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Superconducting Qubits: Current State of Play

Morten Kjaergaard, Mollie E. Schwartz, Jochen Braumüller, Philip Krantz, Joel I-Jan Wang, Simon Gustavsson, William D. Oliver

arXiv:1905.13641v3quant-phcond-mat.mes-hallphysics.app-ph

TL;DR

Superconducting qubits must advance toward scalable quantum computation beyond classical reach. This review synthesizes recent progress across hardware, control, algorithms, readout, and error correction, highlighting high-fidelity interactions and operations on logical qubits.

  • Problem

    Realizing medium- and large-scale quantum computation requires a controllable, low-noise platform capable of quantum tasks beyond modern supercomputers.

  • Method

    The review surveys advances in qubit coherence, gates, readout, memories, NISQ demonstrations, and quantum error-correction experiments.

  • Results

    Two-qubit interaction fidelities greater than 0.99, logical-qubit lifetimes exceeding constituent-element lifetimes, and operations between encoded qubits have been demonstrated.

  • Takeaways & Limitations

    Superconducting qubits are well positioned for NISQ protocols and show experimental progress toward larger-scale error-corrected quantum computers.

  • Takeaways & Limitations

    Scaling requires maintaining coherence and high-fidelity control, developing scalable calibration, and creating efficient verification and validation techniques.

Abstract

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Superconducting qubits are leading candidates in the race to build a quantum computer capable of realizing computations beyond the reach of modern supercomputers. The superconducting qubit modality has been used to demonstrate prototype algorithms in the 'noisy intermediate scale quantum' (NISQ) technology era, in which non-error-corrected qubits are used to implement quantum simulations and quantum algorithms. With the recent demonstrations of multiple high fidelity two-qubit gates as well as operations on logical qubits in extensible superconducting qubit systems, this modality also holds promise for the longer-term goal of building larger-scale error-corrected quantum computers. In this brief review, we discuss several of the recent experimental advances in qubit hardware, gate implementations, readout capabilities, early NISQ algorithm implementations, and quantum error correction using superconducting qubits. While continued work on many aspects of this technology is certainly necessary, the pace of both conceptual and technical progress in the last years has been impressive, and here we hope to convey the excitement stemming from this progress.

1. INTRODUCTION

Superconducting qubits are a leading platform for quantum computation beyond modern supercomputers, with progress spanning high-fidelity gates, NISQ demonstrations, and logical-qubit operations toward fault-tolerant systems. This review highlights advances across hardware, gates, readout, algorithms, and quantum error correction.

  • Motivation: Superconducting qubits enable controlled quantum degrees of freedom and interactions for computations and simulations beyond modern supercomputers.They are collective excitations in superconducting circuits and are among the leading approaches for quantum logic elements.
  • Fault-tolerant quantum computing: Fault-tolerant development has progressed from logical qubits to operations on single logical qubits and logical operations between two encoded, but not yet error-corrected, qubits.A logical qubit with a lifetime longer than any underlying constituent element has also been demonstrated.
  • NISQ quantum computing: Multi-qubit superconducting systems of 10–20 qubits support the NISQ approach, while larger 50–100-qubit systems are under development.NISQ systems target highly optimized quantum algorithms and simulations without requiring fault tolerance.
  • Review scope: The review focuses on recent highlights in superconducting-qubit hardware, gate implementations, readout, early NISQ demonstrations, and quantum error correction.NISQ topics include quantum supremacy, simulation, digital algorithms, and annealing; error-correction coverage includes parity readout and surface-code-related experiments.

2. THE HARDWARE OF SUPERCONDUCTING QUBITS

Superconducting-qubit hardware uses Josephson junctions to create nonlinear circuits, with transmons dominant for gate-based computation and flux qubits prominent in quantum annealing. Microwave control, multiplexed dispersive readout, and bosonic encodings support high-fidelity operations, scalable measurement, and error-syndrome extraction.

  • Qubit hardware: Josephson junctions provide coherent Cooper-pair tunneling and a lossless nonlinear inductance, enabling superconducting circuits to function as qubits.The junction consists of two superconducting electrodes separated by a thin insulating barrier.
  • Qubit modalities: 50 µs to 100 µs coherence times were achieved in capacitively shunted flux qubits by reducing circulating current and sensitivity to flux noise.The added shunt capacitance reduced anharmonicity to around 500 MHz.
  • Qubit modalities: Transmons are the most widely used qubits for gate-based computation, whereas persistent-current and rf-SQUID flux qubits predominate in quantum annealing.Transmons have demonstrated high-fidelity logical operations, quantum simulations, and digital algorithms; flux-qubit platforms include the commercial D-Wave system.
  • Gate implementation: Single-qubit gates routinely reach fidelities ≳0.99 using microwave control, with DRAG enabling fast operations while suppressing leakage into higher levels.Virtual phase shifts implement z-axis rotations.
  • Readout: Fast, high-fidelity readout relies on quantum-limited amplification, while frequency multiplexing reduces hardware overhead by sharing amplifier chains across resonators.Multiplexing is limited by parametric-amplifier bandwidth and saturation power; Purcell filters mitigate readout-cavity-induced energy decay.
  • Bosonic encoding: Dispersive coupling enables photon-number-resolved and parity readout in bosonic encodings, allowing resonator-state characterization and extraction of error syndromes.In the photon-number-resolved regime, the transmon frequency shifts as ωq,n = ωq − nχ; parity flips are common bosonic-QEC error syndromes.

3. EARLY NISQ ERA DEMONSTRATIONS USING SUPERCONDUCTING QUBITS

Early NISQ demonstrations use noisy, non-error-corrected superconducting-qubit hardware to pursue useful computations despite limited resources, but remain mostly proof-of-principle apart from random-circuit sampling. The section organizes these implementations into four overlapping branches, including quantum-supremacy platforms and quantum simulations.

  • NISQ-era implementations: NISQ implementations operate without quantum error correction and tolerate system noise to maximize the effect of limited intermediate-scale quantum resources.These demonstrations seek useful quantum computations on noisy hardware.
  • NISQ-era implementations: Most NISQ demonstrations remain proof-of-principle, with sampling solutions of a random circuit identified as a notable exception.The passage is truncated after introducing this exception.
  • Section organization: The section divides early NISQ implementations into four branches with soft borders.The supplied passage introduces the organizational structure but does not list all four branches.
  • NISQ-Era Platforms and a Demonstration of Quantum Supremacy: NISQ-Era Platforms and a Demonstration of Quantum Supremacy discusses a report of quantum supremacy on a 53-qubit processor and the role of online cloud-based quantum computers.The passage presents this as Section 3.1.
  • Quantum Simulations with Superconducting Circuits: Quantum Simulations with Superconducting Circuits use a physical quantum system to study another quantum system of interest.The passage notes that physical-qubit errors decrease simulation fidelity.

3.1. NISQ-Era Platforms and a Demonstration of Quantum Supremacy

Commercializable NISQ-era algorithms depend on increasingly complex and higher-quality quantum computers. Cloud-based superconducting systems broaden access beyond traditional physics and quantum-hardware experts, with IBM pioneering the approach and access available from multiple providers.

  • Commercializable NISQ-era algorithms will rely on quantum computers of increasing complexity and quality.
  • Cloud-based access lets algorithm designers and experts outside traditional physics or quantum hardware backgrounds test ideas on superconducting quantum systems.
  • IBM pioneered cloud-based access with a 5-transmon qubit device in 2016; access was also available from Rigetti Computing and D-Wave when reviewed.

3.2. Quantum simulations with superconducting circuits

Superconducting circuits enable quantum simulations by emulating complex quantum-system dynamics with highly controllable, tunable hardware, potentially avoiding exponential classical-resource scaling. Demonstrated digital, analog, and analog-digital approaches exploit different trade-offs between versatility, resource scaling, and gate-construction overhead.

  • Motivation and principles: Quantum simulators emulate complex quantum-system dynamics with quantum hardware, potentially avoiding the exponential scaling of classical computational resources.They require a mapping between the target system’s evolution U and the simulator’s evolution U′.
  • Motivation and principles: Superconducting circuits provide precise control, efficient readout, tunable qubit frequencies, and adjustable coupling strengths for quantum simulation experiments.These properties support manipulation and preparation of simulator states while tailoring circuit characteristics to the problem.
  • Digital quantum simulation: Digital quantum simulation decomposes complex evolutions into single- and two-qubit gates and is compatible with universal computation and error-correcting schemes.Lie-Trotter-Suzuki decompositions introduce errors from non-vanishing commutators between decomposed Hamiltonians.
  • Digital quantum simulation: ∼5 Trotter steps was the maximum reached in demonstrated digital spin-model simulations because of gate errors on nine-qubit and two-qubit chips.These experiments demonstrated the versatility and universality of the digital approach while remaining limited in sequence depth.
  • Analog and analog-digital quantum simulation: Analog-digital simulation combines analog unitary blocks with digital gates to reduce gate-construction overhead while preserving analog scaling and enhancing versatility.The strategy was used to simulate the quantum Rabi model in the ultrastrong-coupling regime, where dynamics are difficult to track classically.

3.3. Small-scale quantum algorithms

Small-scale superconducting-qubit algorithms in the NISQ era include early demonstrations of non-error-corrected Deutsch-Jozsa and Shor circuits, hybrid variational methods for chemistry, and quantum machine-learning protocols. These approaches adapt computation to lossy hardware, while QRAM requirements remain an open feasibility question.

  • NISQ algorithm foundations: Early superconducting-circuit demonstrations implemented small, non-QEC versions of Deutsch-Jozsa and Shor algorithms, alongside surface-code primitives.NISQ algorithms can be hardware-informed, adapting to qubit connectivity, low-fidelity qubits, and difficult gates rather than relying on full quantum error correction.
  • Quantum chemistry: Two qubits mapped the H2 ground state with VQE, while experiments using up to six qubits mapped ground states of LiH and BeH2.VQE maps molecular Hamiltonians to qubits, measures expectation values, and uses classical minimization to estimate ground-state energies; QSS and EOM extend estimates to excited states.
  • Quantum machine learning: A four-qubit HHL implementation sampled solutions to linear equations, while two supervised classification algorithms ran on two qubits of a five-qubit processor.Variational quantum machine-learning methods also support supervised and unsupervised data classification and may admit feature maps with provable quantum advantages.
  • Quantum machine learning: QAOA offers approximate solutions to NP-hard multivariate minimization in polynomial time, with accuracy guaranteed by the algorithm and most computation performed classically.The quantum device prepares a state and performs the required measurements, paralleling the hybrid structure of VQE.
  • Quantum memory: QRAM assumptions in several classical-data protocols pose an open feasibility question, although a random-access quantum memory was demonstrated using a single parametrically driven transmon qubit.The demonstrated memory is described as RAQM, in which classical address bits retrieve a quantum state.

3.4. Quantum annealing

Quantum annealing encodes computational problems in the ground state of a time-dependent Hamiltonian and adiabatically evolves from a known initial ground state to the problem Hamiltonian. D-Wave’s superconducting flux-qubit devices implement this approach, enabling lattice simulations while leaving the source of reported runtime advantages unresolved.

  • Principle: Quantum annealing encodes a problem in a Hamiltonian’s ground state and seeks its global minimum through adiabatic quantum evolution.This is formally equivalent to adiabatic quantum computation.
  • Hardware: ∼2000 superconducting flux qubits form D-Wave’s notable quantum-annealing implementation, with eight-qubit unit cells arranged in a Chimera graph.Each qubit is longitudinally coupled to four others in the final Hamiltonian.
  • Annealing protocol: The protocol starts with Γ(0) = 1 and Λ(0) = 0, then ramps Γ to zero while increasing Λ to unity to reach the final Ising Hamiltonian.The initial state is a known ground state represented by an equal superposition in the computational basis.
  • Applications: 512 Ising spins were simulated on a D-Wave device to map a spin-glass magnetic phase diagram, while related work studied a Kosterlitz-Thouless transition.Non-trivial encodings make a variety of relevant lattices accessible for condensed-matter research.
  • Performance: Recent studies report significant runtime advantages for certain problem classes, but whether this results from a quantum mechanism remains an open question.The supplied passage does not specify the magnitude or precise source of the advantage.

Parity measurements - a workhorse in quantum error detection and correction

Parity measurements use an ancilla to infer bit and phase parity of data qubits while preserving the individual-qubit state. Because these parity operators commute, measurements across larger qubit grids can identify bit- or phase-flip errors without directly corrupting the data state.

  • Parity measurements: Ancilla qubits infer bit parity through Z1Z2 and phase parity through X1X2 measurements on two data qubits.The measured parity corresponds to the operators’ eigenvalues, +1 or −1.
  • Parity measurements: Parity measurement reveals whether the two-qubit state has eigenvalue +1 or −1 without collapsing the individual data qubits.This preservation assumes the ancilla qubit is error-free.
  • Parity measurements: Commuting parity operators enable measurements across larger qubit grids to infer if and where bit- or phase-flip errors occurred.The approach extends to combinations involving more Z and X operators.

4. QUANTUM ERROR CORRECTION WITH SUPERCONDUCTING QUBITS

Quantum error correction remains necessary for large-scale superconducting quantum computers, motivating experiments on redundant logical encodings, parity measurements, fault tolerance, and bosonic codes. Recent work has demonstrated increasingly capable error-detection, stabilization, fault-tolerant encoding, and encoded-gate primitives.

  • Motivation and parity measurements: Quantum error correction is required for truly large-scale quantum computers, using redundancy across multiple physical qubits to encode logical qubits.Experimental progress has therefore emphasized multi-qubit parity measurements and surface-code primitives.
  • Surface-code primitives: Superconducting-qubit experiments have implemented parity measurements across surface-code subsections, including repetition codes that correct either bit-flip or phase-flip errors.The repetition code is a one-dimensional surface-code row and cannot simultaneously detect both error types.
  • Error detection and stabilization: Experiments demonstrated full quantum error detection for bit and phase flips using a 2 × 2 surface-code half-plaquette and stabilized Bell states using repeated parity checks.Bell-state experiments maintained fidelity ∼0.74 for up to 12 feedback cycles and achieved fidelity ∼0.8 over 26 rounds with Pauli frame updating.
  • Surface-code primitives: Weight-four parity measurements, required by the surface code, were first demonstrated in superconducting qubits using optimized gates to cancel cross-talk from cross-resonance operations.These measurements involve operators such as Z1Z2Z3Z4 or X1X2X3X4.
  • Fault tolerance: Fault-tolerant encoding with the [[4, 2, 2]]–code has improved logical-gate performance, with logical-gate infidelity decreasing by nearly an order of magnitude versus non-FT physically equivalent gates.The code uses five physical qubits, encodes two logical qubits, and detects but does not correct errors.
  • Bosonic codes: Bosonic codes encode logical qubits in many energy levels of a single superconducting cavity and have advanced from cat-state mapping and error detection to encoded entanglement and two-qubit gates.Demonstrations include logical CNOT, CNOT gate teleportation, logical state transfer, remote entanglement, and exponential-SWAP operations.

5. LOOKING AHEAD

Superconducting-qubit research continues to advance rapidly, but scaling toward fault-tolerant quantum computing faces substantial challenges in error-correcting codes, qubit architectures, control, calibration, and system integration. Current techniques may scale to roughly 1000 qubits, after which new approaches will be required.

  • Quantum error correction: The surface code offers a relatively lenient error threshold and modest connectivity requirements, but its physical-to-logical qubit overhead is daunting and its fault-tolerant gate set is limited.Other topological and concatenated codes demand more stringent error thresholds and connectivity, while enabling a larger fault-tolerant gate set.
  • Quantum error correction: Bosonic codes have shown promising preliminary experiments, but fault-tolerant multi-qubit protocols are currently absent, potentially requiring embedding in a larger error-correcting fabric.Such embedding could introduce the scaling issues associated with surface-code architectures.
  • Qubit architectures: Transmons trade charge-noise resilience for small anharmonicity, increasing leakage from the computational subspace; fluxonium addresses this limitation while combining advantages of other qubit modalities.A voltage-controlled transmon strategy replaces local flux control with local electrostatic-gate control of semiconductor carrier density, modifying EJ.
  • Scaling toward fault tolerance: Demonstrating multiple error-corrected fault-tolerant logical qubits with gate fidelities and lifetimes exceeding those of their constituent degrees of freedom is an important step toward large quantum processors.The field still faces nontrivial obstacles despite ample opportunity for both NISQ demonstrations and large-scale fault-tolerant computers.
  • Scaling challenges: Maintaining high coherence and high-fidelity control across medium- and large-scale chips, while developing scalable calibration techniques, remains a key challenge.Larger processors involve many non-trivial cross-calibration terms, requiring advanced software strategies.
  • Scaling challenges: ∼1000 qubits is the approximate scale current techniques may reach; beyond this, new techniques such as co-located control electronics and on-the-fly quantum-error-correction decoders will be needed.This estimate is explicitly described as rough and notwithstanding the outlined challenges.

DISCLOSURE STATEMENT

The authors report no known affiliations, memberships, funding, or financial holdings that might be perceived as affecting the review’s objectivity.

  • The authors disclose no known affiliations, memberships, funding, or financial holdings that might affect the review’s objectivity.
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