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Beyond NISQ: The Megaquop Machine

John Preskill

arXiv:2502.17368v2quant-ph

TL;DR

The paper asks what useful roles may emerge for megaquop machines when NISQ systems lack demonstrated commercial quantum advantage and practical applications require fault tolerance. It surveys hardware, decoding, error-correction, and error-mitigation advances toward machines capable of roughly a million operations. These advances are bringing megaquop machines closer, but important scaling limitations remain, including postselection, rare error events, and uncertain complexity trade-offs.

  • Problem

    NISQ computing has scientific value but lacks demonstrated commercial quantum advantage, while commercially viable applications are not expected to avoid error correction and fault tolerance.

  • Method

    The paper surveys advances across hardware, control, algorithms, error correction, and error mitigation that could enable megaquop machines.

  • Results

    Advances in hardware, control, algorithms, error correction, and error mitigation are bringing megaquop machines closer.

  • Takeaways & Limitations

    Experience with megaquop machines is expected to guide application development and progress toward gigaquops, teraquops, and broader quantum utility.

  • Takeaways & Limitations

    Atomic-qubit demonstrations remain limited to a few syndrome-measurement rounds and rely on non-scalable error detection and postselection.

Abstract

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Today's Noisy Intermediate-Scale Quantum (NISQ) computers have scientific value, but quantum machines with broad practical value must be protected against noise using quantum error correction and fault-tolerant protocols. Recent studies of quantum error correction on actual hardware are opening a new era of quantum information processing. Error-corrected computers capable of performing one million quantum operations or more may be realized soon, raising a compelling question for the quantum community: What are the potential uses of these megaquop machines?

1 NISQ and beyond

NISQ machines have scientific value but lack demonstrated commercial quantum advantage and are not expected to support commercially viable applications without error correction and fault tolerance. The proposed megaquop stage denotes machines capable of roughly a million quantum operations, bridging NISQ and more distant application-scale systems.

  • 1 NISQ and beyond: NISQ machines are not error-corrected, and noise severely limits their computational power.
  • 1 NISQ and beyond: NISQ computing has no demonstrated commercial quantum advantage over the best classical hardware and algorithms for the same problems.
  • 1 NISQ and beyond: Commercially viable applications are not theoretically expected to avoid quantum error-correcting codes and fault-tolerant quantum computing.
  • 1 NISQ and beyond: A megaquop machine is defined as one capable of executing roughly a million quantum operations, while FASQ machines remain a more distant goal.
  • 1 NISQ and beyond: Megaquop machines may perform tasks beyond classical, NISQ, or analog quantum devices, with a naive logical-gate error rate of about 10^-6.
  • 1 NISQ and beyond: A rough estimate suggests that tens of thousands of high-quality physical qubits could suffice, while likely hardware modality and commercial viability remain uncertain.

2 The road to fault tolerance

Fault tolerance requires stable syndrome measurement, rapid decoding, improving logical-gate fidelity, and acceptable resource and time overheads. Recent Willow results show repeated surface-code measurements and error-rate improvement with increasing code distance, while rare error bursts remain a concern.

  • 2 The road to fault tolerance: Fault-tolerant operation requires accurate repeated syndrome measurements, rapid decoding, improving logical-gate fidelity, and acceptable physical-resource and wall-clock overheads.
  • 2 The road to fault tolerance: Willow performed millions of stable surface-code syndrome-measurement rounds, each lasting about one microsecond.
  • 2 The road to fault tolerance: A factor of 2 improvement in logical error rate per measurement round occurred as code distance increased from 3 to 5 and from 5 to 7.
  • 2 The road to fault tolerance: Superconducting processors can suffer correlated errors from ionizing radiation, potentially exceeding the code’s ability to correct them.
  • 2 The road to fault tolerance: Error bursts in gap-engineered Willow occurred about once per hour, versus once every ten seconds in earlier hardware.
  • 2 The road to fault tolerance: The origin and future sufficiency of the remaining rare error bursts are not yet certain across quantum-computing modalities.

3 Real-time decoding

Real-time syndrome decoding is necessary to preserve logical clock speed during conditioned fault-tolerant operations. Current latency is measurable but should decrease as syndrome rounds and code sizes grow.

  • 3 Real-time decoding: Fast syndrome decoding matters because universal error-corrected computation conditions subsequent operations on frequent encoded-block measurements.
  • 3 Real-time decoding: For distance 5, decoding latency averaged about 63 microseconds, plus roughly 10 microseconds for Ethernet transmission.
  • 3 Real-time decoding: Decoding is slower than the approximately one-microsecond syndrome-measurement round and becomes harder as code size increases.
  • 3 Real-time decoding: FPGAs and decoder integration into the control stack can reduce latency, while reinforcement-learned decoders may lower logical error rates but face steep training costs at larger code distances.

4 Trading simplicity for performance

The paper surveys more complex physical-qubit encodings that bias, detect, or suppress dominant errors and can improve gate or encoded-system performance. Whether their added complexity benefits large-scale operation remains unresolved.

  • 4 Trading simplicity for performance: Transmons are simple superconducting qubits, but low-error logical qubits incur substantial quantum-error-correction overhead.
  • 4 Trading simplicity for performance: Cat qubits exponentially suppress bit flips as resonator photon number increases, while loss-induced phase-flip rates rise linearly.
  • 4 Trading simplicity for performance: Dual-rail encodings detect photon-loss errors by checking for the 00 state without disturbing a coherent superposition of 01 and 10.
  • 4 Trading simplicity for performance: Loss errors were detected over 99% of the time in a Yale/QCI dual-rail device, with undetected errors relatively rare.
  • 4 Trading simplicity for performance: GKP encoding produced 3- and 4-dimensional systems with decay rates 1.8 times better than resonator photon-loss rates.
  • 4 Trading simplicity for performance: Fluxonium enabled two-qubit gates with better than three 9s of fidelity, while Majorana-based protection remains technically difficult and slow to progress.
  • 4 Trading simplicity for performance: The scaling advantage of trading device simplicity for performance remains unclear.

5 Error correction with atomic qubits

Atomic-qubit platforms have demonstrated logical-circuit executions, but current experiments remain limited by few syndrome-measurement rounds, postselection, and slow atomic movement.

  • 48 logical qubits were sampled on a 280-qubit device by the Harvard / MIT / QuEra team.
  • 28 logical qubits were used in an algorithm on a 256-qubit device by Atom Computing and Microsoft.
  • 12 logical qubits were entangled on a 56-qubit device by Quantinuum and Microsoft.
  • Atomic-qubit devices have so far managed only a few syndrome-measurement rounds, with results relying on error detection and postselection.Discarding runs when errors are detected will not scale to large circuits.
  • Atomic movement slows the logical cycle time, so substantially faster movement is needed for deeper circuits using all-to-all coupling.

6 Toward the megaquop machine

Reaching the megaquop regime may require more efficient codes, tailored error mitigation, and application-specific circuit optimization. Near-term opportunities include materials science and simulations of far-from-equilibrium quantum dynamics, although advancing classical methods complicate claims of quantum advantage.

  • Toward the megaquop machine: More efficient quantum codes and logical-circuit error mitigation are proposed routes toward the megaquop regime.The cited codes require geometrically nonlocal connectivity and may therefore suit Rydberg optical tweezer arrays better than superconducting processors for now.
  • Toward the megaquop machine: Materials-science applications may produce informative results in the megaquop regime or only slightly beyond it.The proposal relies on exploiting symmetries and applying circuit optimizations such as those achieved by Phasecraft.
  • Toward the megaquop machine: Simulations of far-from-equilibrium quantum dynamics, particularly in two spatial dimensions, are identified as a potential scientific use of megaquop machines.
  • Toward the megaquop machine: Classical simulation methods for quantum dynamics are also advancing impressively, complicating the pursuit of quantum advantage.
  • Toward the megaquop machine: Progress toward megaquop machines will require innovation across hardware, control, algorithms, error correction, and error mitigation.Early fault-tolerant processor capabilities are expected to guide application development, while application visions guide technological progress.
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