Superconducting metamaterials are a promising resource for quantum-information science. In the context of circuit QED, they provide a means to engineer on-chip dispersion relations and a band structure that could ultimately be utilized for generating complex entangled states of quantum circuitry, for quantum-reservoir engineering, and as an element for quantum-simulation architectures. Here we report on the development and measurement at millikelvin temperatures of a particular type of circuit metamaterial resonator composed of planar superconducting lumped-element reactances in the form of a discrete left-handed transmission line that is compatible with circuit QED architectures. We discuss the details of the design, fabrication, and circuit properties of this system. As well, we provide an extensive characterization of the dense mode spectrum in these metamaterial resonators, which we conduct using both microwave-transmission measurements and laser-scanning microscopy. Results are observed to be in good quantitative agreement with numerical simulations and also an analytical model based upon current-voltage relationships for a discrete transmission line. In particular, we demonstrate that the metamaterial mode frequencies, spatial profiles of current and charge densities, and damping due to external loading can be readily modeled and understood, making this system a promising tool for future use in quantum-circuit applications and for studies of complex quantum systems.

Quantum-limited Josephson parametric amplifiers are crucial components in circuit QED readout chains. The dynamic range of state-of-the-art parametric amplifiers is limited by signal-induced Stark shifts that detune the amplifier from its operating point. Using a superconducting nonlinear asymmetric inductive element (SNAIL) as an active component, we show the ability to in situ tune the device flux and pump to a dressed Kerr-free operating point, which provides a 10-fold increase in the number of photons that can be processed by our amplifier, compared to the nominal operating point. Our proposed and experimentally verified methodology of Kerr-free three-wave mixing can be extended to improve the dynamic range of other pumped operations in quantum superconducting circuits.

Large-scale fiber-based quantum networks will likely employ telecommunication-wavelength photons of around 1550 nm wavelength to exchange quantum information between remote nodes, and quantum memories, ideally operating at the same wavelength, that allow the transmission distances to be increased, as key elements of a quantum repeater. However, the development of a suitable memory remains an ongoing challenge. Here, we demonstrate the storage and reemission of single heralded 1532-nm-wavelength photons using a crystal waveguide. The photons are emitted from a photon-pair source based on spontaneous parametric down-conversion and the memory is based on an atomic frequency comb of 6 GHz bandwidth, prepared through persistent spectral-hole burning of the inhomogeneously broadened absorption line of a cryogenically cooled erbium-doped lithium niobate waveguide. Despite currently limited storage time and efficiency, this demonstration represents an important step toward quantum networks that operate in the telecommunication band and the development of integrated (on-chip) quantum technology using industry-standard crystals.

We demonstrate that a photonic gauge potential, which arises from the phase degree of freedom in dynamic refractive-index modulation and hence is achormatic, can be used to achieve a broadband optical switch using the configuration of a photonic Aharonov-Bohm interferometer (ABI). The resulting ABI switch has a far larger bandwidth and lower cross talk than the conventional Mach-Zehnder interferometer. Using coupled-mode theory and full-wave numerical modeling, we compare the response of the two interferometers in the presence of nonidealities. Our results indicate the importance of the photonic gauge potential for broadband optical signal processing.

Laguerre-Gaussian (LG) beams and their orbital angular momentum (OAM) have found a plethora of applications—from quantum information to gravitational-wave detection. In this work, we probe the OAM of LG beams by using a digital micromirror device programmed as a single slit. We observe the diffraction patterns of the beams through the slit and we show that we can determine the OAM of the incoming beams from the changes in the diffraction pattern as the slit is moved transversely. Moreover, we demonstrate that we can access higher OAM modes compared to previous works involving slit diffraction. Our results are valuable in the study of OAM especially for beams where the current technology for detection is not yet mature, for example, beams whose wavelengths are in the terahertz regime or beams of higher energy such as, electron vortex beams.

A key requirement to perform simulations of large quantum systems on near-term quantum hardware is the design of quantum algorithms with a short circuit depth that finish within the available coherence time. A way to stay within the limits of coherence is to reduce the number of gates by implementing a gate set that matches the requirements of the specific algorithm of interest directly in the hardware. Here, we show that exchange-type gates are a promising choice for simulating molecular eigenstates on near-term quantum devices since these gates preserve the number of excitations in the system. We report on the experimental implementation of a variational algorithm on a superconducting qubit platform to compute the eigenstate energies of molecular hydrogen. We utilize a parametrically driven tunable coupler to realize exchange-type gates that are configurable in amplitude and phase on two fixed-frequency superconducting qubits. With gate fidelities around 95%, we are able to compute the eigenstates to within an accuracy of 50 mHa (milliHartree) on average, a limit set by the coherence time of the tunable coupler.

The variational quantum eigensolver (VQE) is an attractive possible application of near-term quantum computers. Originally, the aim of the VQE is to find a ground state for a given specific Hamiltonian. It is achieved by minimizing the expectation value of the Hamiltonian with respect to an ansatz state by tuning parameters $\mathit{\theta }$ on a quantum circuit, which constructs the ansatz. Here we consider an extended problem of the VQE, namely, our objective in this work is to “generalize” the optimized output of the VQE just like machine learning. We aim to find ground states for a given set of Hamiltonians $\{H(\mathbf{x})\}$, where $\mathbf{x}$ is a parameter that specifies the quantum system under consideration, such as geometries of atoms of a molecule. Our approach is to train the circuit on the small number of $\mathbf{x}$’s. Specifically, we employ the interpolation of the optimal circuit parameter determined at different $\mathbf{x}$’s, assuming that the circuit parameter $\mathit{\theta }$ has simple dependency on a hidden parameter $\mathbf{x}$ as $\mathit{\theta }(\mathbf{x})$. We show by numerical simulations that, using an ansatz, which we call the Hamiltonian-alternating ansatz, the optimal circuit parameters can be interpolated to give near-optimal ground states in between the trained $\mathbf{x}$’s. The proposed method can greatly reduce, on a rough estimation by a few orders of magnitude, the time required to obtain ground states for different Hamiltonians by the VQE. Once generalized, the ansatz circuit can predict the ground state without optimizing the circuit parameter $\mathit{\theta }$ in a certain range of $\mathbf{x}$.

We measure the temperature dependence of the two-photon absorption and optical Kerr nonlinearity of a silicon waveguide over a range of temperatures from 5.5 to 300 K. Measurements are taken at a wavelength of 1.55 $\mu \mathrm{m}$ in the technologically important telecom $\mathrm{C}$ band. We observe a near halving (45% reduction) of the two-photon absorption coefficient at low temperature, whereas a smaller reduction in the Kerr nonlinearity of 25% is found. The increased ratio of Kerr to absorptive nonlinearity at low temperatures indicates an improved operation of integrated photonic devices that make use of a nonlinear phase shift, such as optical switches or parametric photon-pair sources. As an example, we examine how the heralding efficiency of a photon-pair source will change at low temperatures and predict a modest improvement in source performance. In addition, the modeling and experimental techniques developed can readily be extended to other wavelengths or materials of interest.

We investigate alternative annealing schedules on the current generation of quantum-annealing hardware (the D-Wave 2000Q), which includes the use of forward and reverse annealing with an intermediate pause. This work provides new insights into the inner workings of these devices (and quantum devices in general), particularly into how thermal effects govern the system dynamics. We show that a pause midway through the anneal can cause a dramatic change in the output distribution, and we provide evidence suggesting thermalization is indeed occurring during such a pause. We demonstrate that upon pausing the system in a narrow region shortly after the minimum gap, the probability of successfully finding the ground state of the problem Hamiltonian can be increased over an order of magnitude. We relate this effect to relaxation (i.e., thermalization) after diabatic and thermal excitations that occur in the region near to the minimum gap. For a set of large-scale problems of up to 500 qubits, we demonstrate that the distribution returned from the annealer very closely matches a (classical) Boltzmann distribution of the problem Hamiltonian, albeit one with a temperature at least 1.5 times higher than the (effective) temperature of the annealer. Moreover, we show that larger problems are more likely to thermalize to a classical Boltzmann distribution.

A dynamical quantum phase transition can occur during time evolution of sudden quenched quantum systems across a phase transition. It corresponds to the nonanalytic behavior at a critical time of the rate function of the quantum-state return amplitude, analogous to nonanalyticity of the free-energy density at the critical temperature in macroscopic systems. A variety of many-body systems can be represented in momentum space as a spin-1/2 state evolving on the Bloch sphere, where each momentum mode is decoupled and thus can be simulated independently by a single qubit. Here, we report the observation of a dynamical quantum phase transition in a superconducting qubit simulation of the quantum-quench dynamics of many-body systems. We take the Ising model with a transverse field as an example for demonstration. In our experiment, the spin state, which is initially polarized longitudinally, evolves based on a Hamiltonian with adjustable parameters depending on the momentum and strength of the transverse magnetic field. The time-evolving quantum state is read out by state tomography. Evidence of dynamical quantum phase transitions, such as paths of time-evolution states on the Bloch sphere, nonanalytic behavior of the dynamical free energy, and the emergence of Skyrmion lattice in momentum-time space, is observed. The experimental data agrees well with theoretical and numerical calculations. The experiment demonstrates explicitly the topological invariant, both topologically trivial and nontrivial, for dynamical quantum phase transitions. Our results show that the quantum phase transitions of this class of many-body system can be simulated successfully with a single qubit by varying certain control parameters over the corresponding momentum range.

Strong magnetic field gradients can produce a synthetic spin-orbit interaction that allows high-fidelity electrical control of single electron spins. We investigate how a field gradient impacts the spin relaxation time $T_1$ by measuring $T_1$ as a function of the magnetic field $B$ in silicon. The interplay of charge noise, magnetic field gradients, phonons, and conduction-band valleys leads to a maximum relaxation time of $160\mathrm{ms}$ at low fields, a strong spin-valley relaxation hotspot at intermediate fields, and a $B^4$ scaling at high fields. $T_1$ is found to decrease with increasing lattice temperature as well as with added electrical noise. In comparison, samples without micromagnets have a significantly greater $T_1$.

Dispersive sensing is a powerful technique that enables scalable and high-fidelity readout of solid-state quantum bits. In particular, gate-based dispersive sensing has been proposed as the readout mechanism for future topological qubits, which can be measured by single electrons tunneling through zero-energy modes. The development of such a readout requires resolving the coherent charge tunneling amplitude from a quantum dot in a Majorana-zero-mode host system faithfully on short time scales. Here, we demonstrate rapid single-shot detection of a coherent single-electron tunneling amplitude between $\mathrm{In}\mathrm{As}$ nanowire quantum dots. We realize a sensitive dispersive detection circuit by connecting a sub-GHz, lumped-element microwave resonator to a high-lever arm gate on one of the dots. The resulting large dot-resonator coupling leads to an observed dispersive shift that is of the order of the resonator linewidth at charge degeneracy. This shift enables us to differentiate between Coulomb blockade and resonance—corresponding to the scenarios expected for qubit-state readout—with a signal-to-noise ratio exceeding 2 for an integration time of $1\mu \mathrm{s}$. Our result paves the way for single-shot measurements of fermion parity on microsecond time scales in topological qubits.

We present a design for a superconducting, on-chip circulator composed of dynamically modulated transfer switches and delays. Design goals are set for the multiplexed readout of superconducting qubits. Simulations of the device show that it allows for low-loss circulation (insertion loss $<0.35$ dB and isolation $>20$ dB) over an instantaneous bandwidth of 2.3 GHz. This design improves on the bandwidth of previous superconducting circulators by more than an order of magnitude, making it ideal for integration with broadband quantum-limited amplifiers.

Whispering-gallery-(WG) mode resonators are machined from a boule of single-crystal isotopically pure silicon-28. Before machining, the as-grown rod is measured in a cavity, with the best Bragg confined modes exhibiting microwave $Q$ factors on the order of a million for frequencies between 10 and 15 GHz. After machining the rod into smaller cylindrical WG-mode resonators, the frequencies of the fundamental mode families are used to determine the relative permittivity of the material to be $11.488\pm 0.024$ near 4 K, with the precision limited only by the dimensional accuracy of the resonator. However, the machining degraded the $Q$ factors to below $4\times {10}^4$. Raman spectroscopy is used to optimize postmachining surface treatments to restore high-$Q$-factors. This is an enabling step for the use of such resonators for hybrid quantum systems and frequency-conversion applications, as silicon-28 also has very low phonon losses, can host very narrow linewidth spin ensembles, and is a material commonly used in optical applications.

Silicon is the most-developed electronic and photonic technological platform and hosts some of the highest-performance spin and photonic qubits developed to date. A hybrid quantum technology harnessing an efficient spin-photon interface in silicon would unlock considerable potential by enabling ultralong-lived photonic memories, distributed quantum networks, microwave-to-optical photon converters, and spin-based quantum processors, all linked with integrated silicon photonics. However, the indirect band gap of silicon makes identification of efficient spin-photon interfaces nontrivial. Here we build upon the recent identification of chalcogen donors as a promising spin-photon interface in silicon. We determine that the spin-dependent optical degree of freedom has a transition dipole moment stronger than previously thought [here 1.96(8) D], and the spin $T_1$ lifetime in low magnetic fields is longer than previously thought [here longer than $4.6(1.5)$ h]. We furthermore determine the optical excited-state lifetime [7.7(4) ns], and therefore the natural radiative efficiency [0.80(9)%], and by measuring the phonon sideband determine the zero-phonon emission fraction [16(1)%]. Taken together, these parameters indicate that an integrated quantum optoelectronic platform based on chalcogen-donor qubits in silicon is well within reach of current capabilities.

High-fidelity entangling quantum gates based on Rydberg interactions are required for scalable quantum computing with neutral atoms. Their realization, however, meets a major stumbling block—the motion-induced dephasing of the transition between the ground and Rydberg states. By using quantum interference between different detuned Rabi oscillations, we propose a practical scheme to realize a class of accurate entangling Rydberg quantum gates subject to a minimal dephasing error. We show two types of such gates, $U_1$ and $U_2$, in the form of $\mathrm{diag}\{1,e^{i\alpha },e^{i\gamma },e^{i\beta }\}$, where $\alpha$, $\gamma$, and $\beta$ are determined by the parameters of lasers and the Rydberg blockade $V$. $U_1$ is realized by sending to the two qubits a single off-resonant laser pulse, while $U_2$ is realized by individually applying one pulse of detuned laser to each qubit. One can construct the controlled-$z$ ($C_Z$) gate from several $U_1$’s when assisted by single-qubit rotations and phase gates or from two $U_2$’s and two phase gates. Our method has several advantages. First, the gates are accurate because the fidelity of $U_k$ is limited only by a rotation error below ${10}^{-5}$ and the Rydberg-state decay. Decay error on the order of ${10}^{-5}$ can be easily obtained because all transitions are detuned, resulting in a small population in the Rydberg state. Second, the motion-induced dephasing is minimized because there is no gap time in which a population is left in the Rydberg shelving states of either qubit. Third, the gate is resilient to the variation of $V$. This is because among the three phases $\alpha$, $\gamma$, and $\beta$, only the last has a (partial) dependence on $V$. Fourth, the Rabi frequency and $V$ in our scheme are of similar magnitude, which permits a fast implementation of the gate when both of them are of the feasible magnitude of several megahertz. The rapidity, accuracy, and feasibility of this interference method can lay the foundation for entangling gates in universal quantum computing with neutral atoms.

We present and analyze a hybrid quantum system that interfaces a Majorana-hosted semiconductor nanowire with a single nitrogen-vacancy (N-V) center via a magnetized torsional cantilever. We show that the torsional mode of the mechanical resonator can strongly couple to the Majorana qubit and the spin qubit simultaneously, which allows us to interface them for quantum-state conversion through a dark-state protocol. This work provides a promising interface between the topological qubit and the conventional spin qubit. This interface may have interesting applications in quantum information and computation.

Dynamical decoupling can enforce a symmetry on the dynamics of an open quantum system. Here we develop an efficient dynamical-decoupling-based strategy to create the decoherence-free subspaces for a set of qubits by optimally transferring the states of these qubits. Our method is to transfer the state of each qubit to all of the other qubits in an optimal and efficient manner, so as to produce an effective collective-type noise for all qubits. This collective pseudonoise is essentially derived from arbitrarily independent real baths and needs only nearest-neighbor state transfers for its implementation. Moreover, our scheme requires only $N$ steps to produce the effective collective-type noise for a system of $N$ qubits. It provides an experimentally feasible and efficient approach to achieving the decoherence-free subspaces for encoding the protected logical qubits.

Scalable spin-to-photon interfaces require quantum emitters with strong optical-transition dipole moment and low coupling to phonons and stray electric fields. It is known that particularly for coupling to stray electric fields, these conditions can be simultaneously satisfied for emitters that show inversion symmetry. Here, we show that inversion symmetry is not a prerequisite criterion for a spectrally stable quantum emitter. We find that identical electron density in ground and excited states can eliminate the coupling to the stray electric fields. Further, a strong optical-transition dipole moment is achieved in systems with altering sign of the ground and excited wave functions. We use density-functional perturbation theory to investigate an optical center that lacks inversion symmetry. Our results show that this system close to ideally satisfies the criteria for an ideal quantum emitter. Our study opens an additional rationale in seeking promising materials and point defects towards the realization of robust spin-to-photon interfaces.

We demonstrate that a high kinetic inductance disordered-superconductor nanowire can realize a circuit element – known as a superinductor – with a characteristic impedance greater than the quantum resistance ($R_Q=h/4e^2\simeq 6.5\mathrm{k}\mathrm{\Omega }$) and a quality factor of 25 000 at single-photon excitation. By examining loss rates, we demonstrate that the microwave dissipation can be fully understood in the framework of two-level-system dielectric loss. Superinductors can suppress the quantum fluctuations of charge in a circuit, which has applications, for example, in devices for quantum computing, photon detection, and other sensors based on mesoscopic circuits.