Quantum machines beating supercomputers on real problems

How far are quantum annealers and gate-based quantum computers from an advantage over classical methods on a useful problem?

Quantum machines have been reported to beat classical computers on benchmark tasks, but no source reviewed shows one doing a useful job better than the best classical methods. D-Wave's 2025 Science paper claims an advantage on simulating spin-glass dynamics. Classical tensor-network work reports state-of-the-art accuracy on the same kind of problem with modest resources, and D-Wave says that work does not reproduce the full scope of its result. Google reports beyond-classical benchmarks on its Willow chip, and says these benchmarks have no known practical use.

AI illustration · Illustrative scene, not a photograph of the specific device or experiment.
WHERE WE AREScience demonstrated

Far away. The science works, but nobody has built a working system yet.

Several groups have reported runs on quantum hardware that the authors describe as beyond classical reach, for benchmark or model problems. The two most prominent reported advantages are disputed or have no known practical application, and no source reviewed shows a quantum machine beating classical methods on a useful problem. The stage is therefore science demonstrated for benchmark tasks only, with the useful-advantage step still ahead.

The tech tree

Everything recorded on Vrulum that this future needs, oldest foundations at the top and the goal at the bottom. Lines show what each step requires.

What it takes: Quantum machines beating supercomputers on real problems Unlocked Being researched Locked
  1. 2018Topological qubitsLab demonstration Being researched.
  1. 1995Quantum error correctionLab demonstrationRequires: Topological qubits. Being researched.
  1. 1998Quantum annealingPilot and early commercial Unlocked.
  2. 2007Superconducting quantum computersResearch and prototypesRequires: Quantum error correction. Being researched.
  3. 2013Analogue quantum simulationResearch and prototypes Being researched.
  1. 2024Beyond-classical random circuit sampling benchmark on Google's Willow chipDone Unlocked.
  2. 2025Beyond-classical claim on spin-glass dynamics published in ScienceDone Unlocked.
  3. 2025Classical tensor-network simulation of disordered quantum dynamicsDone Unlocked.
  4. 2025Google reports a verifiable advantage in its Quantum Echoes experimentDone Unlocked.
  5. 2026D-Wave disputes the scope of the classical resultDone Unlocked.
  6. Date not recordedIndependent classical checks of Google's 13,000 times estimateIn progress Being researched.
  7. Date not recordedAdvantage on a useful problem with a practical answerNot started Locked.
  1. GoalQuantum machines beating supercomputers on real problemsGoalRequires: Quantum annealing, Superconducting quantum computers, Analogue quantum simulation, Beyond-classical claim on spin-glass dynamics published in Science, Classical tensor-network simulation of disordered quantum dynamics, D-Wave disputes the scope of the classical result, Beyond-classical random circuit sampling benchmark on Google's Willow chip, Google reports a verifiable advantage in its Quantum Echoes experiment, Independent classical checks of Google's 13,000 times estimate, Advantage on a useful problem with a practical answer. Locked.

The road so far

5 of 7 steps done, 1 in progress.

  1. Done · 2025Beyond-classical claim on spin-glass dynamics published in Science

    D-Wave's Science paper reports that superconducting quantum annealing processors can generate samples that closely match solutions of the Schrodinger equation for model quench dynamics of spin glasses. The authors say several leading approximate classical methods cannot achieve the same accuracy as the annealer within a reasonable time. They also say quantum annealers may remain out of reach for classical computation on some questions of practical importance. This is the authors' claim, and it is contested in the next steps. [1]

  2. Done · 7 Mar 2025Classical tensor-network simulation of disordered quantum dynamics

    A preprint by Tindall and colleagues uses two- and three-dimensional tensor networks to simulate the dynamics of disordered quantum systems. It reports state-of-the-art accuracy with modest computational resources, and says the approach is applied to systems involving hundreds of qubits. The abstract gives no error figures or runtimes, so the comparison with D-Wave is not quantified there. [2]

  3. Done · 26 May 2026D-Wave disputes the scope of the classical result

    In a statement filed with the US Securities and Exchange Commission on 26 May 2026, D-Wave says the classical work does not reproduce the full scope of its Science result. It names gaps in the observables computed, the lattice geometries covered, the largest three-dimensional simulations and the couplings used. An earlier March 2025 D-Wave response also names low-precision ensembles. The sources reviewed contain no independent expert ruling on the dispute. [3]

  4. Done · 9 Dec 2024Beyond-classical random circuit sampling benchmark on Google's Willow chip

    Google reports that its 105-qubit Willow chip finished a random circuit sampling benchmark in under five minutes. It estimates that the same task would take Frontier, one of the fastest supercomputers, about 10 septillion years. Google says its estimate rests on conservative assumptions, though it also gives Frontier full access to secondary storage without any bandwidth overhead, which it calls a generous and unrealistic allowance. Google says random circuit sampling has no known real-world applications. [4]

  5. Done · 22 Oct 2025Google reports a verifiable advantage in its Quantum Echoes experiment

    Google reports a Quantum Echoes experiment on Willow, which it describes as demonstrating a verifiable quantum advantage. It estimates that the task would take about 13,000 times longer on a classical supercomputer. The post describes the work as paving the way toward a first real-world application, not as a solution to one. A companion molecular NMR experiment with UC Berkeley is described as not yet beyond classical, and it is a preprint that has not yet been peer reviewed. [5]

  6. In progressIndependent classical checks of Google's 13,000 times estimate

    The sources reviewed contain no independent classical simulation or rebuttal of the Quantum Echoes estimate. Any advantage claim can only be judged against the classical methods available at the time it is made. [5][4]

  7. Not startedAdvantage on a useful problem with a practical answer

    No source reviewed shows a quantum machine beating the best classical methods on a problem with a practical answer. Garnet Chan argues that the theoretical support for exponential quantum advantage on the FeMo-cofactor problem is much weaker than for random circuit sampling. The chemistry horizon covers this problem in more detail. [6][5]

Why it matters

Advantage claims shape where funding and research effort go, so each one needs testing against the best classical methods, not weaker ones. A useful advantage in materials, chemistry or optimisation would change which problems are worth running on quantum hardware. A benchmark win on its own does not show that.

What stands in the way

  • The D-Wave spin-glass advantage is disputed. Classical tensor-network work reports state-of-the-art accuracy with modest resources, and D-Wave says that work does not reproduce the full scope of its result.
  • Google's benchmarks use tasks with no known practical application, so they do not show that quantum machines solve a problem people need solved.
  • The advantage figures depend on the classical method and assumptions chosen. Google's 13,000 times and 10 septillion year figures are estimates, not measured runs of the best classical method.
  • The sources reviewed contain no independent classical check of Google's 13,000 times estimate, so the size of that advantage is untested.
  • No source reviewed shows an advantage on a problem with a practical answer, such as chemistry, materials or optimisation.

Signals to watch

  • A classical simulation that reproduces the D-Wave Science results on the observables, geometries and lattice sizes that D-Wave says were left out.
  • An independent classical check of the Quantum Echoes estimate, or a classical method that reproduces it.
  • Peer review of the Google and Berkeley NMR preprint, and whether its result moves beyond classical reach.
  • A quantum advantage on a task with a practical answer, with the best classical baseline fixed in advance.
  • Advantage results published with enough data and code for outside groups to repeat them.

Sources

  1. peer reviewed paper
    Beyond-classical computation in quantum simulation
    Andrew D. King et al.. Science (arXiv preprint 2403.00910), 2025.
  2. preprint
    Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
    Joseph Tindall, Antonio Mello, Matthew Fishman et al.. arXiv, 7 Mar 2025.
  3. company announcement
    D-Wave statement responding to the classical tensor-network work (Exhibit 99.1 to Form 8-K)
    D-Wave Quantum Inc. (NYSE: QBTS), copy hosted by Boardroom Alpha, 26 May 2026.
  4. company announcement
    Google Willow quantum chip announcement
    Google, 9 Dec 2024.
  5. company announcement
    A verifiable quantum advantage
    Google Research, 22 Oct 2025.
  6. other
    The FeMo-cofactor and classical and quantum computing
    Garnet Chan. Quantum Frontiers (blog), 12 Mar 2026.

Last reviewed 21 Oct 2026.