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.

Demonstration of superadiabatic population transfer in superconducting qubit

We implemented the superadiabatic population transfer within the nonadiabatic regime in a two-level superconducting qubit system. To realize the superadiabatic procedure, we added an additional term in the Hamiltonian, introducing an auxiliary counter-diabatic field to cancel the nonadiabatic contribution in the evolution. Based on the superadiabatic procedure, we further demonstrated quantum Phase and NOT gates. These operations, which possess both of the fast and robust features, are promising for quantum information processing.

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.

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.

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.

Hardware for multi-superconducting qubit control and readout

We have developed an electronic hardware system for the control and readout of multi-superconducting qubit devices.The hardware system is based on the design ideas of good scalability,high synchronization and low latency.The system,housed inside a VPX-6U chassis,includes multiple arbitrary-waveform generator(AWG)channels,analog-digital-converter(ADC)channels as well as direct current source channels.The system can be used for the control and readout of up to twelve superconducting transmon qubits in one chassis,and control and readout of more and more qubit can be carried out by interconnecting the chassis.By using field programmable gate array(FPGA)processors,the system incorporates three features that are specifically useful for superconducting qubit research.Firstly,qubit signals can be processed using the on-board FPGA after being acquired by ADCs,significantly reducing data processing time and data amount for storage and transmission.Secondly,different output modes,such as direct output and sequential output modes,of AWG can be implemented with pre-encoded FPGA.Thirdly,with data acquisition ADCs and control AWGs jointly controlled by the same FPGA,the feedback latency can be reduced,and in our test a 178.4 ns latency time is realized.This is very useful for future quantum feedback experiments.Finally,we demonstrate the functionality of the system by applying the system to the control and readout of a 10 qubit superconducting quantum processor.

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.

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.

Distributed quantum computation with superconducting qubit via LC circuit using dressed states

A scheme is proposed where two superconducting qubits driven by a classical field interacting separately with two distant LC circuits connected by another LO circuit through mutual inductance, are used for implementing quantum gates. By using dressed states, quantum state transfer and quantum entangling gate can be implemented. With the help of the time-dependent electromagnetic field, any two dressed qubits can be selectively coupled to the data bus （the last LC circuit）, then quantum state can be transferred from one dressed qubit to another and multi-mode entangled state can also be formed. As a result, the promising perspectives for quantum information processing of mesoscopic superconducting qubits are obtained and the distributed and scalable quantum computation can be implemented in this scheme.

Improved Superconducting Qubit State Readout by Path Interference

High fidelity single shot qubit state readout is essential for many quantum information processing protocols. In superconducting quantum circuit, the qubit state is usually determined by detecting the dispersive frequency shift of a microwave cavity from either transmission or reflection. We demonstrate the use of constructive interference between the transmitted and reflected signal to optimize the qubit state readout, with which we find a better resolved state discrimination and an improved qubit readout fidelity. As a simple and convenient approach, our scheme can be combined with other qubit readout methods based on the discrimination of cavity photon states to further improve the qubit state readout.

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.

Determination of molecular energies via variational-based quantum imaginary time evolution in a superconducting qubit system

As a valid tool for solving ground state problems,imaginary time evolution(ITE)is widely used in physical and chemical simulations.Different ITE-based algorithms in their quantum counterpart have recently been proposed and applied to some real systems.We experimentally realize the variational-based quantum imaginary time evolution(QITE)algorithm to simulate the ground state energy of hydrogen(H_2)and lithium hydride(Li H)molecules in a superconducting qubit system.The H_2 molecule is directly simulated using the 3-qubit circuit with unitary-coupled clusters(UCC)ansatz.We also combine QITE with the cluster mean-field(CMF)method to obtain an effective Hamiltonian.The Li H molecule is correspondingly simulated using the 3-qubit circuit with hardware-efficient ansatz.For comparison,the Li H molecule is also directly simulated using the 4-qubit circuit with UCC ansatz at the equilibrium point.All the experimental results show a convergence within 4 iterations,with high-fidelity ground state energy obtained.For a more complex system in the future,the CMF may allow further grouping of interactions to obtain an effective Hamiltonian,then the hybrid QITE algorithm can possibly simulate a relatively large-scale system with fewer qubits.

Quantum entanglement generation on magnons assisted with microwave cavities coupled to a superconducting qubit

We present protocols to generate quantum entanglement on nonlocal magnons in hybrid systems composed of yttrium iron garnet(YIG)spheres,microwave cavities and a superconducting(SC)qubit.In the schemes,the YIGs are coupled to respective microwave cavities in resonant way,and the SC qubit is placed at the center of the cavities,which interacts with the cavities simultaneously.By exchanging the virtual photon,the cavities can indirectly interact in the far-detuning regime.Detailed protocols are presented to establish entanglement for two,three and arbitrary N magnons with reasonable fidelities.

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.

Cavity-induced ATS effect on a superconducting Xmon qubit

We couple a ladder-type three-level superconducting artificial atom to a cavity. Adjusting the artificial atom to make the cavity be resonant with the two upper levels, we then probe the lower two levels of the artificial atom. When driving the cavity to a coherent state, the probe spectrum shows energy level splitting induced by the quantized electromagnetic field in the cavity. This splitting size is related to the coupling strength between the cavity and the artificial atom and, thus, is fixed after the sample is fabricated. This is in contrast to the classical Autler-Townes splitting of a three-level system in which the splitting is proportional to the driving amplitude, which can be continuously changed. Our experiment results show the difference between the classical microwave driving field and the quantum field of the cavity.

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.

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.

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.

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.