Digital-analog quantum computation aims to reduce the currently infeasible resource requirements needed for near-term quantum information processing by replacing sequences of one- and two-qubit gates with a unitary transformation generated by the systems’ underlying Hamiltonian. Inspired by this paradigm, we consider superconducting architectures and extend the cross-resonance effect, up to first order in perturbation theory, from a two-qubit interaction to an analog Hamiltonian acting on one-dimensional (1D) chains and two-dimensional (2D) square lattices, which, in an appropriate reference frame, results in a purely two-local Hamiltonian. By augmenting the analog Hamiltonian dynamics with single-qubit gates we show how one may generate a larger variety of distinct analog Hamiltonians. We then synthesize unitary sequences, in which we toggle between the various analog Hamiltonians as needed, simulating the dynamics of Ising, $XY$, and Heisenberg spin models. Our dynamics simulations are Trotter error-free for the Ising and $XY$ models in 1D. We also show that the Trotter errors for 2D $XY$ and 1D Heisenberg chains are reduced, with respect to a digital decomposition, by a constant factor. In order to realize these important near-term speedups, we discuss the practical considerations needed to accurately characterize and calibrate our analog Hamiltonians for use in quantum simulations. We conclude with a discussion of how the Hamiltonian toggling techniques could be extended to derive new analog Hamiltonians, which may be of use in more complex digital-analog quantum simulations for various models of interacting spins.

Many quantum computational tasks have inherent symmetries, suggesting a path to enhancing their efficiency and performance. Exploiting this observation, we propose representation matching, a generic probabilistic protocol for reducing the cost of quantum computation in a quantum network. We show that the representation-matching protocol is capable of reducing the communication or memory cost to almost the minimum in various tasks, including remote execution of unitary gate arrays, permutation gates, and unitary conjugation, as well as the storage and retrieval of unitary gates.

We investigate, in a four-photon interference experiment in a laser-written waveguide structure, how symmetries control the suppression of many-body output events of a $J_x$ unitary. We show that totally destructive interference does not require mutual indistinguishability between all but only between symmetrically paired particles, in agreement with recent theoretical predictions. The outcome of the experiment is well described by a quantitative simulation that accounts for higher-order emission of the photon source, imbalances in the scattering network, partial distinguishability, and photon loss.

We develop a method to connect the infinite-dimensional description of optical continuous-variable quantum key distribution (QKD) protocols to a finite-dimensional formulation. The secure key rates of the optical QKD protocols can then be evaluated using recently developed reliable numerical methods for key-rate calculations. We apply this method to obtain asymptotic key rates for discrete-modulated continuous-variable QKD protocols, which are of practical significance due to their experimental simplicity and potential for large-scale deployment in quantum-secured networks. Importantly, our security proof does not require the photon-number cutoff assumption relied upon in previous works. We also demonstrate that our method can provide practical advantages over the flag-state squasher when applied to discrete-variable protocols.

In order to characterize and calibrate quantum processing devices, a large amount of measurement data has to be collected. Active qubit reset increases the speed at which data can be gathered but requires additional hardware and/or calibration. The experimental apparatus can, however, be operated at elevated repetition rates without reset. In this case, the outcome of a first measurement serves as the initial state for the next experiment. Rol et al. have used this restless operation mode to accelerate the calibration of a single-qubit gate by measuring fixed-length sequences of Clifford gates that compose to $X$ gates [Phys. Rev. Appl. 7, 041001 (2017)]. However, we find that when measuring pulse sequences that compose to arbitrary operations, distortion appears in the measured data. Here, we extend the restless methodology by showing how to efficiently analyze restless measurements and correct distortions to achieve an identical outcome and accuracy as compared to measurements in which the superconducting qubits are reset. This allows us to rapidly characterize and calibrate qubits. We illustrate this bias-corrected restless measurements method by measuring a Rabi oscillation at a $250\mathrm{kHz}$ repetition rate without any reset, for a qubit with a decay rate of $1/2\pi T_1=3\mathrm{kHz}$. We also show that we can measure a single- and a two-qubit average gate fidelity using randomized benchmarking 20 and 8 times faster, respectively, than measurements that reset the qubits through $T_1$ decay.

While a propagating state of light can be generated with arbitrary squeezing by pumping a parametric resonator, the intraresonator state is limited to 3 dB of squeezing. Here, we implement a reservoir-engineering method to surpass this limit using superconducting circuits. Two-tone pumping of a three-wave-mixing element implements an effective coupling to a squeezed bath, which stabilizes a squeezed state inside the resonator. Using an ancillary superconducting qubit as a probe allows us to perform a direct Wigner tomography of the intraresonator state. The raw measurement provides a lower bound on the squeezing at about $6.7\pm 0.2$ dB below the zero-point level. Further, we show how to correct for resonator evolution during the Wigner tomography and obtain a squeezing as high as $8.2\pm 0.8$ dB. Moreover, this level of squeezing is achieved with a purity of $0.91\pm 0.09$.

Precise thermometry for quantum systems is important to the development of new technology, and understanding the ultimate limits to precision presents a fundamental challenge. It is well known that optimal thermometry requires projective measurements of the total energy of the sample. However, this is infeasible in even moderately sized systems, where realistic energy measurements will necessarily involve some coarse-graining. Here we explore the precision limits for temperature estimation when only coarse-grained measurements are available. Using tools from signal processing, we derive the structure of optimal coarse-grained measurements and find that good temperature estimates can generally be attained even with a small number of outcomes. We apply our results to many-body systems and nonequilibrium thermometry. For the former, we focus on interacting spin lattices, both at and away from criticality, and find that the Fisher-information scaling with system size is unchanged after coarse-graining. For the latter, we consider a probe of given dimension interacting with the sample, followed by a measurement of the probe. We derive an upper bound on arbitrary, nonequilibrium strategies for such probe-based thermometry and illustrate it for thermometry on a Bose-Einstein condensate using an atomic quantum-dot probe.

We introduce two kinds of quantum algorithm to explore microcanonical and canonical properties of many-body systems. The first is a hybrid quantum algorithm that, given an efficiently preparable state, computes expectation values in a finite energy interval around its mean energy. This algorithm is based on a filtering operator, similar to quantum phase estimation, which filters out energies outside the desired energy interval. However, instead of performing this operation on a physical state, it recovers the physical values by performing interferometric measurements without the need to prepare the filtered state. We show that the computational time scales polynomially with the number of qubits, the inverse of the prescribed variance, and the inverse error. In practice, the algorithm does not require the evolution for long times, but instead a significant number of measurements in order to obtain sensible results. Our second algorithm is a quantum assisted Monte Carlo sampling method to compute other quantities that approach the expectation values for the microcanonical and canonical ensembles. Using classical Monte Carlo techniques and the quantum computer as a resource, this method circumvents the sign problem that plagues classical quantum Monte Carlo simulations, as long as one can prepare states with suitable energies. All algorithms can be used with small quantum computers and analog quantum simulators, as long as they can perform the interferometric measurements. We also show that this last task can be greatly simplified at the expense of performing more measurements.

How to characterize topological quantum phases is a fundamental issue in the broad field of topological matter. From a dimension reduction approach, we propose the concept of high-order band inversion surfaces (BISs), which enable the optimal schemes to characterize equilibrium topological phases by far-from-equilibrium quantum dynamics, and further report the experimental simulation. We show that characterization of a $d$-dimensional ($d\mathrm{D}$) topological phase can be reduced to lower-dimensional topological invariants in the high-order BISs, of which the $n\mathrm{th}$-order BIS is a $(d-n)\mathrm{D}$ interface in momentum space. In quenching the system from trivial phase to topological regime, we unveil a high-order dynamical bulk-surface correspondence that the quantum dynamics exhibits nontrivial topological pattern in arbitrary $n\mathrm{th}$-order BISs, which universally corresponds to and so characterizes the equilibrium topological phase of the postquench Hamiltonian. This high-order dynamical bulk-surface correspondence provides new and optimal dynamical schemes with fundamental advantages to simulate and detect topological states, in which through the highest-order BISs that are of zero dimension, the detection of topological phase relies on only minimal measurements. We experimentally build up a quantum simulator with spin qubits to investigate a three-dimensional chiral topological insulator through emulating each momentum one by one and measure the high-order dynamical bulk-surface correspondence, with the advantages of topological characterization via highest-order BISs being demonstrated.

Numerous conceptually important quantum algorithms rely on a blackbox device known as an oracle, which is typically difficult to construct without knowing the answer to the problem that the algorithm is intended to solve. A notable example is Grover’s search algorithm. Here we propose a Grover search for solutions to a class of NP-complete decision problems known as subset sum problems, including the special case of number partitioning. Each problem instance is encoded in the couplings of a set of qubits to a central spin or boson, which enables a realization of the oracle without knowledge of the solution. The algorithm provides a quantum speedup across a known phase transition in the computational complexity of the partition problem, and we identify signatures of the phase transition in the simulated performance. Whereas the naive implementation of our algorithm requires a spectral resolution that scales exponentially with system size for NP-complete problems, we also present a recursive algorithm that enables scalability. We propose and analyze implementation schemes with cold atoms, including Rydberg-atom and cavity-QED platforms.

Recently, new insights have been obtained by jointly studying communication and resource theory. This interplay consequently serves as a potential platform for interdisciplinary studies. To continue this line, we analyze the role of dynamical resources in a communication setup, and further apply our analysis to thermodynamics. To start with, we study classical-communication scenarios constrained by a given resource, in the sense that the information-processing channel is unable to supply additional amounts of the resource. We show that the one-shot classical capacity is upper bounded by resource preservability, which is a measure of the ability to preserve the resource. A lower bound can be further obtained when the resource is asymmetry. As an application, unexpectedly, under a recently studied thermalization model, we find that the smallest bath size needed to thermalize all outputs of a Gibbs-preserving coherence-annihilating channel upper bounds its one-shot classical capacity. When the channel is coherence nongenerating, the upper bound is given by a sum of coherence preservability and the bath size of the channel’s incoherent version. In this sense, bath sizes can be interpreted as the thermodynamic cost of transmitting classical information. This finding provides a dynamical analog of Landauer’s principle, and therefore bridges classical communication and thermodynamics. As another implication, we show that, in bipartite settings, classically correlated local baths can admit classical communication even when both local systems are completely thermalized. Hence, thermalizations can transmit information by accessing only classical correlation as a resource. Our results demonstrate interdisciplinary applications enabled by dynamical resource theory.

The accumulation of noise in quantum computers is the dominant issue stymieing the push of quantum algorithms beyond their classical counterparts. We do not expect to be able to afford the overhead required for quantum error correction in the next decade, so in the meantime we must rely on low-cost, unscalable error mitigation techniques to bring quantum computing to its full potential. In this paper we present a new error mitigation technique based on quantum phase estimation that can also reduce errors in expectation value estimation (e.g., for variational algorithms). The general idea is to apply phase estimation while effectively postselecting for the system register to be in the starting state, which allows us to catch and discard errors that knock us away from there. We refer to this technique as “verified phase estimation” (VPE) and show that it can be adapted to function without the use of control qubits in order to simplify the control circuitry for near-term implementations. Using VPE, we demonstrate the estimation of expectation values on numerical simulations of intermediate-scale quantum circuits with multiple orders of magnitude improvement over unmitigated estimation at near-term error rates (even after accounting for the additional complexity of phase estimation). Our numerical results suggest that VPE can mitigate against any single errors that might occur; i.e., the error in the estimated expectation values often scale as $\mathcal{O}(p^2)$, where $p$ is the probability of an error occurring at any point in the circuit. This property reveals VPE as a practical technique for mitigating errors in near-term quantum experiments.

Quantum communication addresses the problem of exchanging information across macroscopic distances by employing encryption techniques based on quantum-mechanical laws. Here, we advance a new paradigm for secure quantum communication by combining backscattering concepts with covert communication in the microwave regime. Our protocol allows communication between Alice, who uses only discrete phase modulations, and Bob, who has access to cryogenic microwave technology. Using notions of quantum channel discrimination and quantum metrology, we find the ultimate bounds for the receiver performance, proving that quantum correlations can enhance the SNR by up to 6 dB. These bounds rule out any quantum illumination advantage when the source is strongly amplified, and shows that a relevant gain is possible only in the low photon-number regime. We show how the protocol can be used for covert communication, where the carrier signal is indistinguishable from the thermal noise in the environment. We complement our information-theoretic results with a feasible experimental proposal in a circuit-QED platform. This work makes a decisive step toward implementing secure quantum communication concepts in the previously uncharted $1$–$10$ GHz frequency range, in the scenario when the disposable power of one party is severely constrained.

We report fast charge-state readout of a double quantum dot in a CMOS split-gate silicon nanowire transistor via the large dispersive interaction with microwave photons in a lumped-element resonator formed by hybrid integration with a superconducting inductor. We achieve a coupling rate $g_0/(2\pi )=204\pm 2\mathrm{MHz}$ by exploiting the large interdot gate lever arm of an asymmetric split-gate device, $\alpha =0.72$, and by inductively coupling to the resonator to increase its impedance, $Z_r=560\mathrm{\Omega }$. In the dispersive regime, the large coupling strength at the double quantum-dot hybridization point produces a frequency shift comparable to the resonator linewidth, the optimal setting for maximum state visibility. We exploit this regime to demonstrate rapid dispersive readout of the charge degree of freedom, with a SNR of 3.3 in 50 ns. In the resonant regime, the fast charge decoherence rate precludes reaching the strong coupling regime, but we show a clear route to spin-photon circuit quantum electrodynamics using hybrid CMOS systems.

Recent developments in the coherent manipulation of electrons in ballistic conductors include the generation of time-periodic electrical currents involving one to few electronic excitations per period. However, using individual electrons as carriers of quantum information for flying qubit computation or quantum metrology applications calls for a general method to unravel the single-particle excitations embedded in a quantum electrical current and how quantum information is encoded within it. Here, we propose a general signal-processing algorithm to extract the elementary single-particle states, called electronic atoms of signal, present in any periodic quantum electrical current. These excitations and their mutual quantum coherence describe the excess single-electron coherence in the same way musical notes and score describe a sound signal emitted by a music instrument. This method, which is the first step towards the development of signal processing of quantum electrical currents is illustrated by assessing the quality of experimentally relevant single electron sources. The example of randomized quantum electrical currents obtained by regularly clocked but randomly injected unit-charge Lorentzian voltage pulses enables us to discuss how interplay of the coherence of the applied voltage and the Pauli principle alter the quantum coherence between the emitted single-particle excitations.

Non-Hermitian descriptions of quantum matter have seen impressive progress recently, with major advances in understanding central aspects such as their topological properties or the physics of exceptional points, the non-Hermitian counterpart of critical points. Here, we use single-photon interferometry to reconstruct the non-Hermitian Kibble-Zurek mechanism and its distinct scaling behavior for exceptional points, by simulating the defect production upon performing slow parameter ramps. We report progress along two axes. First, we realize parameter ramps across higher-order exceptional points, providing experimental access to their theoretically predicted characteristic Kibble-Zurek scaling behavior in the defect production. Second, we extend the scaling properties to the defect fluctuations, which enables us to extract the correlation length and dynamical exponents of the underlying the exceptional point (EP) and therefore to gain direct experimental information about the universality class of the EPs. Our work represents a step toward increasing the experimental complexity of non-Hermitian quantum time evolution, as part of the quest to move the frontier from single-particle physics toward increasingly complex settings.

We use quantum scattering theory to study a fixed quantum system $Y$ subject to collisions with massive particles $X$ described by wave packets. We derive the scattering map for system $Y$ and show that the induced evolution crucially depends on the width of the incident wave packets compared to the level spacing in $Y$. If $Y$ is nondegenerate, sequential collisions with narrow wave packets cause $Y$ to decohere. Moreover, an ensemble of narrow packets produced by thermal effusion causes $Y$ to thermalize. On the other hand, broad wave packets can act as a source of coherences for $Y$, even in the case of an ensemble of incident wave packets given by the effusion distribution, preventing thermalization. We illustrate our findings on several simple examples and discuss the consequences of our results in realistic experimental situations.

Quantum random access memory (QRAM)—memory which stores classical data but allows queries to be performed in superposition—is required for the implementation of numerous quantum algorithms. While naive implementations of QRAM are highly susceptible to decoherence and hence not scalable, it has been argued that the bucket-brigade QRAM architecture [Giovannetti et al., Phys. Rev. Lett. 100, 160501 (2008)] is highly resilient to noise, with the infidelity of a query scaling only logarithmically with the memory size. In prior analyses, however, this favorable scaling followed directly from the use of contrived noise models, thus leaving open the question of whether experimental implementations would actually enjoy the purported scaling advantage. In this work, we study the effects of decoherence on QRAM in full generality. Our main result is a proof that this favorable infidelity scaling holds for arbitrary error channels (including, e.g., depolarizing noise and coherent errors). Our proof identifies the origin of this noise resilience as the limited entanglement among the memory’s components, and it also reveals that significant architectural simplifications can be made while preserving the noise resilience. We verify these results numerically using a novel classical algorithm for the efficient simulation of noisy QRAM circuits. Our findings indicate that QRAM can be implemented with existing hardware in realistically noisy devices, and that high-fidelity queries are possible without quantum error correction. Furthermore, we also prove that the benefits of the bucket-brigade architecture persist when quantum error correction is used, in which case the scheme offers improved hardware efficiency and resilience to logical errors.

Quantum simulation, one of the most promising applications of a quantum computer, is currently being explored intensely using the variational quantum eigensolver. The feasibility and performance of this algorithm depend critically on the form of the wave-function ansatz. Recently in Ref. [Nat. Commun. 10, 3007 (2019)], an algorithm termed ADAPT-VQE was introduced to build system-adapted ansätze with substantially fewer variational parameters compared to other approaches. This algorithm relies heavily on a predefined operator pool with which it builds the ansatz. However, Ref. [Nat. Commun. 10, 3007 (2019)] did not provide a prescription for how to select the pool, how many operators it must contain, or whether the resulting ansatz will succeed in converging to the ground state. In addition, the pool used in that work leads to state-preparation circuits that are too deep for a practical application on near-term devices. Here, we address all these key outstanding issues of the algorithm. We present a hardware-efficient variant of ADAPT-VQE that drastically reduces circuit depths using an operator pool that is guaranteed to contain the operators necessary to construct exact ansätze. Moreover, we show that the minimal pool size that achieves this scales linearly with the number of qubits. Through numerical simulations on ${\mathrm{H}}_4$, $\mathrm{Li}\mathrm{H}$ and ${\mathrm{H}}_6$, we show that our algorithm (“qubit-ADAPT”) reduces the circuit depth by an order of magnitude while maintaining the same accuracy as the original ADAPT-VQE. A central result of our approach is that the additional measurement overhead of qubit-ADAPT compared to fixed-ansatz variational algorithms scales only linearly with the number of qubits. Our work provides a crucial step forward in running algorithms on near-term quantum devices.

Electrons confined in silicon quantum dots exhibit orbital, spin, and valley degrees of freedom. The valley degree of freedom originates from the bulk band structure of silicon, which has six degenerate electronic minima. The degeneracy can be lifted in silicon quantum wells due to strain and electronic confinement, but the “valley splitting” of the two lowest-lying valleys is known to be sensitive to atomic scale disorder. Large valley splittings are desirable to have a well-defined spin qubit. In addition, an understanding of the intervalley tunnel coupling that couples different valleys in adjacent quantum dots is extremely important, as the resulting gaps in the energy-level diagram may affect the fidelity of charge- and spin-transfer protocols in silicon quantum-dot arrays. Here we use microwave spectroscopy to probe variations in the valley splitting, and the intra- and intervalley tunnel couplings ($t_{ij}$ and $t_{ij}^{\prime }$) that couple dots $i$ and $j$ in a triple quantum dot. We uncover large variations in the ratio of intervalley to intravalley tunnel couplings $t_{12}^{\prime }/t_{12}=0.90$ and $t_{23}^{\prime }/t_{23}=0.56$. By tuning the interdot tunnel barrier we also show that $t_{ij}^{\prime }$ scales linearly with $t_{ij}$, as expected from theory. The results indicate strong interactions between different valley states on neighboring dots, which we attribute to local inhomogeneities in the silicon quantum well.