Qubit Architecture with High Coherence and Fast Tunable Coupling

Deterministic quantum state and gate teleportation between distant superconducting chips

Quantum teleportation is of both fundamental interest and great practical importance in quantum information science. To date, quantum teleportation has been implemented in various physical systems, among which superconducting qubits are of particular practical significance as they emerge as a leading system to realize large-scale quantum computation. Nevertheless, scaling up the number of superconducting qubits on a single chip becomes increasing challenging because of some emergent technical difficulties. Realization of quantum teleportation and remote computation over qubits on distant superconducting chips is a key quantum communication technology to scaling up the system through a distributed quantum computational network. However, this goal has not been realized yet in experiments due to the technical challenges including making a quantum interconnect between distant superconducting chips and the inefficient transfer of flying microwave photons over the lossy interconnects. Here we demonstrate deterministic teleportation of quantum states and entangling gates between distant superconducting chips connected by a 64-m-long cable bus featuring an ultralow loss of 0.32 dB/km at cryogenic temperatures, where high fidelity remote entanglement is generated via flying microwave photons. Our work demonstrates a prime building block for distributed quantum computation with superconducting qubits, and opens up a new avenue for waveguide quantum electrodynamics and quantum photonics at microwave frequencies.

Demonstration of two qubit entangling gates in a 2D ring resonator based coupler architecture

We report entangling two-qubit experiments implemented in a novel ring resonator architecture in 2D planar geometry. The ring resonator acts as a multi-path coupler between qubits and can provide beyond nearest neighbour interactions. We demonstrate pairwise coupling between three fixed-frequency transmon qubits connected to the ring resonator with measured coupling strengths (4.70 MHz, 2.80 MHz, and 2.65 MHz) in good agreement with those predicted from finite-element simulations. We implement an all-microwave controlled phase (CPHASE) gate between a pair of qubits with a gate time of 196 ns and demonstrate a two-qubit Bell state with a measured state fidelity of [Formula: see text]. Our results demonstrate the ability to entangle two qubits using the ring resonator and pave the way for creating highly connected multi-qubit networks in this architecture.

Quantum correlations and parameter estimation for two superconducting qubits interacting with a quantized field

In the present manuscript, we introduce a quantum system of two superconducting qubits (S-Qs) interacting with a quantized field under the influence of the Kerr nonlinear medium and Ising interaction. We formulate the Hamiltonian of the quantum model and determine the density operator of whole quantum system as well as quantum subsystems. We examine the dynamics of the quantumness measures for subsequent times including the S-Qs entanglement, S-Qs-field entanglement and quantum Fisher information in relation to the system parameters. Finally, we display the connection among the measures of quantumness during the time evolution.

Scalable interconnection using a superconducting flux qubit

Superconducting quantum computers are rapidly reaching scales where bottlenecks to scaling arise from the practical aspects of the fabrication process. To improve quantum computer performance, implementation technology that guarantees the scalability of the number of qubits is essential. Increasing the degrees of freedom in routing by 2.5-dimensional implementation is important for realizing circuit scalability. We report an implementation technology to overcome the scaling bottlenecks using a reliable connection qubit with a demonstration of quantum annealing. The method comprises interconnection based on quantum annealing using a superconducting flux qubit, precise coupling status control, and flip-chip bonding. We perform experiments and simulations with a proof-of-concept demonstration of qubit coupling via interconnection using a flux qubit. The coupling status is strictly controllable by quantum annealing. A low-temperature flip-chip bonding technology is introduced for the 2.5-dimensional interconnection. The superconducting flux qubit, formed across two different chips via bumps, is demonstrated for the first time to show a state transition like that in a conventional qubit. The quantum annealing flux qubit and flip-chip bonding enable new interconnections between qubits. A perspective on the possibility of applying this technology to the connection between gate-type qubits is described.

A cryogenic on-chip microwave pulse generator for large-scale superconducting quantum computing

For superconducting quantum processors, microwave signals are delivered to each qubit from room-temperature electronics to the cryogenic environment through coaxial cables. Limited by the heat load of cabling and the massive cost of electronics, such an architecture is not viable for millions of qubits required for fault-tolerant quantum computing. Monolithic integration of the control electronics and the qubits provides a promising solution, which, however, requires a coherent cryogenic microwave pulse generator that is compatible with superconducting quantum circuits. Here, we report such a signal source driven by digital-like signals, generating pulsed microwave emission with well-controlled phase, intensity, and frequency directly at millikelvin temperatures. We showcase high-fidelity readout of superconducting qubits with the microwave pulse generator. The device demonstrated here has a small footprint, negligible heat load, great flexibility to operate, and is fully compatible with today's superconducting quantum circuits, thus providing an enabling technology for large-scale superconducting quantum computers.

Bidirectional Multiphoton Communication between Remote Superconducting Nodes

Quantum communication test beds provide a useful resource for experimentally investigating a variety of communication protocols. Here we demonstrate a superconducting circuit test bed with bidirectional multiphoton state transfer capability using time-domain shaped wave packets. The system we use to achieve this comprises two remote nodes, each including a tunable superconducting transmon qubit and a tunable microwave-frequency resonator, linked by a 2 m-long superconducting coplanar waveguide, which serves as a transmission line. We transfer both individual and superposition Fock states between the two remote nodes, and additionally show that this bidirectional state transfer can be done simultaneously, as well as being used to entangle elements in the two nodes.

State preparation in a Jaynes-Cummings lattice with quantum optimal control

High-fidelity preparation of quantum states in an interacting many-body system is often hindered by the lack of knowledge of such states and by limited decoherence times. Here, we study a quantum optimal control (QOC) approach for fast generation of quantum ground states in a finite-sized Jaynes-Cummings lattice with unit filling. Our result shows that the QOC approach can generate quantum many-body states with high fidelity when the evolution time is above a threshold time, and it can significantly outperform the adiabatic approach. We study the dependence of the threshold time on the parameter constraints and the connection of the threshold time with the quantum speed limit. We also show that the QOC approach can be robust against control errors. Our result can lead to advances in the application of the QOC to many-body state preparation.

Variational Quantum Simulators Based on Waveguide QED

Waveguide QED simulators are analog quantum simulators made by quantum emitters interacting with one-dimensional photonic band gap materials. One of their remarkable features is that they can be used to engineer tunable-range emitter interactions. Here, we demonstrate how these interactions can be a resource to develop more efficient variational quantum algorithms for certain problems. In particular, we illustrate their power in creating wave function Ansätze that capture accurately the ground state of quantum critical spin models (XXZ and Ising) with fewer gates and optimization parameters than other variational Ansätze based on nearest-neighbor or infinite-range entangling gates. Finally, we study the potential advantages of these waveguide Ansätze in the presence of noise. Overall, these results evidence the potential of using the interaction range as a variational parameter and place waveguide QED simulators as a promising platform for variational quantum algorithms.

Splitting phonons: Building a platform for linear mechanical quantum computing

Linear optical quantum computing provides a desirable approach to quantum computing, with only a short list of required computational elements. The similarity between photons and phonons points to the interesting potential for linear mechanical quantum computing using phonons in place of photons. Although single-phonon sources and detectors have been demonstrated, a phononic beam splitter element remains an outstanding requirement. Here we demonstrate such an element, using two superconducting qubits to fully characterize a beam splitter with single phonons. We further use the beam splitter to demonstrate two-phonon interference, a requirement for two-qubit gates in linear computing. This advances a new solid-state system for implementing linear quantum computing, further providing straightforward conversion between itinerant phonons and superconducting qubits.

Observing the quantum topology of light

Topological photonics provides a powerful platform to explore topological physics beyond traditional electronic materials and shows promising applications in light transport and lasers. Classical degrees of freedom are routinely used to construct topological light modes in real or synthetic dimensions. Beyond the classical topology, the inherent quantum nature of light provides a wealth of fundamentally distinct topological states. Here we implement experiments on topological states of quantized light in a superconducting circuit, with which one- and two-dimensional Fock-state lattices are constructed. We realize rich topological physics including topological zero-energy states of the Su-Schrieffer-Heeger model, strain-induced pseudo-Landau levels, valley Hall effect, and Haldane chiral edge currents. Our study extends the topological states of light to the quantum regime, bridging topological phases of condensed-matter physics with circuit quantum electrodynamics, and offers a freedom in controlling the quantum states of multiple resonators.

High-Quality Ferromagnetic Josephson Junctions Based on Aluminum Electrodes

Aluminum Josephson junctions are the building blocks for the realization of superconducting quantum bits. Attention has been also paid to hybrid ferromagnetic Josephson junctions, which allow switching between different magnetic states, making them interesting for applications such as cryogenic memories, single-photon detectors, and spintronics. In this paper, we report on the fabrication and characterization of high-quality ferromagnetic Josephson junctions based on aluminum technology. We employed an innovative fabrication process inspired by niobium-based technology, allowing us to obtain very high-quality hybrid aluminum Josephson junctions; thus, supporting the use of ferromagnetic Josephson junctions in advanced quantum circuits. The fabrication process is described in detail and the main DC transport properties at low temperatures (current-voltage characteristic, critical current as a function of the temperature, and the external magnetic field) are reported. Here, we illustrate in detail the fabrication process, as well as the main DC transport properties at low temperatures (current-voltage characteristic, critical current as a function of the temperature, and the external magnetic field).

Fast Driving of a Particle in Two Dimensions without Final Excitation

Controlling the motional state of a particle in a multidimensional space is key for fundamental science and quantum technologies. Applying a recently found two-dimensional invariant combined with linear invariants, we propose protocols to drive a particle in two dimensions so that the final harmonic trap is translated and rotated with respect to the initial one. These protocols realize a one-to-one mapping between initial and final eigenstates at some predetermined time and avoid any final excitations.

Hamiltonian Engineering with Multicolor Drives for Fast Entangling Gates and Quantum Crosstalk Cancellation

Quantum computers built with superconducting artificial atoms already stretch the limits of their classical counterparts. While the lowest energy states of these artificial atoms serve as the qubit basis, the higher levels are responsible for both a host of attractive gate schemes as well as generating undesired interactions. In particular, when coupling these atoms to generate entanglement, the higher levels cause shifts in the computational levels that lead to unwanted ZZ quantum crosstalk. Here, we present a novel technique to manipulate the energy levels and mitigate this crosstalk with simultaneous off-resonant drives on coupled qubits. This breaks a fundamental deadlock between qubit-qubit coupling and crosstalk. In a fixed-frequency transmon architecture with strong coupling and crosstalk cancellation, additional cross-resonance drives enable a 90 ns CNOT with a gate error of (0.19±0.02)%, while a second set of off-resonant drives enables a novel CZ gate. Furthermore, we show a definitive improvement in circuit performance with crosstalk cancellation over seven qubits, demonstrating the scalability of the technique. This Letter paves the way for superconducting hardware with faster gates and greatly improved multiqubit circuit fidelities.

Realization of an Error-Correcting Surface Code with Superconducting Qubits

Quantum error correction is a critical technique for transitioning from noisy intermediate-scale quantum devices to fully fledged quantum computers. The surface code, which has a high threshold error rate, is the leading quantum error correction code for two-dimensional grid architecture. So far, the repeated error correction capability of the surface code has not been realized experimentally. Here, we experimentally implement an error-correcting surface code, the distance-three surface code which consists of 17 qubits, on the Zuchongzhi 2.1 superconducting quantum processor. By executing several consecutive error correction cycles, the logical error can be significantly reduced after applying corrections, achieving the repeated error correction of surface code for the first time. This experiment represents a fully functional instance of an error-correcting surface code, providing a key step on the path towards scalable fault-tolerant quantum computing.

Partial randomized benchmarking

In randomized benchmarking of quantum logical gates, partial twirling can be used for simpler implementation, better scaling, and higher accuracy and reliability. For instance, for two-qubit gates, single-qubit twirling is easier to realize than full averaging. We analyze such simplified, partial twirling and demonstrate that, unlike for the standard randomized benchmarking, the measured decay of fidelity is a linear combination of exponentials with different decay rates (3 for two qubits and single-bit twirling). The evolution with the sequence length is governed by an iteration matrix, whose spectrum gives the decay rates. For generic two-qubit gates one slowest exponential dominates and characterizes gate errors in three channels. Its decay rate is close, but different from that in the standard randomized benchmarking, and we find the leading correction. Using relations to the local invariants of two-qubit gates we identify all exceptional gates with several slow exponentials and analyze possibilities to extract their decay rates from the measured curves.

Circuit quantum electrodynamics simulator of the two-dimensional Su-Schrieffer-Heeger model: higher-order topological phase transition induced by a continuously varying magnetic field

Higher-order topological insulator (HOTI) occupies an important position in topological band theory due to its exotic bulk-edge correspondence. Recently, it has been predicted that external magnetic field can induce novel topological phases in 2D HOTIs. However, up to now the theoretical description is still incomplete and the experimental realization is still lacking. Here we proposed a superconducting quantum circuit simulator of 2D Su-Schriffer-Heeger lattice, which is one of the most celebrated HOTI models, and investigate consequently the influence of the continuously varying magnetic field. By using the parametric conversion coupling method, we can establish in principle the time- and site-resolved tunable hopping constants in the proposed architecture, thus providing an ideal platform for investigating the higher-order topological phase transitions induced by continuously varying magnetic field. Our numerical calculation further shows that the higher-order topology of the lattice, which manifests itself through the existence of the zero energy corner modes, exhibit exotic and rich dependence on the imposed magnetic field and the inhomogeneous hopping strength. To probe the proposed magnetic-field-induced topological phase transition, we study the response of the lattice to the corner site pumping in the steady state limit, with results implying that the predicted topological phase boundaries can be unambiguously identified by the measurement of the corner sites and their few neighbors. Requiring only current level of technology, our scheme can be readily tested in experiment and may pave an alternative way towards the future investigation of HOTIs under various mechanisms including magnetic field, disorder, and strong correlation.

Entanglement Purification and Protection in a Superconducting Quantum Network

High-fidelity quantum entanglement is a key resource for quantum communication and distributed quantum computing, enabling quantum state teleportation, dense coding, and quantum encryption. Any sources of decoherence in the communication channel, however, degrade entanglement fidelity, thereby increasing the error rates of entangled state protocols. Entanglement purification provides a method to alleviate these nonidealities by distilling impure states into higher-fidelity entangled states. Here we demonstrate the entanglement purification of Bell pairs shared between two remote superconducting quantum nodes connected by a moderately lossy, 1-meter long superconducting communication cable. We use a purification process to correct the dominant amplitude damping errors caused by transmission through the cable, with fractional increases in fidelity as large as 25%, achieved for higher damping errors. The best final fidelity the purification achieves is 94.09±0.98%. In addition, we use both dynamical decoupling and Rabi driving to protect the entangled states from local noise, increasing the effective qubit dephasing time by a factor of 4, from 3 to 12  μs. These methods demonstrate the potential for the generation and preservation of very high-fidelity entanglement in a superconducting quantum communication network.

Dissipative Topological Phase Transition with Strong System-Environment Coupling

A primary motivation for studying topological matter regards the protection of topological order from its environment. In this work, we study a topological emitter array coupled to an electromagnetic environment. The photon-emitter coupling produces nonlocal interactions between emitters. Using periodic boundary conditions for all ranges of environment-induced interactions, the chiral symmetry inherent to the emitter array is preserved. This chiral symmetry protects the Hamiltonian and induces parity in the Lindblad operator. A topological phase transition occurs at a critical photon-emitter coupling related to the energy spectrum width of the emitter array. Interestingly, the critical point nontrivially changes the dissipation rates of edge states, yielding a dissipative topological phase transition. In the protected topological phase, edge states suffer from environment-induced dissipation for weak photon-emitter coupling. However, strong coupling leads to robust dissipationless edge states with a window at the emitter spacing. Our work shows the potential to manipulate topological quantum matter with electromagnetic environments.

Demonstration of a High-Fidelity cnot Gate for Fixed-Frequency Transmons with Engineered ZZ Suppression

Improving two-qubit gate performance and suppressing cross talk are major, but often competing, challenges to achieving scalable quantum computation. In particular, increasing the coupling to realize faster gates has been intrinsically linked to enhanced cross talk due to unwanted two-qubit terms in the Hamiltonian. Here, we demonstrate a novel coupling architecture for transmon qubits that circumvents the standard relationship between desired and undesired interaction rates. Using two fixed frequency coupling elements to tune the dressed level spacings, we demonstrate an intrinsic suppression of the static ZZ while maintaining large effective coupling rates. Our architecture reveals no observable degradation of qubit coherence (T_{1},T_{2}>100  μs) and, over a factor of 6 improvement in the ratio of desired to undesired coupling. Using the cross-resonance interaction, we demonstrate a 180 ns single-pulse controlled not (cnot) gate, and measure a cnot fidelity of 99.77(2)% from interleaved randomized benchmarking.

Impact of Spectators on a Two-Qubit Gate in a Tunable Coupling Superconducting Circuit

Cross-resonance (CR) gates have emerged as a promising scheme for fault-tolerant quantum computation with fixed-frequency qubits. We experimentally implement an entangling CR gate by using a microwave-only control in a tunable coupling superconducting circuit, where the tunable coupler provides extra degrees of freedom to verify optimal conditions for constructing a CR gate. By developing a three-qubit Hamiltonian tomography protocol, we systematically investigate the dependency of gate fidelities on spurious qubit interactions and present the first experimental approach to the evaluation of the perturbation impact arising from spectator qubits. Our results reveal that the spectator qubits lead to reductions in CR gate fidelity dependent on ZZ interactions and particular frequency detunings between spectator and gate qubits. The target spectator demonstrates a more serious impact than the control spectator under a standard echo pulse scheme, whereas the degradation of gate fidelity is observed up to 22.5% as both the spectators are present with a modest ZZ coupling to the computational qubits. Our experiments uncover an optimal CR operation regime, and the method we develop here can readily be applied to improving other kinds of two-qubit gates in large-scale quantum circuits.

One-Photon Solutions to the Multiqubit Multimode Quantum Rabi Model for Fast W-State Generation

General solutions to the quantum Rabi model involve subspaces with an unbounded number of photons. However, for the multiqubit multimode case, we find special solutions with at most one photon for an arbitrary number of qubits and photon modes. Such solutions exist for arbitrary single qubit-photon coupling strength with constant eigenenergy, while still being qubit-photon entangled states. Taking advantage of their peculiarities and the reach of the ultrastrong coupling regime, we propose an adiabatic scheme for the fast and deterministic generation of a two-qubit Bell state and arbitrary single-photon multimode W states with nonadiabatic error less than 1%. Finally, we propose a superconducting circuit design to catch and release the W states, and shows the experimental feasibility of the multimode multiqubit quantum Rabi model.

Accurately computing the electronic properties of a quantum ring

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform^1-4. However, the accuracy needed to outperform classical methods has not been achieved so far. Here, using 18 superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to investigate fundamental electronic properties. We benchmark the underlying method by reconstructing the single-particle band structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors, and measure the energy eigenvalues of this wire with an error of approximately 0.01 rad, whereas typical energy scales are of the order of 1 rad. Insight into the fidelity of this algorithm is gained by highlighting the robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 10^-4 rad. We also synthesize magnetic flux and disordered local potentials, which are two key tenets of a condensed-matter system. When sweeping the magnetic flux we observe avoided level crossings in the spectrum, providing a detailed fingerprint of the spatial distribution of local disorder. By combining these methods we reconstruct electronic properties of the eigenstates, observing persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation^5,6 and paves the way to study new quantum materials with superconducting qubits.

Intermittent decoherence blockade in a chiral ring environment

It has long been recognized that emission of radiation from atoms is not an intrinsic property of individual atoms themselves, but it is largely affected by the characteristics of the photonic environment and by the collective interaction among the atoms. A general belief is that preventing full decay and/or decoherence requires the existence of dark states, i.e., dressed light-atom states that do not decay despite the dissipative environment. Here, we show that, contrary to such a common wisdom, decoherence suppression can be intermittently achieved on a limited time scale, without the need for any dark state, when the atom is coupled to a chiral ring environment, leading to a highly non-exponential staircase decay. This effect, that we refer to as intermittent decoherence blockade, arises from periodic destructive interference between light emitted in the present and light emitted in the past, i.e., from delayed coherent quantum feedback.

High-Fidelity Controlled-Z Gate with Maximal Intermediate Leakage Operating at the Speed Limit in a Superconducting Quantum Processor

Simple tuneup of fast two-qubit gates is essential for the scaling of quantum processors. We introduce the sudden variant (SNZ) of the net zero scheme realizing controlled-Z (CZ) gates by flux control of transmon frequency. SNZ CZ gates realized in a multitransmon processor operate at the speed limit of transverse coupling between computational and noncomputational states by maximizing intermediate leakage. Beyond speed, the key advantage of SNZ is tuneup simplicity, owing to the regular structure of conditional phase and leakage as a function of two control parameters. SNZ is compatible with scalable schemes for quantum error correction and adaptable to generalized conditional-phase gates useful in intermediate-scale applications.

Topological Two-Dimensional Floquet Lattice on a Single Superconducting Qubit

Current noisy intermediate-scale quantum (NISQ) devices constitute powerful platforms for analog quantum simulation. The exquisite level of control offered by state-of-the-art quantum computers make them especially promising to implement time-dependent Hamiltonians. We implement quasiperiodic driving of a single qubit in the IBM Quantum Experience and thus experimentally realize a temporal version of the half-Bernevig-Hughes-Zhang Chern insulator. Using simple error mitigation, we achieve consistently high fidelities of around 97%. From our data we can infer the presence of a topological transition, thus realizing an earlier proposal of topological frequency conversion by Martin, Refael, and Halperin. Motivated by these results, we theoretically study the many-qubit case, and show that one can implement a wide class of Floquet Hamiltonians, or time-dependent Hamiltonians in general. Our study highlights promises and limitations when studying many-body systems through multifrequency driving of quantum computers.

New material platform for superconducting transmon qubits with coherence times exceeding 0.3 milliseconds

The superconducting transmon qubit is a leading platform for quantum computing and quantum science. Building large, useful quantum systems based on transmon qubits will require significant improvements in qubit relaxation and coherence times, which are orders of magnitude shorter than limits imposed by bulk properties of the constituent materials. This indicates that relaxation likely originates from uncontrolled surfaces, interfaces, and contaminants. Previous efforts to improve qubit lifetimes have focused primarily on designs that minimize contributions from surfaces. However, significant improvements in the lifetime of two-dimensional transmon qubits have remained elusive for several years. Here, we fabricate two-dimensional transmon qubits that have both lifetimes and coherence times with dynamical decoupling exceeding 0.3 milliseconds by replacing niobium with tantalum in the device. We have observed increased lifetimes for seventeen devices, indicating that these material improvements are robust, paving the way for higher gate fidelities in multi-qubit processors.

Quantum computers based on superconducting transmon qubits are limited by single qubit lifetimes and coherence times, which are orders of magnitude shorter than limits imposed by bulk material properties. Here, the authors fabricate two-dimensional transmon qubits with both lifetimes and coherence times longer than 0.3 milliseconds by replacing niobium with tantalum in the device.

Deterministic multi-qubit entanglement in a quantum network

The generation of high-fidelity distributed multi-qubit entanglement is a challenging task for large-scale quantum communication and computational networks^1-4. The deterministic entanglement of two remote qubits has recently been demonstrated with both photons^5-10 and phonons¹¹. However, the deterministic generation and transmission of multi-qubit entanglement has not been demonstrated, primarily owing to limited state-transfer fidelities. Here we report a quantum network comprising two superconducting quantum nodes connected by a one-metre-long superconducting coaxial cable, where each node includes three interconnected qubits. By directly connecting the cable to one qubit in each node, we transfer quantum states between the nodes with a process fidelity of 0.911 ± 0.008. We also prepare a three-qubit Greenberger-Horne-Zeilinger (GHZ) state^12-14 in one node and deterministically transfer this state to the other node, with a transferred-state fidelity of 0.656 ± 0.014. We further use this system to deterministically generate a globally distributed two-node, six-qubit GHZ state with a state fidelity of 0.722 ± 0.021. The GHZ state fidelities are clearly above the threshold of 1/2 for genuine multipartite entanglement¹⁵, showing that this architecture can be used to coherently link together multiple superconducting quantum processors, providing a modular approach for building large-scale quantum computers^16,17.

Fusing the single-excitation subspace with [Formula: see text]

There is a tremendous interest in developing practical applications for noisy intermediate-scale quantum processors without the overhead required by full error correction. Near-term quantum information processing is especially challenging within the standard gate model, as algorithms quickly lose fidelity as the problem size and circuit depth grow. This has lead to a number of non-gate-model approaches such as analog quantum simulation and quantum annealing. These come with specific hardware requirements that are different than that of a universal gate-based quantum computer. We have previously proposed an approach called the single-excitation subspace (SES) method, which uses a complete graph of superconducting qubits with tunable coupling. Without error correction the SES method is not scalable, but it offers several algorithmic components with constant depth, which is highly desirable for near-term use. The challenge of the SES method is that it requires a physical qubit for every basis state in the computer's Hilbert space. This imposes exponentially large resource costs for algorithms using registers of ancillary qubits, as each ancilla would double the required graph size. Here we show how to circumvent this doubling by leaving the SES and fusing it with a multi-ancilla Hilbert space. Specifically, we implement the tensor product of an SES register holding "data" with one or more ancilla qubits, which are able to independently control arbitrary [Formula: see text] unitary operations on the data in a constant number of steps. This enables a hybrid form of quantum computation where fast SES operations are performed on the data, traditional logic gates and measurements are performed on the ancillas, and controlled-unitaries act between. As example applications, we give ancilla-assisted SES implementations of quantum phase estimation and the quantum linear system solver of Harrow, Hassidim, and Lloyd.

Implementation of Conditional Phase Gates Based on Tunable ZZ Interactions

High fidelity two-qubit gates exhibiting low cross talk are essential building blocks for gate-based quantum information processing. In superconducting circuits, two-qubit gates are typically based either on rf-controlled interactions or on the in situ tunability of qubit frequencies. Here, we present an alternative approach using a tunable cross-Kerr-type ZZ interaction between two qubits, which we realize with a flux-tunable coupler element. We control the ZZ-coupling rate over 3 orders of magnitude to perform a rapid (38 ns), high-contrast, low leakage (0.14±0.24%) conditional phase CZ gate with a fidelity of 97.9±0.7% as measured in interleaved randomized benchmarking without relying on the resonant interaction with a noncomputational state. Furthermore, by exploiting the direct nature of the ZZ coupling, we easily access the entire conditional phase gate family by adjusting only a single control parameter.

High-Fidelity, High-Scalability Two-Qubit Gate Scheme for Superconducting Qubits

High-quality two-qubit gate operations are crucial for scalable quantum information processing. Often, the gate fidelity is compromised when the system becomes more integrated. Therefore, a low-error-rate, easy-to-scale two-qubit gate scheme is highly desirable. Here, we experimentally demonstrate a new two-qubit gate scheme that exploits fixed-frequency qubits and a tunable coupler in a superconducting quantum circuit. The scheme requires less control lines, reduces cross talk effect, and simplifies calibration procedures, yet produces a controlled-Z gate in 30 ns with a high fidelity of 99.5%, derived from the interleaved randomized benchmarking method. Error analysis shows that gate errors are mostly coherence limited. Our demonstration paves the way for large-scale implementation of high-fidelity quantum operations.

Localized photonic states and dynamic process in nonreciprocal coupled Su-Schrieffer-Heeger chain

We investigate the localized photonic states and dynamic process in one-dimensional nonreciprocal coupled Su-Schrieffer-Heeger chain. Through numerical calculation of energy eigenvalue spectrum and state distributions of the system, we find that different localized photonic states with special energy eigenvalues can be induced by the nonreciprocal coupling, such as zero-energy edge states, interface states and bound states with pure imaginary energy eigenvalues. Moreover, we analyze the dynamic process of photonic states in such non-Hermitian system. Interestingly, it is shown that the nonreciprocal coupling has an evident gathering effect on the photons, which also break the trapping effect of topologically protected edge states. In addition, we consider the impacts of on-site defect potentials on the dynamic process of photonic states for the system. It is indicated that the photons go around the defect lattice site and still present the gathering effect, and different forms of laser pulses can be induced with the on-site defect potentials in different lattice sites. Furthermore, we present the method for the quantum simulation of current model based on the circuit quantum electrodynamic lattice.

High-Contrast ZZ Interaction Using Superconducting Qubits with Opposite-Sign Anharmonicity

For building a scalable quantum processor with superconducting qubits, ZZ interaction is of great concern because its residual has a crucial impact to two-qubit gate fidelity. Two-qubit gates with fidelity meeting the criterion of fault-tolerant quantum computation have been demonstrated using ZZ interaction. However, as the performance of quantum processors improves, the residual static ZZ can become a performance-limiting factor for quantum gate operation and quantum error correction. Here, we introduce a superconducting architecture using qubits with opposite-sign anharmonicity, a transmon qubit, and a C-shunt flux qubit, to address this issue. We theoretically demonstrate that by coupling the two types of qubits, the high-contrast ZZ interaction can be realized. Thus, we can control the interaction with a high on-off ratio to implement two-qubit controlled-Z gates, or suppress it during two-qubit gate operation using XY interaction (e.g., an iSWAP gate). The proposed architecture can also be scaled up to multiqubit cases. In a fixed coupled system, ZZ crosstalk related to neighboring spectator qubits could also be heavily suppressed.

High-Fidelity Software-Defined Quantum Logic on a Superconducting Qudit

We present an efficient approach to achieving arbitrary, high-fidelity control of a multilevel quantum system using optimal control techniques. As an demonstration, we implement a continuous, software-defined microwave pulse to realize a 0↔2 SWAP gate that achieves an average gate fidelity of 99.4%. We describe our procedure for extracting the system Hamiltonian, calibrating the quantum and classical hardware chain, and evaluating the gate fidelity. Our work represents an alternative, fully generalizable route towards achieving universal quantum control by leveraging optimal control techniques.

Demonstrating a Continuous Set of Two-Qubit Gates for Near-Term Quantum Algorithms

Quantum algorithms offer a dramatic speedup for computational problems in material science and chemistry. However, any near-term realizations of these algorithms will need to be optimized to fit within the finite resources offered by existing noisy hardware. Here, taking advantage of the adjustable coupling of gmon qubits, we demonstrate a continuous two-qubit gate set that can provide a threefold reduction in circuit depth as compared to a standard decomposition. We implement two gate families: an imaginary swap-like (iSWAP-like) gate to attain an arbitrary swap angle, θ, and a controlled-phase gate that generates an arbitrary conditional phase, ϕ. Using one of each of these gates, we can perform an arbitrary two-qubit gate within the excitation-preserving subspace allowing for a complete implementation of the so-called Fermionic simulation (fSim) gate set. We benchmark the fidelity of the iSWAP-like and controlled-phase gate families as well as 525 other fSim gates spread evenly across the entire fSim(θ,ϕ) parameter space, achieving a purity-limited average two-qubit Pauli error of 3.8×10^{-3} per fSim gate.

Remote Entanglement via Adiabatic Passage Using a Tunably Dissipative Quantum Communication System

Effective quantum communication between remote quantum nodes requires high fidelity quantum state transfer and remote entanglement generation. Recent experiments have demonstrated that microwave photons, as well as phonons, can be used to couple superconducting qubits, with a fidelity limited primarily by loss in the communication channel [P. Kurpiers et al., Nature (London) 558, 264 (2018)NATUAS0028-083610.1038/s41586-018-0195-y; C. J. Axline et al., Nat. Phys. 14, 705 (2018)NPAHAX1745-247310.1038/s41567-018-0115-y; P. Campagne-Ibarcq et al., Phys. Rev. Lett. 120, 200501 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.200501; N. Leung et al., npj Quantum Inf. 5, 18 (2019)2056-638710.1038/s41534-019-0128-0; Y. P. Zhong et al., Nat. Phys. 15, 741 (2019)NPAHAX1745-247310.1038/s41567-019-0507-7; A. Bienfait et al., Science 364, 368 (2019)SCIEAS0036-807510.1126/science.aaw8415]. Adiabatic protocols can overcome channel loss by transferring quantum states without populating the lossy communication channel. Here, we present a unique superconducting quantum communication system, comprising two superconducting qubits connected by a 0.73 m-long communication channel. Significantly, we can introduce large tunable loss to the channel, allowing exploration of different entanglement protocols in the presence of dissipation. When set for minimum loss in the channel, we demonstrate an adiabatic quantum state transfer protocol that achieves 99% transfer efficiency as well as the deterministic generation of entangled Bell states with a fidelity of 96%, all without populating the intervening communication channel, and competitive with a qubit-resonant mode-qubit relay method. We also explore the performance of the adiabatic protocol in the presence of significant channel loss, and show that the adiabatic protocol protects against loss in the channel, achieving higher state transfer and entanglement fidelities than the relay method.

Controlled dc Monitoring of a Superconducting Qubit

Creating a transmon qubit using semiconductor-superconductor hybrid materials not only provides electrostatic control of the qubit frequency, it also allows parts of the circuit to be electrically connected and disconnected in situ by operating a semiconductor region of the device as a field-effect transistor. Here, we exploit this feature to compare in the same device characteristics of the qubit, such as frequency and relaxation time, with related transport properties such as critical supercurrent and normal-state resistance. Gradually opening the field-effect transistor to the monitoring circuit allows the influence of weak-to-strong dc monitoring of a "live" qubit to be measured. A model of this influence yields excellent agreement with experiment, demonstrating a relaxation rate mediated by a gate-controlled environmental coupling.

Microwave-based arbitrary CPHASE gates for transmon qubits

Superconducting transmon qubits are of great interest for quantum computing and quantum simulation. A key component of quantum chemistry simulation algorithms is breaking up the evolution into small steps, which naturally leads to the need for nonmaximally entangling, arbitrary CPHASE gates. Here we design such microwave-based gates using an analytically solvable approach leading to smooth, simple pulses. We use the local invariants of the evolution operator in SU(4) to develop a method of constructing pulse protocols, which allows for the continuous tuning of the phase. We find CPHASE fidelities of more than 0.999 and gate times as low as 100 ns.

Quantum supremacy using a programmable superconducting processor

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor¹. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits^2-7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 2⁵³ (about 10¹⁶). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times-our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy^8-14 for this specific computational task, heralding a much-anticipated computing paradigm.

Phonon-mediated quantum state transfer and remote qubit entanglement

Phonons, and in particular surface acoustic wave phonons, have been proposed as a means to coherently couple distant solid-state quantum systems. Individual phonons in a resonant structure can be controlled and detected by superconducting qubits, enabling the coherent generation and measurement of complex stationary phonon states. We report the deterministic emission and capture of itinerant surface acoustic wave phonons, enabling the quantum entanglement of two superconducting qubits. Using a 2-millimeter-long acoustic quantum communication channel, equivalent to a 500-nanosecond delay line, we demonstrate the emission and recapture of a phonon by one superconducting qubit, quantum state transfer between two superconducting qubits with a 67% efficiency, and, by partial transfer of a phonon, generation of an entangled Bell pair with a fidelity of 84%.

Realization of efficient quantum gates with a superconducting qubit-qutrit circuit

Building a quantum computer is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations as possible, to reduce the amount of required control and operation time and thus improve the quantum state coherence. Here we propose a superconducting circuit for implementing a tunable system consisting of a qutrit coupled to two qubits. This system can efficiently accomplish various quantum information tasks, including generation of entanglement of the two qubits and conditional three-qubit quantum gates, such as the Toffoli and Fredkin gates. Furthermore, the system realizes a conditional geometric gate which may be used for holonomic (non-adiabatic) quantum computing. The efficiency, robustness and universality of the presented circuit makes it a promising candidate to serve as a building block for larger networks capable of performing involved quantum computational tasks.

Observation of the Crossover from Photon Ordering to Delocalization in Tunably Coupled Resonators

Networks of nonlinear resonators offer intriguing perspectives as quantum simulators for nonequilibrium many-body phases of driven-dissipative systems. Here, we employ photon correlation measurements to study the radiation fields emitted from a system of two superconducting resonators in a driven-dissipative regime, coupled nonlinearly by a superconducting quantum interference device, with cross-Kerr interactions dominating over on-site Kerr interactions. We apply a parametrically modulated magnetic flux to control the linear photon hopping rate between the two resonators and its ratio with the cross-Kerr rate. When increasing the hopping rate, we observe a crossover from an ordered to a delocalized state of photons. The presented coupling scheme is intrinsically robust to frequency disorder and may therefore prove useful for realizing larger-scale resonator arrays.

Tunable Superconducting Cavity using Superconducting Quantum Interference Device Metamaterials

Here we consider a tunable superconducting cavity that can be used either as a tunable coupler to a qubit inside the cavity or as a tunable low noise, low temperature, RF filter. Our design consists of an array of radio-frequency superconducting quantum interference devices (rf SQUIDs) inside a superconducting cavity. This forms a tunable metamaterial structure which couples to the cavity through its magnetic plasma frequency. By tuning the resonant frequency of the metamaterial through an applied magnetic flux, one can tune the cavity mode profile. This allows us to detune the cavity initially centered at 5.593 GHz by over 200 MHz. The maximum quality factor approaches that of the empty cavity, which is 4.5 × 10⁶. The metamaterial electromagnetic response is controlled via a low-frequency or dc magnetic flux bias, and we present a control line architecture that is capable of applying sufficient magnetic flux bias with minimal parasitic coupling. Together this design allows for an in-situ tunable cavity which enables low-temperature quantum control applications.

Circuit QED: single-step realization of a multiqubit controlled phase gate with one microwave photonic qubit simultaneously controlling n - 1 microwave photonic qubits

We present a novel method to realize a multi-target-qubit controlled phase gate with one microwave photonic qubit simultaneously controlling n - 1 target microwave photonic qubits. This gate is implemented with n microwave cavities coupled to a superconducting flux qutrit. Each cavity hosts a microwave photonic qubit, whose two logic states are represented by the vacuum state and the single photon state of a single cavity mode, respectively. During the gate operation, the qutrit remains in the ground state and thus decoherence from the qutrit is greatly suppressed. This proposal requires only a single-step operation and thus the gate implementation is quite simple. The gate operation time is independent of the number of the qubits. In addition, this proposal does not need applying classical pulse or any measurement. Numerical simulations demonstrate that high-fidelity realization of a controlled phase gate with one microwave photonic qubit simultaneously controlling two target microwave photonic qubits is feasible with current circuit QED technology. The proposal is quite general and can be applied to implement the proposed gate in a wide range of physical systems, such as multiple microwave or optical cavities coupled to a natural or artificial Λ-type three-level atom.

Quantum Mechanical Engine for the Quantum Rabi Model

We consider a purely mechanical quantum cycle comprised of adiabatic and isoenergetic processes. In the latter, the system interacts with an energy bath keeping constant the expectation value of the Hamiltonian. In this work, we study the performance of the quantum cycle for a system described by the quantum Rabi model for the case of controlling the coupling strength parameter, the resonator frequency, and the two-level system frequency. For the cases of controlling either the coupling strength parameter or the resonator frequency, we find that it is possible to closely approach to maximal unit efficiency when the parameter is sufficiently increased in the first adiabatic stage. In addition, for the first two cases the maximal work extracted is obtained at parameter values corresponding to high efficiency, which constitutes an improvement over current proposals of this cycle.

Superconducting gatemon qubit based on a proximitized two-dimensional electron gas

The coherent tunnelling of Cooper pairs across Josephson junctions (JJs) generates a nonlinear inductance that is used extensively in quantum information processors based on superconducting circuits, from setting qubit transition frequencies¹ and interqubit coupling strengths² to the gain of parametric amplifiers³ for quantum-limited readout. The inductance is either set by tailoring the metal oxide dimensions of single JJs, or magnetically tuned by parallelizing multiple JJs in superconducting quantum interference devices with local current-biased flux lines. JJs based on superconductor-semiconductor hybrids represent a tantalizing all-electric alternative. The gatemon is a recently developed transmon variant that employs locally gated nanowire superconductor-semiconductor JJs for qubit control^4,5. Here we go beyond proof-of-concept and demonstrate that semiconducting channels etched from a wafer-scale two-dimensional electron gas (2DEG) are a suitable platform for building a scalable gatemon-based quantum computer. We show that 2DEG gatemons meet the requirements⁶ by performing voltage-controlled single qubit rotations and two-qubit swap operations. We measure qubit coherence times up to ~2 μs, limited by dielectric loss in the 2DEG substrate.

Superconducting metamaterials for waveguide quantum electrodynamics

Embedding tunable quantum emitters in a photonic bandgap structure enables control of dissipative and dispersive interactions between emitters and their photonic bath. Operation in the transmission band, outside the gap, allows for studying waveguide quantum electrodynamics in the slow-light regime. Alternatively, tuning the emitter into the bandgap results in finite-range emitter-emitter interactions via bound photonic states. Here, we couple a transmon qubit to a superconducting metamaterial with a deep sub-wavelength lattice constant (λ/60). The metamaterial is formed by periodically loading a transmission line with compact, low-loss, low-disorder lumped-element microwave resonators. Tuning the qubit frequency in the vicinity of a band-edge with a group index of ng = 450, we observe an anomalous Lamb shift of -28 MHz accompanied by a 24-fold enhancement in the qubit lifetime. In addition, we demonstrate selective enhancement and inhibition of spontaneous emission of different transmon transitions, which provide simultaneous access to short-lived radiatively damped and long-lived metastable qubit states.

Toward the first quantum simulation with quantum speedup

With quantum computers of significant size now on the horizon, we should understand how to best exploit their initially limited abilities. To this end, we aim to identify a practical problem that is beyond the reach of current classical computers, but that requires the fewest resources for a quantum computer. We consider quantum simulation of spin systems, which could be applied to understand condensed matter phenomena. We synthesize explicit circuits for three leading quantum simulation algorithms, using diverse techniques to tighten error bounds and optimize circuit implementations. Quantum signal processing appears to be preferred among algorithms with rigorous performance guarantees, whereas higher-order product formulas prevail if empirical error estimates suffice. Our circuits are orders of magnitude smaller than those for the simplest classically infeasible instances of factoring and quantum chemistry, bringing practical quantum computation closer to reality.

Perfect Strain Relaxation in Metamorphic Epitaxial Aluminum on Silicon through Primary and Secondary Interface Misfit Dislocation Arrays

Understanding the atomically precise arrangement of atoms at epitaxial interfaces is important for emerging technologies such as quantum materials that have function and performance dictated by bonds and defects that are energetically active on the micro-electronvolt scale. A combination of atomistic modeling and dislocation theory analysis describes both primary and secondary dislocation networks at the metamorphic Al/Si (111) interface, which is experimentally validated by atomic resolution scanning transmission electron microscopy. The electron microscopy images show primary misfit dislocations for the majority of the strain relief and evidence of a secondary structure allowing for complete relaxation of the Al-Si misfit strain. This study demonstrates the equilibrium interface that represents the lowest energy structure of a highly mismatched and semicoherent single-crystal interface with complete strain relief in an atomically abrupt structure.

Dynamical Phase Transitions in Sampling Complexity

We make the case for studying the complexity of approximately simulating (sampling) quantum systems for reasons beyond that of quantum computational supremacy, such as diagnosing phase transitions. We consider the sampling complexity as a function of time t due to evolution generated by spatially local quadratic bosonic Hamiltonians. We obtain an upper bound on the scaling of t with the number of bosons n for which approximate sampling is classically efficient. We also obtain a lower bound on the scaling of t with n for which any instance of the boson sampling problem reduces to this problem and hence implies that the problem is hard, assuming the conjectures of Aaronson and Arkhipov [Proceedings of the Forty-Third Annual ACM Symposium on Theory of Computing (ACM Press, New York, New York, USA, 2011), p. 333]. This establishes a dynamical phase transition in sampling complexity. Further, we show that systems in the Anderson-localized phase are always easy to sample from at arbitrarily long times. We view these results in light of classifying phases of physical systems based on parameters in the Hamiltonian. In doing so, we combine ideas from mathematical physics and computational complexity to gain insight into the behavior of condensed matter, atomic, molecular, and optical systems.