Entanglement properties of superconducting qubits coupled to a semi-infinite transmission line

Quantum entanglement, a key resource in quantum information processing, is reduced by interaction between the quantum system concerned and its unavoidable noisy environment. Therefore it is of particular importance to study the dynamical properties of entanglement in open quantum systems. In this work, we mainly focus on two qubits coupled to an adjustable environment, namely a semi-infinite transmission line. The two qubits' relaxations, through individual channels or collective channel or both, can be adjusted by the qubits' transition frequencies. We examine entanglement dynamics in this model system with initial Werner state, and show that the phenomena of entanglement sudden death and revival can be observed. Due to the hardness of preparing the Werner state experimentally, we introduce a new type of entangled state called pseudo-Werner state, which preserves as much entangling property as the Werner state, and more importantly,it is experiment friendly. Furthermore, we provide detailed procedures for generating pseudo-Werner state and studying entanglement dynamics with it, which can be straightforwardly implemented in a superconducting waveguide quantum electrodynamics system.

Fast generating W state of three superconducting qubits via Lewis–Riesenfeld invariants

We propose a scheme for a fast generating three-qubit W state in a superconducting system by using a technique of shortcuts to adiabaticity, Lewis–Riesenfeld invariants. Three identical superconducting qubits（SQs） are connected by two coplanar waveguide resonators（CPWRs） capacitively. Under a certain limit condition, we convert the complicated SQ system into a simple three-state system. By designing experimentally accessible harmonic pulses, a three-SQ W state is implemented with quite short operation time and high fidelity. Numerical simulations prove that the scheme is robust against the parameter deviation. In addition, we also give detailed discussion about the scheme robustness against decoherence.

Resonant interaction scheme for GHZ state preparation and quantum phase gate with superconducting qubits in a cavity

A scheme is proposed to generate GHZ state and realize quantum phase gate for superconducting qubits placed in a microwave cavity. This scheme uses resonant interaction between the qubits and the cavity mode, so that the interaction time is short, which is important in view of decoherence. In particular, the phase gate can be realized simply with a single interaction between the qubits and the cavity mode. With cavity decay being considered, the fidelity and success probability are both very close to unity.

Invariants-based shortcuts for fast generating Greenberger-Horne-Zeilinger state among three superconducting qubits

As one of the most promising candidates for implementing quantum computers, superconducting qubits（SQs） are adopted for fast generating the Greenberger–Horne–Zeilinger（GHZ） state by using invariants-based shortcuts. Three SQs are separated and connected by two coplanar waveguide resonators（CPWRs） capacitively. The complicated system is skillfully simplified to a three-state system, and a GHZ state among three SQs is fast generated with a very high fidelity and simple driving pulses. Numerical simulations indicate the scheme is insensitive to parameter deviations. Besides, the robustness of the scheme against decoherence is discussed in detail.

Increasing energy relaxation time of superconducting qubits with nonmagnetic infrared filter and shield

One of the primary origins of the energy relaxation in superconducting qubits is the quasiparticle loss. The quasiparticles can be excited remarkably by infrared radiation. In order to minimize the density of quasiparticle and increase the qubit relaxation time, we design and fabricate the infrared filter and shield for superconducting qubits. In comparison with previous filters and shields, a nonmagnetic dielectric is used as the infrared absorbing material, greatly suppressing the background magnetic fluctuations. The filters can be made to impedance-match with other microwave devices. Using the as-fabricated infrared filter and shield, we increased the relaxation time of a transmon qubit from 519 ns to 1125 ns.

Progress in superconducting qubits from the perspective of coherence and readout

Superconducting qubits are Josephson junction-based circuits that exhibit macroscopic quantum behavior and can be manipulated as artificial atoms. Benefiting from the well-developed technology of microfabrication and microwave engineering, superconducting qubits have great advantages in design flexibility, controllability, and scalability. Over the past decade, there has been rapid progress in the field, which greatly improved our understanding of qubit decoherence and circuit optimization. The single-qubit coherence time has been steadily raised to the order of 10 to 100 p.s, allowing for the demonstration of high-fidelity gate operations and measurement-based feedback control. Here we review recent progress in the coherence and readout of superconducting qubits.

Shortcut-based quantum gates on superconducting qubits in circuit QED

Construction of optimal gate operations is significant for quantum computation.Here an efficient scheme is proposed for performing shortcut-based quantum gates on superconducting qubits in circuit quantum electrodynamics(QED).Two four-level artificial atoms of Cooper-pair box circuits,having sufficient level anharmonicity,are placed in a common quantized field of circuit QED and are driven by individual classical microwaves.Without the effect of cross resonance,one-qubit NOT gate and phase gate in a decoupled atom can be implemented using the invariant-based shortcuts to adiabaticity.With the assistance of cavity bus,a one-step SWAP gate can be obtained within a composite qubit-photon-qubit system by inversely engineering the classical drivings.We further consider the gate realizations by adjusting the microwave fields.With the accessible decoherence rates,the shortcut-based gates have high fidelities.The present strategy could offer a promising route towards fast and robust quantum computation with superconducting circuits experimentally.

Quantum computation and simulation with superconducting qubits

Superconducting circuits based on Josephson junctions are regarded as one of the most promising technologies for the implementation of scalable quantum computers.This review presents the basic principles of superconducting qubits and shows the progress of quantum computing and quantum simulation based on superconducting qubits in recent years.The experimental realization of gate operations,readout,error correction codes,as well as some quantum algorithms are summarized,followed by an introduction of quantum simulation.And then some important applications in fields including condensed matter physics,quantum annealing,and quantum chemistry are discussed.

Transfer of quantum entangled states between superconducting qubits and microwave field qubits

Transferring entangled states between matter qubits and microwave-field(or optical-field)qubits is of fundamental interest in quantum mechanics and necessary in hybrid quantum information processing and quantum communication.We here propose a way for transferring entangled states between superconducting qubits(matter qubits)and microwave-field qubits.This proposal is realized by a system consisting of multiple superconducting qutrits and microwave cavities.Here,“qutrit”refers to a three-level quantum system with the two lowest levels encoding a qubit while the third level acting as an auxiliary state.In contrast,the microwave-field qubits are encoded with coherent states of microwave cavities.Because the third energy level of each qutrit is not populated during the operation,decoherence from the higher energy levels is greatly suppressed.The entangled states can be deterministically transferred because measurement on the states is not needed.The operation time is independent of the number of superconducting qubits or microwave-field qubits.In addition,the architecture of the circuit system is quite simple because only a coupler qutrit and an auxiliary cavity are required.As an example,our numerical simulations show that high-fidelity transfer of entangled states from two superconducting qubits to two microwave-field qubits is feasible with present circuit QED technology.This proposal is quite general and can be extended to transfer entangled states between other matter qubits(e.g.,atoms,quantum dots,and NV centers)and microwave-or optical-field qubits encoded with coherent states.

Realization of high-fidelity and robust geometric gates with time-optimal control technique in superconducting quantum circuit

One of the key features required to realize fault-tolerant quantum computation is the robustness of quantum gates against errors.Since geometric quantum gate is naturally insensitivity to noise,it appears to be a promising routine to achieve high-fidelity,robust quantum gates.The implementation of geometric quantum gate however faces some troubles such as its complex interaction among multiple energy levels.Moreover,traditional geometric schemes usually take more time than equivalent dynamical ones.Here,we experimentally demonstrate a geometric gate scheme with the time-optimal control(TOC)technique in a superconducting quantum circuit.With a transmon qubit and operations restricted to two computational levels,we implement a set of geometric gates which exhibit better robustness features against control errors than the dynamical counterparts.The measured fidelities of TOC X gate and X/2 gate are 99.81%and 99.79%respectively.Our work shows a promising routine toward scalable fault-tolerant quantum computation.

Superconducting phase qubits with shadow-evaporated Josephson junctions

We develop a fabrication process for the superconducting phase qubits in which Josephson junctions for both the qubit and superconducting quantum interference device（SQUID） detector are prepared by shadow evaporation with a suspended bridge. Al junctions with areas as small as 0.05 μm^2 are fabricated for the qubit, in which the number of the decoherencecausing two-level systems（TLS） residing in the tunnel barrier and proportional to the junction area are greatly reduced. The measured energy spectrum shows no avoided crossing arising from coherent TLS in the experimentally reachable flux bias range of the phase qubit, which demonstrates the energy relaxation time T1 and dephasing time Tφ on the order of 100 ns and 50 ns, respectively. We discuss several possible origins of decoherence from incoherent or weakly-coupled coherent TLS and further improvements of the qubit performance.

Optimal readout of superconducting qubits exploiting high-level states

High-fidelity initialization,manipulation,and measurement of qubits are important in quantum computing.For the Google’s Sycamore processor,the gate fidelity of single-and two-qubit logic operations has improved to>99.6%,whereas single-shot measurement fidelity remains at the level of 97%,which severely limits the ap-plication of the superconducting approach to large-scale quantum computing.The current measurement scheme relies on the dispersive interaction between the qubit and the readout resonator,which was proposed back in 2004.However,the measurement fidelity is limited by the trade-offbetween the state separation and relax-ation time of the two-level system.Recently,an exciting phenomenon was observed experimentally,wherein the separation-decay limit could be alleviated by exploiting the cascade decay nature of the higher levels;however,the mechanism and effectiveness of this phenomenon are still unclear.Herein,we present a theoretical tool to extract different types of errors in high-level states encoding dispersive measurement.For the realistic parame-ters of Google’s Sycamore processor,the use of state|2>is sufficient to suppress 92%of the decay readout error on average,where the total readout error is dominated by the background thermal excitation.We also show counter-intuitively that,the assistance of high-level states is effective in the measurement of logic 0,where there is no decay process.

Controllably Coupling Superconducting Charge and Flux Qubits by Using Nanomechanical Resonator

We propose an effective mechanism to couple superconducting charge and flux qubits by using a quantized nanomechanical resonator. The coupling between the charge and flux qubits can be controlled by the external flux of the charge qubit. Under the strong coupling limR, an iSWAP gate can be generated by this scheme. The experimental feasibility in our scheme is also presented.

Bell States and Two-Qubit Logic Gate with Superconducting Charge Qubits Coupling to a Nanomechanical Resonator

We propose a scheme for generating Bell states involving two SQUID-based charge qubits by coupling themto a nanomechanical resonator.We also show that it is possible to implement a two-qubit logic gate between the twocharge qubits by choosing carefully the interaction time.

Multiplexing Read-Out of Charge Qubits by a Superconducting Resonator

Wavelength division multiplexing （WDM） is widely used in modern optics and electronics. For future quantum computers, the integration of readout is also vitally important. Here we incorporate an idea of WDM to demon- strate multiplexing readout of charge qubits by using a single integrated on-chip superconducting microwave resonator. Two distant qubits formed by two graphene double quantum dots （DQDs） are simultaneously readout by an interconnected superconducting resonator. This readout device is found to have 2 MHz bandwidth and 1.1 x 10-4 e/x/-H-z charge sensitivity. Different frequency gate-modulations, which are used selectively to change the impedance of the qubits, are applied to different DQDs, which results in separated sidebands in the spectrum. These sidebands enable a multiplexing readout for the multi-qubits circuit. This architecture can largely reduce the amount of detectors and can improve the prospect for scaling-up of semiconductor qubits.

Multipartite entanglement in the interaction system between a single-mode microwave cavity field and superconducting charge qubits

This paper proposes a method of generating multipartite entanglement through using d.c. superconducting quan- tum interference devices （SQUID） inside a standing wave cavity. In this scheme, the d.c. SQUID works in the charge region. It is shown that, a large number of important multipartite entangled states can be generated by a controllable interaction between a cavity field and qubits. It is even possible to produce entangled states involving different cavity modes based on the measurement of charge qubits states. After such superpositions states are created, the interaction can be switched off by the classical magnetic field through the SQUID, and there is no information transfer between the cavity field and the charge qubits.

Variational quantum simulation of thermal statistical states on a superconducting quantum processer

Quantum computers promise to solve finite-temperature properties of quantum many-body systems,which is generally challenging for classical computers due to high computational complexities.Here,we report experimental preparations of Gibbs states and excited states of Heisenberg X X and X X Z models by using a 5-qubit programmable superconducting processor.In the experiments,we apply a hybrid quantum–classical algorithm to generate finite temperature states with classical probability models and variational quantum circuits.We reveal that the Hamiltonians can be fully diagonalized with optimized quantum circuits,which enable us to prepare excited states at arbitrary energy density.We demonstrate that the approach has a self-verifying feature and can estimate fundamental thermal observables with a small statistical error.Based on numerical results,we further show that the time complexity of our approach scales polynomially in the number of qubits,revealing its potential in solving large-scale problems.

Demonstrate chiral spin currents with nontrivial interactions in superconducting quantum circuit

Quantum many-body systems in which time-reversal symmetry is broken give rise to a wealth of exotic phases,and thus constitute one of the frontiers of modern condensed matter physics.Quantum simulation allows us to better understand many-body systems with huge Hilbert space,where classical simulation is usually inefficient.With superconducting quantum circuit as a platform for quantum simulation,we realize synthetic Abelian gauge fields by using microwave drive and tunable coupling in loop configurations to break the time-reversal symmetry of the system.Based on high-precision manipulation and readout of circuit-QED architecture,we demonstrate the chiral ground spin current of a time-reversal symmetry broken system with nontrivial interactions.Our work is a significant attempt to simulate quantum many-body systems with time-reversal symmetry breaking in multi-qubit superconducting processors.

Calibration and cancellation of microwave crosstalk in superconducting circuits

The precise control and manipulation of the qubit state are vital for quantum simulation and quantum computation.In superconducting circuits,one notorious error comes from the crosstalk of microwave signals applied to different qubit control lines.In this work,we present a method for the calibration and cancellation of the microwave crosstalk and experimentally demonstrate its effectiveness in a superconducting 10-qubit chain.The method is convenient and efficient especially for calibrating the microwave crosstalk with large amplitudes and variations,which can be performed successively to reduce the microwave crosstalk by two to three orders.The qubit chain with microwave driving is governed by one-dimensional(1D)Bose-Hubbard model in transverse field,which is nonintegrable and shows thermalization behaviour during the time evolution from certain initial states.Such thermalization process is observed with excellent agreement between experiment and theory further confirming the effective global cancellation of the microwave crosstalk.

Universal quantum control based on parametric modulation in superconducting circuits

As superconducting quantum circuits are scaling up rapidly towards the noisy intermediate-scale quantum(NISQ)era,the demand for electronic control equipment has increased significantly.To fully control a quantum chip of N qubits,the common method based on up-conversion technology costs at least 2×N digital-to-analog converters(DACs)and N IQ mixers.The expenses and complicate mixer calibration have become a hinderance for intermediate-scale quantum control.Here we propose a universal control scheme for superconducting circuits,fully based on parametric modulation.To control N qubits on a chip,our scheme only requires N DACs and no IQ mixer,which significantly reduces the expenses.One key idea in the control scheme is to introduce a global pump signal for single-qubit gates.We theoretically explain how the universal gates are constructed using parametric modulation.The fidelity analysis shows that parametric single-qubit(two-qubit)gates in the proposed scheme can achieve low error rates of 10^(4),with a gate time of about 60 ns(100 ns).