## Can a Classical Simulator Now Handle 64-Qubit Quantum Circuits?

MPStab, a new hybrid classical simulator from researchers at the Universities of Trieste and Helsinki, CERN, and Chalmers University of Technology, can accurately simulate quantum circuits containing up to 64 qubits — and in specific regimes, it outperforms established tensor network simulators by over two orders of magnitude. That speedup figure is the headline claim from a preprint posted to arXiv (2607.24258) by Giulio Crognaletti, Mattia Robbiano, Michele Grossi, and Matteo Robbiati. Standard statevector simulation methods typically max out at a few dozen qubits before computational demands become intractable. MPStab's hybrid approach — formally called HSMPO — combines stabilizer techniques with tensor networks to push that frontier substantially further.

The practical implication is direct: classical simulators that reach farther into the NISQ regime tighten the upper bound on where [quantum advantage](https://quantumintel.tech/glossary/quantum-advantage) can legitimately be claimed. Every additional qubit a classical machine handles credibly is one fewer qubit that quantum hardware vendors can cite as evidence of supremacy. For enterprise buyers and investors evaluating quantum platforms, this work is a calibration instrument, not a threat — but it is one that the industry needs to take seriously.

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## What HSMPO Actually Does

The core technical problem MPStab addresses is well known to anyone who has tried to scale classical quantum simulation: the state space dimension grows exponentially with qubit number. Two existing approaches each cover part of the problem.

**Stabilizer methods** efficiently handle circuits composed primarily of [Clifford gates](https://quantumintel.tech/glossary/clifford-gates) — operations that can be tracked compactly through the Pauli group. The catch is that Clifford-only circuits are classically efficient precisely because they are computationally weak; add non-Clifford rotations (T-gates, for instance) and the stabilizer representation balloons rapidly.

**Tensor networks** excel when entanglement is geometrically constrained — when connections between qubits are local and the entanglement entropy of subsystems remains bounded. They struggle with circuits that generate high global entanglement across many qubits simultaneously.

HSMPO stitches these two formalisms together. Circuits with a mix of highly entangling operations and local interactions — the exact regime that breaks both pure stabilizer and pure tensor network approaches individually — are where the hybrid method earns its speedup. According to the preprint, benchmarks show MPStab outperforms existing methods in scenarios containing both Clifford gates and non-Clifford rotations, with speedups exceeding two orders of magnitude against established tensor network simulators in certain cases.

The modular architecture supports direct integration with Qiskit and PennyLane, which means quantum software teams can drop MPStab into existing verification workflows without substantial re-engineering.

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## Where the Skepticism Lives

The authors themselves flag the primary limitation: benchmarking against all major classical simulation tools is incomplete. The performance gains reported cover a limited number of simulation regimes. A systematic comparison against Qiskit's PauliProp and SciPost's tensor network tools — among others — has not yet been published.

This matters for a few reasons. First, two-orders-of-magnitude speedup claims in simulation research frequently turn out to be regime-specific; a tool that crushes a competitor on Clifford-heavy circuits with sparse non-Clifford gates may look less impressive on random circuit sampling benchmarks closer to what Google Quantum AI and IBM Quantum use for supremacy demonstrations. Second, 64 qubits is the advertised ceiling, but the hardest NISQ circuits — those with deep random entanglement across all qubits — are precisely where statevector and tensor network methods both struggle most. How MPStab performs on those worst-case circuits is not yet established.

None of this invalidates the work. A new hybrid formalism that demonstrably extends the classical simulation frontier — even in specific regimes — is a genuine contribution. It simply needs more adversarial benchmarking before the 64-qubit ceiling should be treated as a reliable general limit rather than a favorable-conditions headline.

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## Industry Implications

The quantum industry's narrative around fault-tolerant quantum computing rests on a moving baseline: as [fault-tolerant quantum computing](https://quantumintel.tech/glossary/fault-tolerant-quantum-computing) approaches become more capable, classical simulation must be shown to fall further behind. Work like MPStab applies pressure in the opposite direction — demonstrating that classical methods still have room to grow.

For algorithm developers, a simulator that handles 64 qubits with sub-exponential overhead in the right regimes is a valuable verification tool. Circuits that can be classically simulated should be classically simulated — it is cheaper, faster, and doesn't require queue time on hardware. The practical rule of thumb this work reinforces: circuits dominated by Clifford structure with sparse non-Clifford gates are not strong candidates for quantum advantage demonstrations, regardless of qubit count.

For hardware companies marketing NISQ devices in the 50-100 qubit range, this is a useful reminder to be precise about the circuit architectures where classical simulation genuinely fails. Qubit count alone has never been a sufficient metric — circuit depth, gate fidelity, and entanglement structure all determine whether a given computation sits in classically hard territory.

For VCs evaluating quantum software and simulation startups, MPStab illustrates that the classical simulation landscape continues to advance. Any thesis predicated on a static classical baseline should be revisited periodically.

The arXiv preprint (2607.24258) is publicly available for technical review. Peer review and expanded benchmarking will determine whether the 64-qubit figure and the two-order-of-magnitude speedup hold up across a broader simulation landscape.

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## Key Takeaways

- MPStab, developed by researchers from the Universities of Trieste and Helsinki, CERN, and Chalmers University of Technology, simulates quantum circuits up to 64 qubits — beyond the reach of standard statevector methods.
- The hybrid HSMPO formalism combines stabilizer techniques (efficient for Clifford-dominated circuits) with tensor networks (efficient for locally entangled systems), addressing the failure modes of each individually.
- In benchmarked scenarios mixing Clifford and non-Clifford operations, MPStab achieved speedups exceeding two orders of magnitude over established tensor network simulators.
- Benchmarking is incomplete — systematic comparison against all major classical simulation packages has not yet been published, and performance across adversarial circuit regimes remains to be characterized.
- The simulator integrates directly with Qiskit and PennyLane, enabling immediate adoption in existing quantum software workflows.
- Extended classical simulation capability tightens the evidentiary bar for quantum advantage claims in the NISQ regime.

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## Frequently Asked Questions

**What is MPStab and who developed it?**
MPStab is a hybrid quantum circuit simulator developed by Giulio Crognaletti, Mattia Robbiano, Michele Grossi, and Matteo Robbiati, affiliated with the Universities of Trieste and Helsinki, CERN, and Chalmers University of Technology. It combines stabilizer methods and tensor networks in a formalism called HSMPO to extend classical simulation capabilities beyond the few-dozen-qubit ceiling of standard statevector methods.

**How many qubits can MPStab simulate?**
According to the published preprint, MPStab handles circuits with up to 64 qubits — a substantial extension over standard statevector simulation, which the authors note typically manages only a few dozen qubits.

**How much faster is MPStab than existing tensor network simulators?**
In specific simulation regimes — particularly circuits containing a mix of Clifford gates and non-Clifford rotations — the preprint reports speedups of over two orders of magnitude compared to established tensor network simulators. The authors acknowledge that comprehensive benchmarking across all simulation regimes is still outstanding.

**Does MPStab threaten quantum advantage claims?**
Not broadly, but it does tighten them. By extending classical simulation to 64 qubits in certain regimes, MPStab narrows the circuit space where quantum hardware can claim a credible advantage without rigorous classical comparison. Circuits with deep random entanglement and high non-Clifford gate density remain classically hard, but Clifford-heavy circuits at 64 qubits are now more plausibly within classical reach.

**Which quantum software frameworks does MPStab support?**
The simulator is designed with a modular architecture that integrates with Qiskit and PennyLane, the two most widely used quantum software frameworks, allowing direct use in existing algorithm development and verification pipelines.

**Where can I read the full technical paper?**
The preprint is available on arXiv at arxiv.org/abs/2607.24258. It has not yet undergone formal peer review as of the publication date of this article.