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Superconducting Quantum Computing: A Review

He-Liang Huang, Dachao Wu, Daojin Fan, Xiaobo Zhu

arXiv:2006.10433v3quant-ph

TL;DR

Building a practical large-scale quantum computer remains a major challenge, while superconducting qubits have become a leading candidate for scalable processors. This review synthesizes progress in qubit design, control, readout, error correction, and algorithms, reporting rapid advances that include a 53-qubit quantum-supremacy demonstration and high-fidelity gates. It also identifies coherence, leakage, cryogenic capacity, connectivity, gate fidelity, and useful applications as continuing concerns.

  • Problem

    Constructing a practical large-scale quantum computer requires a scalable platform that can meet demanding hardware and computational requirements.

  • Method

    The paper reviews superconducting quantum computing through its qubit designs, control and readout techniques, error-correction and algorithm experiments, and future outlook.

  • Results

    Superconducting quantum computing has advanced rapidly, reaching a 53-qubit quantum-supremacy demonstration in 2019 alongside improvements in gate operation, readout, error correction, and algorithms.

  • Takeaways & Limitations

    Superconducting qubits remain a leading candidate for scalable quantum computing, but practical systems still require higher-quality qubits and useful applications.

  • Takeaways & Limitations

    The platform remains constrained by short coherence times, unwanted higher-level transitions, cryogenic requirements, and unresolved questions about its first killer application.

Abstract

from arXiv · show

Over the last two decades, tremendous advances have been made for constructing large-scale quantum computers. In particular, the quantum processor architecture based on superconducting qubits has become the leading candidate for scalable quantum computing platform, and the milestone of demonstrating quantum supremacy was first achieved using 53 superconducting qubits in 2019. In this work, we provide a brief review on the experimental efforts towards building a 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.

I. INTRODUCTION

Superconducting qubits have emerged as a leading scalable quantum-computing platform amid rapid growth in quantum technologies. This review surveys their design, control, readout, error correction, and algorithms while outlining both practical advantages and remaining hardware challenges.

  • Quantum computers promise efficient solutions for problems that are intractable for classical computers, including factoring and quantum simulation.
  • Superconducting qubits have rapidly improved in scale and quality, including 99.4% two-qubit gate fidelity in 2014 and a 53-qubit quantum-supremacy demonstration in 2019.
  • The review covers superconducting-qubit theory, design, control, readout, error correction, quantum algorithms, experimental progress, and future perspectives.
  • Superconducting systems offer designable Hamiltonians, semiconductor-compatible fabrication, relatively easy coupling, and microwave-compatible control and measurement.
  • The main hardware challenges are short coherence times, unwanted higher-level transitions, and the need for larger-capacity dilution refrigerators.
  • Charge, flux, and phase qubits use different circuit variables and bias controls to define their relevant quantum states and energy structures.

C. Three superconducting qubit archetypes

Superconducting qubits are categorized by EJ/EC into charge, flux, and phase archetypes, from which designs such as Transmon, Xmon, Gmon, and 3D Transmon derive. These architectures trade noise sensitivity, controllability, coupling flexibility, decoherence, and scalability in different ways.

  • C. Three superconducting qubit archetypes: The three archetypes are charge, flux, and phase qubits, distinguished by the ratio EJ/EC.Charge qubits have EJ ≪ EC, flux qubits have EJ/EC much greater than 1 but below 100, and phase qubits have EJ ≫ EC.
  • 1. Transmon-type qubit: Transmon reduces charge sensitivity by increasing EJ/EC with a large parallel capacitor while retaining sufficient anharmonicity.The large capacitor lowers the charge energy and produces EJ/EC∼100.
  • 1. Transmon-type qubit: Xmon modifies Transmon with a cross capacitor, resonant-cavity coupling, and independent XY and Z control lines.Its qubits can also be directly coupled through capacitance.
  • 1. Transmon-type qubit: Gmon uses a tunable inductive junction to control coupling strength, avoiding fixed-coupling frequency crowding but adding decoherent channels and layout complexity.A generic tunable-coupler design instead uses a flux-tunable center mode in a three-body chain and does not introduce additional components.
  • 1. Transmon-type qubit: 3D Transmon replaces planar cavities with a three-dimensional waveguide cavity, reducing surface dielectric sensitivity and providing a controlled electromagnetic environment.Scalability remains its major difficulty for large-scale devices.

2. 3-JJ flux qubit

The review presents flux-qubit variants and related architectures that reduce noise sensitivity or improve coherence through circuit design. It also describes hybridization with diamond NV centers and reports broad improvements in qubit lifetime.

  • 2. 3-JJ flux qubit: The 3-JJ flux qubit uses a micrometer-sized loop whose opposite persistent-current directions encode the two qubit states.Pulsed microwave modulation of the enclosed magnetic flux can create superpositions of these states.
  • 3. C-shunt flux qubit: C-shunt flux qubits add a capacitor across the smaller junction to reduce charging energy and suppress charge-noise effects.The architecture is described as suppressing both flux and charge noise.
  • Fluxonium: Fluxonium connects a series array of large-capacitance junctions in parallel with a small junction, making the array behave as an inductive wire below the plasma frequency.The architecture was proposed to address inductance and offset-charge-noise problems.
  • 0-π qubit: The 0-π qubit uses a symmetrical circuit with an interleaved double-well potential, localizing its ground states in separate 0 and π valleys.The corresponding ground-state transition matrix elements are very small.
  • Hybrid qubit: A hybrid system couples superconducting flux qubits to diamond NV centers to combine their distinct properties.Flux qubits provide control, while NV centers provide longer coherence times.
  • E. Qubit’s lifetime: Improved qubit structures, parameters, preparation techniques, and materials have greatly enhanced superconducting-qubit lifetime.The review summarizes this development in a table covering the highest reported value for each year.

F. Number of entangled qubits

The review highlights rapid growth in superconducting-qubit entanglement and introduces the control mechanisms used to manipulate these qubits, including microwave driving and SQUID-based frequency tuning.

  • F. Number of entangled qubits: 2019 marked the first demonstration of quantum supremacy using 53 superconducting qubits.The number of entangled superconducting qubits is presented as a critical indicator of full multi-qubit control.
  • 1. XY operating principle: Single-qubit rotations use microwave control, with the drive phase determining the rotation axis in the XY-plane when the qubit is resonant.The drive is capacitively coupled to an Xmon qubit and is expressed as Ω(t) = Ωx cos(ωdt − φ).
  • 1. Frequency tuning gates: A SQUID loop changes the qubit frequency by generating extra magnetic flux when current is applied through its control line.The loop consists of two Josephson junctions and is integrated beneath the Xmon.
  • 1. Frequency tuning gates: The rotation angle around the X-axis can be controlled by changing only the magnitude and duration of the current.This provides a direct current-based control mechanism for the rotation.

3. Virtual Z operation

Virtual Z operations implement Z rotations by changing the phase reference of later microwave-driven gates, enabling efficient construction of arbitrary single-qubit gates.

  • 3. Virtual Z operation: Virtual Z operations apply a phase offset to subsequent X and Y microwave gates without consuming experimental time.Only the phases in the microwave pulse sequence are modified.
  • 3. Virtual Z operation: Any single-qubit gate can be decomposed as U(θ, φ, λ) = Zφ · Xθ · Zλ for suitable angles.The decomposition combines Z and X rotations into a general single-qubit operation.
  • 3. Virtual Z operation: Two-qubit gates require a coupling Hamiltonian, commonly involving σxσx and σyσy terms in superconducting systems.For resonant Xmon qubits, the coupling produces iSWAP and sqrt(iSWAP) gates at selected interaction times.

1. Frequency tuning gates

The review surveys frequency-tuning and related approaches for implementing high-fidelity two-qubit and multi-qubit gates, including adiabatic, diabatic, parametric, and resonator-mediated control.

  • 1. Frequency tuning gates: Fast adiabatic tuning realizes a CZ gate by bringing |1, 1⟩ near the avoided crossing with |0, 2⟩, producing a selective π phase on |1, 1⟩.Barends et al. reported 99.4% fidelity for an adiabatically tuned two-qubit gate.
  • 1. Frequency tuning gates: 40 ns gate times and 99.54 ± 0.08% fidelity were achieved for a non-adiabatic CZ gate.Diabatic iSWAP-like and CPHASE gates were also reported with fidelities of 0.9966(2) and 0.9954(2), respectively, in 18 ns.
  • 2. Cross resonance: Cross-resonance gates entangle fixed-frequency qubits by applying a microwave drive to two coupled qubits.Interleaved randomized benchmarking reported fidelities exceeding 99% with a 160 ns gate time.
  • 3. Parametric gates: Parametric gates modulate flux bias to drive population between |1, 1⟩ and |0, 2⟩, accumulating a geometric phase for CZ operations.Reported CZ fidelities reached 98.8%, while an eight-qubit processor achieved 93% average process fidelity for three two-qubit gates.
  • 4. Resonator-induced gates: Resonator-induced phase gates use a shared driven bus to implement CZ gates between qubit pairs while returning the cavity to vacuum.In a four-qubit 3D cQED system, fidelities ranged from 96.55% to 98.53% across 12 qubit pairs.
  • D. Multi-qubit gates: Multi-qubit gates have been demonstrated with fidelities of 86.8% for CCZ, 93.3% for non-adiabatic CCZ, and 81.7% for CCCZ.These results were obtained in superconducting circuits using optimized waveforms or quantum process tomography.

IV. QUBIT READOUT

Superconducting-qubit readout commonly uses dispersive coupling to infer the qubit state from the readout resonator’s transmission. However, dispersive readout alone is often insufficient for fast, high-fidelity single-shot measurements.

  • Dispersive readout: Dispersive readout detects the qubit state by measuring the transmission coefficient of a coupled readout resonator.The qubit and resonator are coupled capacitively or inductively.
  • Dispersive readout: When the qubit-resonator detuning greatly exceeds the coupling strength, the qubit shifts the resonator frequency by the dispersive shift χ.This frequency change is reflected in the measured transmission coefficient.
  • Dispersive readout: The measurement integrates the outgoing microwave signal into an I+iQ point, separating |0⟩ and |1⟩ into distinguishable clusters.The resonator response therefore provides a state-dependent signal in the complex plane.
  • High-fidelity single-shot readout: Dispersive readout alone is often insufficient for fast, high-fidelity single-shot performance.Purcell filters and parametric amplifiers are typically added to improve the measurement.

1. Purcell filters

Purcell filters protect qubit lifetime while preserving rapid readout, and parametric amplifiers address the low signal levels and noise of single-shot measurements. Experiments demonstrate improved T1, multiplexed high-fidelity readout, and broadband amplification, while conventional JPAs remain bandwidth-limited.

  • Purcell filters: The Purcell effect limits qubit lifetime through resonator-mediated photon emission, so filters suppress emission near the qubit frequency while remaining transparent at the readout frequency.The lifetime is inversely proportional to qubit-resonator coupling strength and readout-resonator bandwidth.
  • Purcell filters: A quarter-wave bandpass Purcell filter enabled simultaneous measurement of four qubits with 99% intrinsic fidelity in less than 200 ns.The design targets multiplexed fast measurement without increasing environmental damping.
  • Purcell filters: A stepped-impedance Purcell filter improved qubit T1 by up to a factor of 9 relative to predicted unfiltered devices.Its wide stopband protects qubits across a broad frequency range.
  • Purcell filters: 98.25% readout fidelity in 48 ns and 99.2% in 88 ns were achieved using optimized circuit parameters, a Purcell filter, and phase-sensitive parametric amplification.These results combine filtering and amplification to improve fast readout.
  • Parametric amplifiers: Josephson parametric amplifiers reduce noise through nearly nondissipative pump-to-signal conversion, but traditional JPAs generally have bandwidths no greater than 30 MHz.This bandwidth and dynamic-range limitation constrains scaling to large systems.
  • Parametric amplifiers: Broadband amplifiers use engineered transmission lines or thousands of Josephson junctions to increase amplification bandwidth and gain.IMPA changes characteristic impedance along a tapered line, while TWPA uses phase matching in a junction array.

C. Real-time quantum feedback

Real-time quantum feedback is sought for error correction and coherence preservation, but it requires tightly coordinated, rapidly responding measurement and control. The reviewed error-correction experiments span repetition, surface, and bosonic codes, with further logical-gate demonstrations supporting progress toward universal correction.

  • Real-time quantum feedback: Real-time quantum feedback can support quantum error correction and maintenance of quantum coherence.Its full loop must combine readout, data analysis, and feedback generation before decoherence occurs.
  • Quantum error correction: Quantum error correction remains necessary for large-scale computation despite progress in coherence time, gate fidelity, and readout fidelity.The review therefore surveys several experimentally demonstrated correction schemes.
  • Repetition code: Repetition codes protect against either bit-flip or phase-flip errors, but cannot detect both error types simultaneously.They are one-dimensional variants of the surface code.
  • Surface code: Surface-code experiments progressed from repetition-code demonstrations toward two-dimensional parity measurements and planar-lattice error detection.The two-dimensional surface code can detect both bit-flip and phase-flip errors, but requires advanced feedback and repeated detection techniques.
  • Bosonic codes: Bosonic codes encode information in a multidimensional oscillator space rather than duplicating many two-level qubits.Cat and binomial codes are examples of this hardware-efficient approach.
  • Bosonic codes: Experiments demonstrated universal gates on cat-code logical qubits and ancilla-enabled operations designed to limit coherence loss from ancilla errors.These operations address the need to manipulate encoded logical qubits for universal error correction.

C. Other error-correction method

Beyond surface and bosonic codes, superconducting processors have demonstrated other error-correction codes, quantum simulation of diverse models, and algorithms for linear systems, chemistry, and machine learning. These experiments remain small-scale demonstrations, but they illustrate the platform’s programmable scope and candidate applications.

  • Other error-correction methods: The code was implemented in a five-qubit transmon device, and logical-space randomized benchmarking reduced two-qubit infidelity from 5.8(2)% to 0.60(3)%.The reported reduction was approximately one order of magnitude.
  • Scope: Current quantum devices remain small-scale and have not surpassed small demonstration algorithms.The review presents these demonstrations as useful for understanding system performance and architecture.
  • Quantum simulation: Superconducting transmon processors support analog simulation when their Hamiltonians resemble the Bose-Hubbard model.Experiments resolved the entire energy spectrum of a Hamiltonian on a linear transmon array.
  • Quantum simulation: Digital quantum simulation uses gate decompositions and has been applied to quantum Rabi, spin, fermionic, and anyonic models.Unlike analog simulation, it is not constrained by the types of systems that can be simulated.
  • Quantum algorithms: A four-qubit superconducting processor implemented the HHL algorithm for solving a two-dimensional system of linear equations.The review also describes homomorphic encryption for linear-equation solving on a cloud quantum computer.
  • Quantum algorithms: VQE experiments calculated the H2 energy spectrum with near chemical accuracy and addressed molecular problems up to BeH2 using six qubits.Parameterized hybrid algorithms are presented as promising for NISQ devices.
  • Quantum algorithms: Superconducting processors have implemented variational classifiers, quantum kernel estimation, and quantum generative models for machine-learning tasks.These demonstrations present routes to quantum machine learning on NISQ hardware.

C. Quantum supremacy

Quantum supremacy is defined as demonstrating that a programmable quantum device can solve a problem classical computers practically cannot. Google’s 2019 Sycamore experiment achieved this milestone, while the review emphasizes that practical quantum computing still requires improved hardware and useful applications.

  • Quantum supremacy means demonstrating that a programmable quantum device can solve a problem that classical computers practically cannot.
  • Google’s 2019 experiment used a programmable superconducting processor with 53 available qubits called Sycamore.
  • The experiment implemented a depth-20 two-qubit circuit containing 430 two-qubit and 1,113 single-qubit gates, with predicted total fidelity of 0.2%.
  • Improved two-qubit gate fidelity and reduced crosstalk during parallel gate operations were critical techniques in the demonstration.
  • The review identifies qubit connectivity, gate fidelity, and coherence time as key challenges, with useful applications and error-correcting quantum computers still needed.
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