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Quantum information processing with superconducting circuits: a review

G. Wendin

arXiv:1610.02208v2quant-ph

TL;DR

Superconducting circuits have become contenders for useful and scalable QIP, motivating a review of practical devices, systems, protocols, and applications. The paper surveys implemented hardware and protocols, highlights foundational control and coupling capabilities, and discusses applications in computation and simulation, while identifying remaining coherence, calibration, and remote-entanglement constraints.

  • Problem

    The paper addresses how superconducting circuits can support useful and scalable QIP applications beyond demonstrations that remain difficult for classical simulation.

  • Method

    The review surveys current superconducting hardware and implemented QIP protocols, with detailed treatment of one- and two-qubit gates, control, readout, characterisation, and interfaces.

  • Results

    The review reports foundational microwave control, qubit-resonator coupling, dispersive readout, excitation swapping, and experimental demonstrations involving superconducting qubits and coupled systems.

  • Takeaways & Limitations

    Superconducting circuits offer a practical platform for near-term QIP in computation, simulation, and quantum communication protocols.

  • Takeaways & Limitations

    Applications remain constrained by challenges including limited coherence for long calculations, calibration inaccuracies in analogue annealing, and difficulty detecting microwave photons for remote entanglement.

Abstract

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During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments have been shown with up to nine qubits, while a demonstration of Quantum Supremacy with fifty qubits is anticipated in just a few years. Quantum Supremacy means that the quantum system can no longer be simulated by the most powerful classical supercomputers. Integrated classical-quantum computing systems are already emerging that can be used for software development and experimentation, even via web interfaces. Therefore, the time is ripe for describing some of the recent development of superconducting devices, systems and applications. As such, the discussion of superconducting qubits and circuits is limited to devices that are proven useful for current or near future applications. Consequently, the centre of interest is the practical applications of QIP, such as computation and simulation in Physics and Chemistry.

11 Adiabatic quantum optimisation

Section 11 covers adiabatic quantum algorithms and quantum annealing as approaches to adiabatic quantum optimisation.

  • Adiabatic quantum algorithms and quantum annealing are presented as subsections of adiabatic quantum optimisation.

1. Introduction

The review surveys practical progress in superconducting-circuit QIP, focusing on implemented hardware and protocols while anticipating scalable applications in Physics, Chemistry, and Materials Science.

  • Quantum computing controls complex, entangled quantum states in physical hardware for computation and simulation.
  • Microwave control, strong qubit-resonator coupling, and dispersive readout were demonstrated as foundational superconducting-circuit capabilities.
  • Coupling CPB qubits and swapping excitations provided an experimental basis for multi-qubit superconducting systems.
  • Transmon development established a basis for potentially scalable systems with long coherence times and high-fidelity gates, control, and readout.A 3D-cavity transmon increased coherence times toward 100 µs.
  • The review focuses on hardware and protocols implemented on current superconducting devices and on developments promising for scaling circuits and systems.The authors note experimental scaling to systems with several tens of qubits.
  • The review treats one- and two-qubit gate construction and implementation in detail for a broad QIP readership, while referring broader theory and experimental work to other sources.
  • The review looks beyond current experiments toward applications addressing real-world problems in Physics, Chemistry, and Materials Science.

2. Easy and hard problems

Quantum-computing complexity classes distinguish tractable, classically hard, and quantumly tractable problems, while quantum speedup depends on nonclassical correlations and remains difficult to establish in practice.

  • Complexity classes: Polynomial-time problems belong to P, whereas BQP contains problems efficiently solvable by quantum computers with bounded error.BPP is believed to equal P because probabilistic computation can be simulated deterministically with only polynomial overhead.
  • Complexity classes: BQP extends beyond P through algorithms such as Shor’s, but it excludes much of NP, which contains many problems hard for classical computers.The review therefore distinguishes quantum advantage from solving genuinely hard computational problems.
  • Limits of physical computation: Finite analogue computers cannot efficiently solve NP-complete problems because digital simulation requires only polynomially related resources.This supports the view that physical systems do not automatically overcome worst-case computational hardness.
  • Sources of quantum advantage: Entanglement and other nonclassical correlations provide the basis for quantum speedup, although several entanglement measures are themselves NP-hard to compute classically.Examples include concurrence, entropy of entanglement, negativity, and quantum discord.
  • Assessing quantum advantage: Quantum speedup is an asymptotic scaling property, but present digital quantum systems of 5–10 qubits and limited coherence times restrict long calculations.Quantum Supremacy instead targets a device, currently described as roughly 50 qubits, that cannot be simulated by available classical computers in reasonable time.

3. Superconducting circuits and systems

Superconducting JJ qubits use nonlinear LC circuits whose parameters determine their energy structure, noise sensitivity, and device family. Recent platforms demonstrate scalable systems, high-fidelity control, single-shot readout, and improving coherence, although some qubit types remain limited by short coherence times.

  • Scalable platforms: Transmon, Xmon, and related platforms form the basis of scalable systems, with systematic transmon development targeting control, benchmarking, error correction, and simulation up to 50 qubits.The 2D transmon is established in scalable platforms, while systems with up to 9 Xmon qubits are being investigated.
  • Circuit foundations: The circuit is characterized by charging, inductive, and Josephson energies, while induced charge and external flux provide electrical and magnetic control parameters.The equivalent circuit defines EC, EL, and EJ0, with ng set by capacitive coupling and φe controlled by external flux.
  • Circuit foundations: Superconducting qubits are nonlinear LC circuits in which Josephson junctions provide the anharmonicity needed to address selected energy levels.The underlying circuit uses charge and phase as noncommuting variables; adding the junction makes the oscillator anharmonic.
  • Circuit families: Increasing EJ0/EC exponentially suppresses charge dispersion while reducing anharmonicity only algebraically, enabling individually addressable transitions at large ratios.Large capacitance produces flat low-lying bands and reduced sensitivity to charge fluctuations; this principle underlies the transmon.
  • Device limitations: Phase and three-JJ flux qubits remain constrained by coherence: phase-qubit coherence stays below 1 µs, while limited flux-qubit improvement has restricted applications.By contrast, the C-shunt flux qubit shows coherence times above 40 µs at its flux-insensitive point.
  • System capabilities: Universal high-fidelity one- and two-qubit operations, single-shot readout, and substantially improved coherence have been demonstrated across superconducting platforms.Entangling gates have reached 99.4% fidelity, and dispersive readout uses quantum-limited amplifiers; high-fidelity gates may require 10-40 µs shaped pulses.

4. Transmon quantum circuits

The transmon combines a charge-noise-insensitive CPB with resonators and tunable couplings, providing a platform for qubit control, readout, and multi-qubit interactions. Its circuit behavior spans Jaynes–Cummings and quantum Rabi regimes, with several experimentally demonstrated coupling configurations.

  • The transmon section focuses on coupling transmon-type qubits with quantum oscillators for operation, readout, and memory.The review presents a compact circuit model and a schematic hardware implementation.
  • The transmon uses a CPB with one or two Josephson junctions, a large shunt capacitance, a resonator, coupling capacitance, and microwave and flux drives.The qubit is modeled as an anharmonic oscillator coupled to a harmonic resonator.
  • The transmon–resonator Hamiltonian is the quantum Rabi model; retaining only Jaynes–Cummings terms gives the rotating-wave approximation.The coupling contains both rotating and counter-rotating contributions.
  • Strong coupling enables vacuum Rabi oscillations, while ultra-strong and deep-strong regimes require counter-rotating terms or driven simulation schemes.The coupling regimes are distinguished by g relative to qubit and oscillator frequencies and decay rates.
  • Dispersive coupling shifts both qubit and oscillator energies in a state-dependent way, enabling qubit-state discrimination through readout.The condition is detuning Δ = ϵ − ħω much larger than g.

5. Hybrid circuits and systems

Hybrid superconducting systems connect transmons to resonators, spins, magnons, and mechanical or acoustic modes for memory, conversion, and communication. Experiments demonstrate coherent transfer, storage, strong coupling, and quantum swaps, while coherent end-to-end interfaces remain challenging.

  • Hybrid architectures combine fast superconducting qubit processors with longer-lived memories and microwave–optical interfaces.This motivation reflects the shorter coherence times of JJ qubits compared with spin qubits and trapped ions.
  • Strong coupling mixes excitations from different components, enabling entanglement, information storage, and conversion between localized and flying qubits.The review uses sideband structures as an indicator of such mixing.
  • Spin ensembles have stored multiple picowatt-level microwave pulses and retrieved them after up to 35 µs, a three-orders-of-magnitude improvement over previous experiments.The protocol used optical reset and Hahn-echo refocusing.
  • Transmons have been entangled with NV spin ensembles through a frequency-tunable resonator bus, demonstrating spin-ensemble quantum memory in principle.The passage notes that lifetime, coherence, and fidelity remain relevant considerations.
  • Strong coupling has also been demonstrated between transmons and magnon modes, including magnon-vacuum-induced Rabi splitting and tunable coupling.Parametric driving provides control and measurement of magnon excitations.
  • Quantum-regime coupling of propagating SAW phonons to a transmon reproduces quantum-optics effects while exploiting sound’s low propagation speed and short wavelength.The approach motivates circuit quantum acoustodynamics and related acoustic cavities.
  • An HBAR strongly coupled to a transmon demonstrated qubit–phonon swaps, with qubit T1 = 6 µs and lowest-phonon-level T1 = 17 µs and T2 = 27 µs.The device is presented as a potential resource for scalable hybrid systems.
  • Microwave–optical interfaces have shown coherent bidirectional conversion and theoretical full quantum conversion, but coherent coupling across complete component chains remains a major challenge.Candidate components include optomechanical, micromechanical, magnon, and SAW oscillators.

6. Quantum gates

Quantum computation and simulation are described through time evolution under a controlled many-body Hamiltonian. Control pulses selectively activate single-qubit terms, interactions, tuning, and readout to implement gates and computational sequences.

  • QIP maps classical data into a circuit’s Hilbert space, evolves the quantum state, measures registers, and analyzes the classical output.At this level, quantum computing and quantum simulation share the same workflow.
  • The time-evolution operator U(t,t0) is determined by the time-dependent many-body Hamiltonian containing intrinsic system terms and applied controls.It describes the complete many-particle evolution over [t0,t].
  • Control pulses make Hamiltonian terms time-dependent, enabling qubit and resonator tuning, coupling, readout, and Hamiltonian evolution.Environmental noise can also appear as time dependence of control parameters.
  • The control Hamiltonian provides single-qubit gates, externally driven qubit–qubit coupling, and oscillator tuning.These functions correspond to distinct terms in the transmon control model.
  • Sequentially switching selected Hamiltonian terms implements stepwise evolution, while time ordering is unnecessary when the Hamiltonian commutes with itself at different times.Constant Hamiltonians yield the simple exponential evolution operator.
  • Computation uses sequentially activated one- and two-qubit gates, potentially operating in parallel on different qubit groups to induce effective N-qubit gates.An ideal computational step activates only the selected Hamiltonian terms.

6.3. 1q rotation gates

Single-qubit rotations arise from time-dependent control terms that act sequentially when control operators do not commute. The resulting operators implement rotations about the x, y, and z axes.

  • Single-qubit gates are generated by the time-dependent one-qubit component of the control Hamiltonian.The control function determines the applied rotation angle.
  • Noncommuting σν operators prevent factorization into a single product, so the corresponding controls must be applied sequentially in separate time slots.This sequencing yields a product of rotation operations.
  • The resulting rotation operators implement single-qubit rotations around the x-, y-, and z-axes.

6.4. 2q resonance gates

Resonance-based two-qubit gates use tunable qubit energies and interactions to implement iSWAP and CPHASE operations. These gates support broader controlled operations, including CNOT, controlled rotations, and phase estimation circuits.

  • The 2q interaction evolution is derived from matrix elements of the interaction Hamiltonian, with resonance simplifying the resulting time-evolution operator.The derivation expands the exponential evolution operator and evaluates it in an extended computational basis.
  • The iSWAP gate emerges when two qubits are tuned into resonance, enabling excitation oscillations between |01⟩ and |10⟩.A π pulse first prepares |01⟩ from |00⟩, after which the interaction swaps the excitation between the qubits.
  • The CPHASE gate uses avoided-level-crossing repulsion between |11⟩ and |02⟩ to generate an interaction-dependent phase shift.One qubit is tuned near resonance, held at the crossing for a prescribed time, and then returned; the resulting phase is set by the integrated bias excursion.
  • The CPHASE operation is obtained when the |11⟩ state accumulates a phase φ11(t) = π during the controlled excursion.The relevant frequency shift is ζ = f10 + f01 − f11.
  • CNOT is implemented from CPHASE with two Hadamard gates, while CPHASE generalizes to controlled Z rotations and controlled time evolution.The same circuit family supports phase estimation by mapping states to an ancilla.

6.5. 2q gates induced by microwave driving

Microwave driving provides tunable effective couplings between superconducting qubits and resonators without always requiring tunable coupling elements. The section surveys cross-resonance, bus-mediated, resonator-induced, and multiqubit gate strategies alongside their scaling constraints.

  • Parametric microwave driving creates sidebands that bridge frequency gaps and enable entanglement between qubits with different frequencies.The approach can use fixed linear couplings, microwave control signals, and tunable effective interactions.
  • Cross-resonance drives one qubit at the transition frequency of another, producing an effective coupling whose strength grows with drive amplitude divided by frequency difference.The mechanism can be interpreted through resonance between a dressed-state transition of the driven qubit and the bare transition of the other.
  • CR and MAP gates may be difficult to scale because their couplings depend sensitively on transmon level structure and weak anharmonicity.MAP uses resonance between the |03⟩ and |12⟩ states, while CR is limited by transmon weak anharmonicity.
  • A tunable bus can mediate resonant exchange between frequency-detuned qubits, including a 183 ns iSWAP with measured average fidelity 0.98.The demonstrated qubits were separated by 854 MHz, and the result is identified as potentially relevant to surface-code architectures.
  • RIP gates use fixed-frequency transmons coupled through a driven bus resonator, and experiments demonstrated high-fidelity CZ gates between all qubit pairs in a four-qubit setup.The demonstrated system covered frequency detunings up to 1.8 GHz and generated a four-qubit GHZ-type state.
  • Multiqubit gates can be built sequentially, through optimized single-shot pulses, or through collective bus dynamics.The surveyed approaches include proposals for transmon implementations of Mølmer-Sørensen-type gates and controlled multiqubit operations.

6.6. Gate synthesis and universal sets of gates

Quantum circuits are synthesized from finite gate libraries, with Clifford gates generated by H, S, and a two-qubit gate such as CNOT or CPHASE. Adding a non-Clifford T gate yields a universal set, although general synthesis can require exponentially many gates.

  • The Clifford stabilizer group is generated by the Hadamard gate H, the phase gate S, and a two-qubit gate such as CNOT or CPHASE.
  • Adding the non-Clifford T gate forms the universal set {H, S, CNOT, T}, capable in principle of generating all quantum circuits.Universality does not necessarily imply efficient polynomial-time computation.
  • General quantum-circuit synthesis may require an exponential number of elementary gates, despite efficient single-qubit approximation guaranteed by Solovay-Kitaev.
  • A classical simulation algorithm for Clifford + T circuits is polynomial in qubit number and Clifford gates but exponential in the number of T gates.Its mild exponential scaling enabled simulation of a 40-qubit hidden-shift circuit with nearly 50 T gates.

7. Quantum state preparation and characterisation

Quantum state preparation and characterization use gate sequences, measurements, tomography, and entanglement protocols. The section emphasizes both demonstrations of multiqubit states and the exponential cost of full characterization as systems grow.

  • Tomography characterizes quantum states and processes by measuring and presenting large quantities of quantum information.In solid-state devices, rotation gates are applied before measurement because integrated detectors cannot be rotated.
  • An N-qubit density matrix requires 22N −1 independent measurements for full characterization, making complete tomography impractical for large systems.For two qubits, 15 matrix elements are determined through 15 measurements at different angles.
  • Reduced-information methods such as randomized benchmarking, compressed-sensing QPT, and adaptive Bayesian tomography address the scaling limits of full QPT.Randomized benchmarking measures accumulated error over long gate sequences and accounts for state-preparation and measurement errors.
  • Cross entropy compares sampled output distributions from experimental random circuits with ideal distributions simulated by a supercomputer and is related to circuit fidelity.The example considers a 7 x 6 qubit lattice with gate depth 25, close to the classical simulation limit described there.
  • Five capacitively coupled Xmon qubits were characterized in GHZ-type experiments using quantum state tomography, with later work reporting tomographic results for a 10-qubit GHZ state.
  • Parity measurement can prepare Bell states by using an ancilla whose measurement projects the remaining qubits into a state with definite parity.The protocol begins with Hadamard-generated superpositions and CNOT operations that create a sum of Bell pairs with opposite parities.
  • Transmon teleportation demonstrated state transfer over a millimeter on one chip, while longer-distance communication still requires microwave or microwave-optical links.A four-transmon experiment also identified Bell states of two remote output qubits through tomography after measuring intermediate qubits.

8. Quantum state protection

Quantum state protection combines optimized control, measurement-based feedback, repetition codes, cat-state encodings, and engineered environments to preserve and manipulate superconducting quantum states. Experiments demonstrate improved gate fidelities, error correction, and logical-state lifetimes, while entangling logical qubits remains an open requirement.

  • Quantum control: An adaptive hybrid control method enhanced gate fidelities by an order of magnitude in typical solid-state quantum-information settings.Ad-HOC combines gradient-based pulse optimization with experimental, gradient-free fidelity estimation.
  • Quantum error correction: Repetition-code processing preserved a GHZ state without dynamic quantum-gate feedback by detecting errors and applying classical post-processing.The protocol corrected bit-flip errors when present and preserved the state when no errors occurred.
  • Quantum error correction: Five-qubit and nine-qubit repetition codes reduced input-state retrieval failure rates by factors of 2.7 and 8.5, respectively, after eight cycles.The nine-qubit experiment implemented three cycles of a repetition code and later extended the work to a five-qubit code.
  • Cat-state protection: Two-mode cat states were reconstructed over Hilbert spaces exceeding 100 dimensions, supporting logical operations between redundantly encoded qubits.The states were characterized through quantum nondemolition measurements of joint photon-number parity.
  • Cat-state protection: A corrected cat-code qubit reached a 320 µs lifetime, exceeding the lifetime of every constituent system component.The protocol used real-time feedback to encode, monitor, decode, and correct naturally occurring energy-loss errors.
  • Logical gates: Universal computation still requires entangling gates between two logical qubits, and efficient microwave-photon detection remains challenging for remote-entanglement schemes.A microwave photon detector enabled a robust form of concurrent remote entanglement, potentially supporting modular three-dimensional architectures.

9. Quantum simulation of many-body systems

Quantum simulation maps dynamical or ground-state problems onto quantum hardware through Hamiltonian evolution, Trotterized operations, and phase estimation. Superconducting circuits have experimentally demonstrated digital simulations of spin models, the Fermi-Hubbard model, and molecular hydrogen.

  • Simulation framework: Quantum simulators propagate an initial state under a Hamiltonian to solve the time-dependent Schrödinger equation and reveal system dynamics or energy spectra.The initial state may be a basis state, superposition, product state, Hartree–Fock determinant, coupled-cluster state, or matrix-product state.
  • Simulation framework: Trotterization expresses time evolution as a sequence of operations generated by individual Hamiltonian terms, implemented with quantum gates, control fields, or both.Higher-order Trotter formulas are used in practice to reduce approximation errors.
  • Phase estimation: Phase estimation connects dynamical simulation with eigenvalue estimation by storing evolution phases in ancillas and analyzing them with an inverse quantum Fourier transform.Iterative phase estimation reduces the ancilla requirement to a single qubit by using classical feedback.
  • Phase estimation: Large-molecule phase estimation can require very large gate counts and long coherence times because the required controlled rotations scale with target accuracy.The state-preparation circuit may remain polynomial, while energy estimation becomes demanding at chemical precision.
  • Spin-model simulation: Digital quantum simulation on transmon platforms has reproduced dynamics of small spin systems using sequences of qubit gates.The reviewed spin models include Ising, transverse-field Ising, XY, and anisotropic Heisenberg models.
  • Experimental applications: Superconducting circuits produced the first experimental applications of these methods to the Fermi-Hubbard model and the H2 ground-state binding curve.The approaches had previously been developed theoretically and simulated classically for about 15 years.

10. Toward quantum chemistry simulation

Quantum chemistry motivates hybrid quantum-classical methods because accurate molecular energy surfaces are computationally demanding. Quantum energy estimation and variational eigensolvers reduce coherence requirements, and experiments achieved chemical accuracy for small molecules, while fully quantum protocols remain demanding.

  • Motivation: Quantum chemistry is a major target for quantum computing, but demanding complexity bounds and QMA-hard two-body Hamiltonian problems constrain scalable simulation.Reaching chemical accuracy may require a prohibitive number of gates even when the scaling is polynomial.
  • Quantum energy estimation: Quantum energy estimation computes a Hamiltonian expectation value using local measurements of Pauli-operator products, requiring O(1) coherence time per measurement.The approach trades the phase-estimation method’s coherence demands for a polynomial increase in repetitions.
  • Quantum energy estimation: Quantum energy estimation dramatically reduces coherence-time requirements while retaining an exponential advantage over classical computation with only polynomially more repetitions than phase estimation.The method’s central calculation is quantum, while surrounding coefficient determination and processing can remain classical.
  • Variational eigensolver: The quantum variational eigensolver prepares a parameterized trial state, evaluates Hamiltonian terms through quantum energy estimation, and updates parameters using classical optimization.Only the expectation-value evaluation is quantum; preparation, comparison, and feedback are performed classically.
  • Molecular simulation: For H2 and He-H+ with two electrons, restricting the cluster operators to T1 and T2 enables approximations that reach chemical accuracy.The full coupled-cluster series can generate all configurations and correlations, but small molecules permit truncation to the two-electron case.
  • Molecular simulation: The H2 bonding-energy curve achieved chemical accuracy better than 10^-3 hartree, whereas canonical Trotterization plus phase estimation was much less accurate.The comparison demonstrates the coherence-time demands of the fully quantum approach.
  • Chemical applications: Quantum computers can serve as accelerators for classical chemistry workflows, including estimating, validating, or correcting energies of intermediates and transition states.Resource estimates for nitrogenase reaction mechanisms include quantum-error-correction and discrete-gate compilation overheads while remaining feasible on small quantum computers.

11. Adiabatic quantum optimisation

Adiabatic quantum optimisation evolves a simple initial Hamiltonian toward a problem-encoding target Hamiltonian, while quantum annealing uses thermal and quantum processes to seek low-energy solutions. Current evidence supports quantum-annealing behaviour but not quantum speedup, with performance constrained by problem embedding, calibration, and barrier structure.

  • 11.1. Adiabatic quantum algorithms: AQO interpolates from a simple starting Hamiltonian to an Ising-type target Hamiltonian whose ground state encodes the final solution.The evolution searches for a path toward the target Hamiltonian’s global energy minimum.
  • 11.2. Quantum annealing: QA lowers system temperature during Hamiltonian evolution, typically trapping the system in a local rather than global energy minimum.QA is also described as adding quantum tunnelling to classical thermal hopping.
  • 11.2. Quantum annealing: D-Wave machine behaviour is consistent with quantum annealing, but no scaling advantage or quantum speedup has so far been observed.The review presents this as the consensus from recent studies.
  • 11.2. Quantum annealing: QA efficiently finds good solutions when barriers are narrow but ultimately becomes stuck when broad barriers are encountered.This barrier dependence limits how broadly current annealing approaches can perform well.
  • 11.2. Quantum annealing: Most current problem instances are outperformed by more efficient classical optimisation algorithms, despite prospects for 100x faster annealing and readout.The projected speed improvement concerns run time, not demonstrated quantum speedup.
  • 11.2. Quantum annealing: Calibration inaccuracies can misspecify the cost function, while limited connectivity makes embedding generic problems challenging.Performance also suffers when problems do not map well onto the hardware graph.

12. Perspectives

Superconducting QIP has progressed from small demonstrations toward multi-qubit platforms, quantum annealing systems, and practical hybrid access. The broader field now spans applications in simulation, chemistry, networks, sensing, and emerging quantum technologies, while scalable interfaces and functional Majorana qubits remain open challenges.

  • 12.1. Looking back: Superconducting devices have progressed from 2–3-qubit demonstrations to multi-qubit platforms addressing proof-of-principles simulations in Materials Science, Chemistry, and Physics.The review also notes operating 2000-qubit D-Wave systems for quantum annealing.
  • 12.3. Emerging technologies: Quantum information research is broadening beyond superconducting circuits to spins, ion traps, quantum networks, sensors, and non-equilibrium quantum dynamics.Examples include error correction and simulation in diamond, 219-ion simulations, quantum-network memory, and discrete time crystals.
  • 12.2. Looking forward: IBM’s cloud-enabled quantum platform expanded from a 5-qubit processor in 2016 to 16 qubits one year later.The platform enabled users to run algorithms and experiments through a web interface.
  • 12.2. Looking forward: Hybrid quantum platforms depend on efficient communication interfaces between quantum and classical components.The review treats comparison of scalable alternatives as important while emphasizing hybrid architectures.
  • 12.2. Looking forward: Experimental and applied superconducting QIP is preparing for 20–50-qubit platforms targeting algorithms and benchmarking against classical systems.The review presents this as an expected development within a few years.
  • 12.3. Emerging technologies: Functional Majorana qubits remain distant despite experimental evidence for Majorana bound states.Efficient manipulation and functional operation are identified as unresolved goals.
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