical system. The realization of a trajectory without quantum uncertainties implies entanglement between the subsystems, and allows for measurements of motion, fields, and forces with, in principle, unlimited precision. To date, these principles have been developed theoretically and demonstrated experimentally for a number of composite systems. However, the utility of the concept has been limited by the dominating requirement of close proximity of the resonance frequencies of the system of interest and the negative-mass reference system, and by the need to embed the subsystems in a narrowband cavity, which could be problematic while at the same time achieving good overcoupling. Here we propose a general approach that overcomes these limitations by employing periodic modulation of the driving fields (e.g., two-tone driving) in combination with coherent or measurement-based antinoise paths. This approach makes it possible to engineer a QMFS of two systems with vastly different spectra and with arbitrary signs of their masses, while dispensing with the need to embed the subsystems in a sideband-resolving cavity. We discuss the advantages of this novel approach for applications such as QBA evasion in gravitational wave detection, force sensing, and entanglement generation between disparate systems.

We present two classical algorithms for the simulation of universal quantum circuits on $n$ qubits constructed from $c$ instances of Clifford gates and $t$ arbitrary-angle $Z$-rotation gates such as $T$ gates. Our algorithms complement each other by performing best in different parameter regimes. The Estimate algorithm produces an additive precision estimate of the Born-rule probability of a chosen measurement outcome with the only source of run-time inefficiency being a linear dependence on the stabilizer extent (with scaling approximately equal to ${1.17}^t$ for $T$ gates). Our algorithm is state of the art for this task: as an example, in approximately $13$ h (on a standard desktop computer), we estimate the Born-rule probability to within an additive error of $0.03$, for a $50$-qubit, $60$ non-Clifford gate quantum circuit with more than $2000$ Clifford gates. Our second algorithm, Compute, calculates the probability of a chosen measurement outcome to machine precision with run time $O\left(2^{t-r}t\right)$, where $r$ is an efficiently computable, circuit-specific quantity. With high probability, $r$ is very close to $min\left\{t,n-w\right\}$ for random circuits with many Clifford gates, where $w$ is the number of measured qubits. Compute can be effective in surprisingly challenging parameter regimes, e.g., we can randomly sample Clifford+$T$ circuits with $n=55$, $w=5$, $c={10}^5$, and $t=80T$ gates, and then compute the Born-rule probability with a run time consistently less than $10$ min using a single core of a standard desktop computer. We provide a C+Python implementation of our algorithms and benchmark them using random circuits, the hidden-shift algorithm, and the quantum approximate optimization algorithm.

Although quantum computation is regarded as a promising numerical method for computational quantum chemistry, current applications of quantum-chemistry calculations on quantum computers are limited to small molecules. This limitation can be ascribed to technical problems in building and manipulating more quantum bits (qubits) and the associated complicated operations of quantum gates in a quantum circuit when the size of the molecular system becomes large. As a result, reducing the number of required qubits is necessary to make quantum computation practical. Currently, the minimal STO-3G basis set is commonly used in benchmark studies because it requires the minimum number of spin orbitals. Nonetheless, the accuracy of using STO-3G is generally low and thus can not provide useful predictions. Herein, we propose to adopt Daubechies wavelet functions as an accurate and efficient method for quantum computations of molecular electronic properties. We demonstrate that a minimal basis set constructed from Daubechies wavelet basis can yield accurate results through a better description of the molecular Hamiltonian, while keeping the number of spin orbitals minimal. With the improved Hamiltonian through Daubechies wavelets, we calculate vibrational frequencies for ${\mathrm{H}}_2$ and $\mathrm{LiH}$ using quantum-computing algorithm to show that the results are in excellent agreement with experimental data. As a result, we achieve quantum calculations in which accuracy is comparable with that of the full configuration interaction calculation using the cc-pVDZ basis set, whereas the computational cost is the same as that of a STO-3G calculation. Thus, our work provides a more efficient and accurate representation of the molecular Hamiltonian for efficient quantum computations of molecular systems, and for the first time demonstrates that predictions in agreement with experimental measurements are possible to be achieved with quantum resources available in near-term quantum computers.

Entanglement distribution over quantum networks has the promise of realizing fundamentally new technologies. Entanglement between separated quantum processing nodes has been achieved on several experimental platforms in the past decade. To move toward metropolitan-scale quantum network test beds, the creation and transmission of indistinguishable single photons over existing telecom infrastructure is key. Here, we report the interference of photons emitted by remote spectrally detuned NV-center-based network nodes, using quantum frequency conversion to the telecom $L$ band. We find a visibility of $0.79\pm 0.03$ and an indistinguishability between converted NV photons around $0.9$ over the full range of the emission duration, confirming the removal of the spectral information present. Our approach implements fully separated and independent control over the nodes, time multiplexing of control and quantum signals, and active feedback to stabilize the output frequency. Our results demonstrate a working principle that can be readily employed on other platforms and shows a clear path toward generating metropolitan-scale solid-state entanglement over deployed telecom fibers.

The ability to perform high-precision optical measurements is paramount in science and engineering. Laser interferometry enables interaction-free sensing with a precision ultimately limited by shot noise. Quantum optical sensors can surpass this limit but single- or multiphoton schemes are challenged by low experimental sampling rates, while squeezed-light approaches require complex optical setups and sophisticated time gating. Here, we introduce a simple method that infers optical phase shifts through standard intensity measurements while still maintaining the quantum advantage in the measurement precision. Capitalizing on the robustness and high sampling rates of our device, we implement a quantum optical microphone in the audio band. Its performance is benchmarked against a classical laser microphone in a standardized medically approved speech-recognition test on 45 subjects. We find that quantum-recorded words improve the speech-recognition threshold by $-0.57{\mathrm{dB}}_{\mathrm{SPL}}$, thus making the quantum advantage audible. Not only do these results open the door toward applications in quantum nonlinear interferometry but they also show that quantum phenomena can be experienced by humans.

Randomized benchmarking refers to a collection of protocols that in the past decade have become central methods for characterizing quantum gates. These protocols aim at efficiently estimating the quality of a set of quantum gates in a way that is resistant to state preparation and measurement errors. Over the years many versions have been developed, however a comprehensive theoretical treatment of randomized benchmarking has been missing. In this work, we develop a rigorous framework of randomized benchmarking general enough to encompass virtually all known protocols as well as novel, more flexible extensions. Overcoming previous limitations on error models and gate sets, this framework allows us, for the first time, to formulate realistic conditions under which we can rigorously guarantee that the output of any randomized benchmarking experiment is well described by a linear combination of matrix exponential decays. We complement this with a detailed analysis of the fitting problem associated with randomized benchmarking data. We introduce modern signal processing techniques to randomized benchmarking, prove analytical sample complexity bounds, and numerically evaluate performance and limitations. In order to reduce the resource demands of this fitting problem, we introduce novel, scalable postprocessing techniques to isolate exponential decays, significantly improving the practical feasibility of a large set of randomized benchmarking protocols. These postprocessing techniques overcome shortcomings in efficiency of several previously proposed methods such as character benchmarking and linear-cross entropy benchmarking. Finally, we discuss, in full generality, how and when randomized benchmarking decay rates can be used to infer quality measures like the average fidelity. On the technical side, our work substantially extends the recently developed Fourier-theoretic perspective on randomized benchmarking by making use of the perturbation theory of invariant subspaces, as well as ideas from signal processing.

We reformulate the continuous-space Schrödinger equation in terms of spin Hamiltonians. For the kinetic energy operator, the critical concept facilitating the reduction in model complexity is the idea of position encoding. A binary encoding of position produces a spin-$1/2$ Heisenberg-like model and yields exponential improvement in space complexity when compared to classical computing. Encoding with a binary reflected Gray code (BRGC), and a Hamming-distance-2 Gray code (H2GC) reduces the model complexity down to the $XZ$ and transverse Ising model, respectively. For $A$ qubits BRGC yields $2^A$ positions and is reduced to its 2-local form with $\mathrm{O}(A)$ ancillary qubits. H2GC yields $2^{A/2+1}$ positions with $\mathrm{O}(A^2)$ three-local penalty terms. We also identify the bijective mapping between diagonal unitaries and the Walsh series, producing the mapping of any real potential to a series of $k$-local Ising models through the fast Walsh transform. Finally, in a finite volume, we provide some numerical evidence to support the claim that the total time needed for adiabatic evolution is protected by the infrared cutoff of the system. As a result, initial state preparation from a free-field wave function to an interacting system is expected to exhibit polynomial time complexity with volume and constant scaling with respect to lattice discretization for all encodings. For H2GC, if the evolution starts with the transverse Hamiltonian due to hardware restrictions, then penalties are dynamically introduced such that the low-lying spectrum reproduces the energy levels of the Laplacian. The adiabatic evolution of the penalty Hamiltonian is therefore sensitive to the ultraviolet scale. It is expected to exhibit polynomial time complexity with lattice discretization, or exponential time complexity with respect to the number of qubits given a fixed volume.

Geometric quantum mechanics, through its differential-geometric underpinning, provides additional tools of analysis and interpretation that bring quantum mechanics closer to classical mechanics: state spaces in both are continuous and equipped with symplectic geometry. This opens the door to revisiting foundational questions and issues, such as the nature of quantum entropy, from a geometric perspective. Central to this is the concept of a geometric quantum state—the probability measure on a system’s space of pure states. This space’s continuity leads us to introduce two analysis tools, inspired by Renyi’s approach to information theory of continuous variables, to characterize and quantify fundamental properties of geometric quantum states: the quantum information dimension, which is the rate of geometric quantum state compression, and the dimensional geometric entropy that monitors information stored in quantum states. We recount their classical definitions, information-theoretic interpretations, and adapt them to quantum systems via the geometric approach. We then explicitly compute them in various examples and classes of quantum system. We conclude commenting on future directions for information in geometric quantum mechanics.

We demonstrate that it is possible to effectively eliminate radiative losses during excitonic energy transport in systems with an intrinsic energy gradient. By considering chainlike systems of repeating “unit” cells that can each consist of multiple sites, we show that tuning a single system parameter (the intra-unit-cell coupling) leads to efficient and highly robust transport over relatively long distances. This remarkable transport performance is shown to originate from a partitioning of the system’s eigenstates into energetically separated bright and dark subspaces, allowing long-range transport to proceed efficiently through a “dark chain” of eigenstates. Finally, we discuss the effects of intrinsic dipole moments, which are of particular relevance to molecular architectures, and demonstrate that appropriately aligned dipoles can lead to additional protection against other (nonradiative) loss processes. Our dimensionless open quantum systems model is designed to be broadly applicable to a range of experimental platforms.

Privacy amplification is the key step to guarantee the security of quantum communication. The existing security proofs require the accumulation of a large number of raw key bits for privacy amplification. This is similar to block ciphers in classical cryptography that would delay the final key generation since an entire block must be accumulated ahead of privacy amplification. Moreover, any leftover errors after information reconciliation would corrupt the entire block. By modifying the security proof based on quantum error correction, we develop a stream privacy-amplification scheme, which resembles the classical stream cipher. This scheme can output the final key in a stream way, prevent error from spreading, and hence can put privacy amplification ahead of information reconciliation. The stream scheme can also help to enhance the security of trusted-relay quantum networks and improve the practicality of randomness extraction for quantum random number generators.

The generating functional of a self-interacting scalar quantum field theory (QFT), which contains all the relevant information about real-time dynamics and scattering experiments, can be mapped onto a collection of multipartite-entangled two-level sensors via an interferometric protocol that exploits a specific set of source functions. Although one typically focuses on impulsive $\delta$-like sources, as these give direct access to $n$-point Feynman propagators, we show in this work that using always-on harmonic sources can simplify substantially the sensing protocol. In a specific regime, the effective real-time dynamics of the quantum sensors can be described by a quantum Ising model with long-range couplings, the range and strength of which contains all the relevant information about the renormalization of the QFT, which can now be extracted in the absence of multipartite entanglement. We present a detailed analysis of how this sensing protocol can be relevant to characterize the long-wavelength QFT that describes quantized sound waves of trapped-ion crystals in the vicinity of a structural phase transition, opening a new route to characterize the associated renormalization of sound.

We present a method for encoding second-quantized fermionic systems in qubits when the number of fermions is conserved, as in the electronic structure problem. When the number $F$ of fermions is much smaller than the number $M$ of modes, this symmetry reduces the number of information-theoretically required qubits from $\mathrm{\Theta }(M)$ to $O(F\log M)$. In this limit, our encoding requires $O(F^2{\log }^4M)$ qubits, while encoded fermionic creation and annihilation operators have cost $O(F^2{\log }^5M)$ in two-qubit gates. When incorporated into randomized simulation methods, this permits simulating time evolution with only polylogarithmic explicit dependence on $M$. This is the first second-quantized encoding of fermions in qubits whose costs in qubits and gates are both polylogarithmic in $M$, which permits studying fermionic systems in the high-accuracy regime of many modes.

The performance of quantum gate operations is experimentally determined by how correctly operational parameters can be determined and set, and how stable these parameters can be maintained. In addition, gates acting on different sets of qubits require unique sets of control parameters. Thus, an efficient multidimensional parameter estimation procedure is crucial to calibrate even medium-sized quantum processors. Here, we develop and characterize an efficient calibration protocol to automatically estimate and adjust experimental parameters of the widely used two-qubit Mølmer-Sørensen entangling gate operation in a trapped-ion quantum information processor. The protocol exploits Bayesian parameter estimation methods that include a stopping criterion based on a desired gate infidelity. We experimentally demonstrate a tune-up procedure that leads to a residual median gate infidelity due to miscalibration of $1.3(1)\times {10}^{-3}$, requiring $1200\pm 500$ experimental cycles, while completing the entire gate calibration procedure in less than one minute, which provides a significant speedup over commonly used manual tune-up routines. This approach is applicable to other quantum information processor architectures with known or sufficiently characterized theoretical models.

Interfaced single-photon sources and quantum memories for photons together form a foundational component of quantum technology. Achieving compatibility between heterogeneous, state-of-the-art devices is a long-standing challenge. We built and successfully interfaced a heralded single-photon source based on cavity-enhanced spontaneous parametric down-conversion in periodically poled potassium titanyl phosphate and a matched memory based on electromagnetically induced transparency in warm ${}^{87}\mathrm{Rb}$ vapor. The bandwidth of the photons emitted by the source is $370\mathrm{MHz}$, placing its speed in the technologically relevant regime while remaining well within the acceptance bandwidth of the memory. Simultaneously, the experimental complexity is kept low, with all components operating at or above room temperature. Read-out noise of the memory is considerably reduced by exploiting polarization selection rules in the hyperfine structure of spin-polarized atoms. For the first time, we demonstrate single-photon storage and retrieval in a ground-state vapor cell memory, with $g_{c,\mathrm{ret}}^{(2)}=0.177(23)$ demonstrating the single-photon character of the retrieved light. Our platform of single-photon source and atomic memory is attractive for future experiments on room-temperature quantum networks operating at high bandwidth.

An important challenge in non-Markovian open quantum systems is to understand what information we gain from continuous measurement of an output field. For example, atoms in multimode cavity QED systems provide an exciting platform to study many-body phenomena in regimes where the atoms are strongly coupled amongst themselves and with the cavity, but the strong coupling makes it complicated to infer the conditioned state of the atoms from the output light. In this work we address this problem, describing the reduced atomic state via a conditioned hierarchy of equations of motion, which provides an exact conditioned reduced description under monitoring (and continuous feedback). We utilize this formalism to study how different monitoring for modes of a multimode cavity affects our information gain for an atomic state, and to improve spin squeezing via measurement and feedback in a strong coupling regime. This work opens opportunities to understand continuous monitoring of non-Markovian open quantum systems, both on a practical and fundamental level.