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SCIENCE CHINA Information Sciences, Volume 63 , Issue 8 : 180501(2020) https://doi.org/10.1007/s11432-020-2881-9

Superconducting quantum computing: a review

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  • ReceivedFeb 25, 2020
  • AcceptedApr 16, 2020
  • PublishedJul 15, 2020

Abstract

Over the last two decades, tremendous advances have been made for constructing large-scale quantum computers. In particular, quantum computing platforms based on superconducting qubits have become the leading candidate for scalable quantum processor architecture, and the milestone of demonstrating quantum supremacy has been first achieved using 53 superconducting qubits in 2019. In this study, we provide a brief review on the experimental efforts towards the large-scale superconducting quantum computer, including qubit design, quantum control, readout techniques, and the implementations of error correction and quantum algorithms. Besides the state of the art, we finally discuss future perspectives, and which we hope will motivate further research.


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  • Figure 1

    Superconducting qubit circuit diagram. (a) Charge qubit composed of a Josephson junction and a capacitor. Adjusting the voltage $V_g$ can control the number of Cooper pairs. (b) Flux qubit. $L$ is the loop inductance. Changing the bias flux $\Phi$ can adjust the energy level structure of the qubit. (c) Phase qubit. Adjusting the bias current $I_b$ can tilt the potential energy surface.

  • Figure 2

    (Color online) Schematic of a Transmon qubit and its effective circuit. (a) The effective circuit model of a transmon qubit. $C_B$ is a large capacitor in parallel with superconducting quantum interference device (SQUID). $L_r$ and $C_r$ are connected in parallel to form an equivalent circuit of the readout resonator. The circuit on the far right is the flux bias of SQUID. (b) Schematic of 2D structure of a transmon qubit. Taken from [31].

  • Figure 3

    (Color online) (a) Optical micrograph of Xmon qubit; (b) enlarged image of SQUID; (c) the electrical circuit of the qubit. Taken from [32].

  • Figure 4

    (Color online) Optical micrograph of two inductively coupled Gmon qubits. Taken from [33].

  • Figure 5

    (Color online) Circuit diagram of a superconducting circuit implementing a tunable coupler, consisting of two qubit modes (red and blue) and a coupler mode (black). Taken from [34].

  • Figure 6

    (Color online) (a) Schematic of a transmon qubit inside a 3D cavity; (b) photograph of a half of the 3D aluminum waveguide cavity. Taken from [35].

  • Figure 9

    The electrical circuit representation of Fluxonium qubit.

  • Figure 10

    (Color online) (a) Circuit diagram of 0-$\displaystyle~\pi$ superconducting qubits. The circuit has a ring with four nodes. The four nodes are connected by a pair of Josephson junctions ($E_J$, $C_J$), a large capacitor ($C$) and superinductors ($L$). (b) In the absence of a magnetic field, the double-well potential function $V(\theta~,\phi~)$ of the circuit. The ground state of the 0 valley is localized along $\theta=0$, and the lowest state of the $\displaystyle~\pi$ valley is localized along $\theta=\displaystyle~\pi$. Taken from [40].

  • Figure 11

    (Color online) Experimental setup of the hybrid system that coupling a superconducting flux qubit to an electron spin ensemble in diamond. (a) Diamond crystal glued on top of a flux qubit (red box); (b) NV centre. Taken from [42].

  • Figure 12

    The changes in the number of entangled superconducting qubits over the past decade ( [11,13,25,47,66-68]).

  • Figure 13

    Diagram of SQUID loop. ${\delta~_1}({\delta~_2})$ represents the phase different of Josephson junction. Its critical current varies with the change of extra magnetic flux change.

  • Figure 14

    (Color online) Schematic diagram of realizing CZ gate by using the avoided level crossing between $|1,1\rangle$ and $|0,2\rangle$ states with the fast adiabatic tuning. Taken from [25].

  • Figure 15

    (Color online) FLICFORQ-style qubits (circles) have fixed transition frequencies and fixed linear off-diagonal coupling. ${\Omega~_1}$ is the amplitude of microwave. Q1 and Q2 would weakly couple when $\omega_1^{rf}$ approximately equals to $\Delta$. Taken from [73].

  • Figure 16

    (Color online) Diagram of the 4-qubit 3D cQED system. The four qubits are coupled with each other via common bus. Different microwave pulses input into the common cavity will cause indirect coupling of different qubit pairs. Taken from [81].

  • Figure 17

    (Color online) The measurement results for $|0\rangle$ or $|1\rangle$ state.

  • Figure 18

    (Color online) Design and realization of the Purcell filter. (a) Circuit model of the Purcell-filtered cavity design; (b) optical micrograph of the device with inset zoom on transmon qubit. Taken from [99].

  • Figure 19

    (Color online) Device layout. $C_g$ is the coupling capacitance between the qubit $q$ and the readout resonator $r$. $C_k$ is the coupling capacitance between the readout resonator and the filter resonator $F$. Taken from [100].

  • Figure 24

    (Color online) (a) 2D surface code. Data qubits and measurement qubits are open circles and filled circles, respectively. (b) Geometry and quantum circuit for a measure-$Z$ qubit. (c) Geometry and quantum circuit for a measure-$X$ qubit. Taken from [26].

  • Figure 25

    (Color online) (a) The five qubits repetition code; (b) the quantum circuit for three cycles of the nine-qubit repetition code. Taken from [67].

  • Figure 26

    (Color online) The cat-code cycle. Taken from [120].

  • Figure 27

    (Color online) (a) Quantum circuit for the five-qubit code; (b) expectation values of 31 stabilizers for the encoded logical state ${\rm{|}}T{\rangle~_L}=~{(|0\rangle~_L}+~{{\rm~e}^{{\rm~i}\pi~/4}}|1{\rangle~_L})/\sqrt~2$; (c) expectation values of logical Pauli operators and state fidelity of the encoded magic state ${\rm{|}}T{\rangle~_L}$. Taken from [128].

  • Figure 28

    (Color online) Quantum walks of one and two photons in a 1D lattice of a superconducting processor. protectłinebreak (a) Optical micrograph of the 12-qubit chain; (b) one photon quantum walk; (c) and (d) are quantum walk for two weakly interacting photons and two strongly interacting photons, respectively; (e) and (f) are the experimental waveform sequences for single-photon quantum walk and two-photon quantum walk, respectively. Taken from [129].

  • Figure 29

    (Color online) Ergodic-localized junction with superconducting qubits. (a) When disordered and driven domains are coupled, localization can be destroyed owing to the overlap between localized and delocalized states; (b) depicts stadium and circular billiards, which exhibit ergodic and regular behavior, respectively; (c) optical micrograph of the superconducting chip; (d) experimental waveform sequences to generate the ergodic-localized junctions; (e) the quasienergy level statistics of the ergodic-localized junction for an array of $L=12$ qubits. Taken from [130].

  • Figure 30

    (Color online) (a) Illustration of the toric code model; (b) the minimal unit of the toric code using for qubits; (c) schematic of the superconducting circuit featuring four qubits coupled to a central resonator. Taken from [147].

  • Figure 31

    (Color online) Compiled quantum circuits for solving $2~\times~2$ linear equations using four qubits. Taken from [155].

  • Figure 32

    The homomorphic encryption scheme for solving linear equations using cloud quantum computer. Taken from [156].

  • Figure 33

    (Color online) Quantum chemistry on a superconducting quantum processor. (a) Parity mapping of spin orbitals to qubits; (b) optical micrograph of the superconducting quantum processor with seven transmon qubits; protect łinebreak (c) quantum circuit for trial-state preparation and energy estimation; (d) an example of the pulse sequence for the preparation of a six-qubit trial state. Taken from [164].

  • Table 1  

    Table 1The development in the lifetime of qubits in recent years$^{*}$

    $T_1~(\mu~$s) Transmon Xmon 3D Transmon3-JJ flux qubitC-shunt flux qubit Fluxonium0-$\pi$ qubit
    20101.2 [47]4 [48]1.5 [49]
    20111.6 [50] 60 [35] 12 [51]5.7 [52]
    20129.7 [53] 70 [54] 4 [55]
    201311.6 [56] 44 [32]
    201429 [57] 95 [58] 8100 [59]
    201536 [60]
    201656 [61] 162 [62] 55 [63]
    201780 [64]
    2018
    2019240 [65] 1560 [40]

    * Each data uses the highest value reported in the literature of the current year, and is not recorded if it is smaller than in previous years.

  • Table 2  

    Table 2Two-qubit gate based on superconducting quantum system in recent years

    Year Gate type Fidelity (%) Gate timeMethod of measurement
    2009CZ gate [70] 87 NONQST$^{\rm~a)}$
    2010$i$SWAP gate [84]78 NONQST
    2011CR gate [85] 81 220 nsQPT
    2012$\sqrt{b{\rm~SWAP}}$ gate [86] 86 800 nsQPT
    2012$\sqrt{i{\rm~SWAP}}$ gate [87] 90 31 nsQPT
    2013CZ gate [88] 87 510 nsQPT
    2013CNOT gate [56] 93.47 420 nsRB
    2014CZ gate [25] 99.44 43 nsRB
    2014CZ gate [33] 99.07 30 nsRB
    2016CR gate [74] 99 160 nsRB
    2016CZ gate [81] 98.53 413 nsRB
    2016$\sqrt{i{\rm~SWAP}}$ gate [69] 98.23 183 nsRB
    2017CZ gate [89] 93.60 250 nsQPT
    2018CZ gate [80] 95 278 nsQPT
    2018CZ gate [90] 92 210 nsRB
    2018$i$SWAP gate [90] 94 150 nsRB
    2018CNOT gate [91] 89 190 nsQPT
    2018CNOT gate [92] 79 4.6 $\mu$sQPT
    2019CZ gate [71] 99.54 40 nsRB
    2019$i$SWAP-like gate [72] 99.66 18 nsXEB
    2020CZ gate [78] 98.8 176 nsRB

    a

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