Quantum-inspired methods: the classical spin-off
What "quantum-inspired" means, the main families of these classical methods, and how to judge and report them.
What you’ll learn
- Explain that quantum-inspired methods run on classical hardware.
- Say how to judge them against the best classical method.
- Explain why they shouldn't be reported as quantum advantage.
Recommended background: What quantum computers are good at
Some products marketed under the quantum banner never touch a quantum computer. They are "quantum-inspired": algorithms or chips that borrow ideas from quantum physics or quantum algorithms, but execute entirely on classical hardware, such as standard processors (CPUs), graphics processors (GPUs), programmable chips (FPGAs) or specialised classical accelerators. Some of them work well on particular problems today. The point of this piece is not to dismiss them, but to make sure auditors, project managers and approvers know which kind of thing they're paying for, because that changes what it should be compared against and how it should be governed.
Three things the label can mean
The quickest test is where the computation runs.
The main families
- "Dequantised" algorithms. In 2018, Ewin Tang showed that a celebrated quantum algorithm for recommendation systems could be matched by a classical algorithm that is only polynomially slower, removing its claimed exponential advantage. A 2022 paper in the Journal of the ACM by Tang and colleagues extended the approach to a range of quantum machine-learning methods that rely on low-rank data, including principal component analysis, support vector machines and low-rank regression. These results matter in two ways: they produce new classical algorithms, and they weaken some of the advantage claims made for quantum machine learning. A 2020 peer-reviewed study by researchers at Xanadu found that such algorithms work well in practice only under stringent conditions: low rank, low condition number and very large matrices.
- Tensor networks. These are mathematical tools developed in physics to describe quantum systems compactly, and they are now used in other fields, including artificial intelligence. They run on classical computers. A 2022 peer-reviewed portfolio study by Multiverse Computing and BBVA included a tensor-network solver run on a laptop alongside quantum hardware, and found no single method best on every measure. A preprint by Multiverse Computing and Crédit Agricole replaced layers of neural networks used to price options with tensor networks, and reported training up to twelve times faster than standard networks with the same number of parameters, on cloud graphics processors; the authors call some of their results preliminary.
- Physics-inspired optimisation. These methods attack the same optimisation problems that quantum annealers do, on classical hardware. Fujitsu's Digital Annealer is a custom digital chip based on simulated annealing, a classical method from the 1980s. A 2019 peer-reviewed benchmark found it about a hundred times faster than single-core simulated annealing on one hard class of problems, and no faster on another. Toshiba's simulated bifurcation algorithm, published in Science Advances in 2019, runs on programmable chips and graphics processors. The largest speed-up Toshiba has quoted, about 1,000 times, was measured against standard simulated annealing software, a specific baseline, as IEEE Spectrum reported in 2020. Plain simulated annealing itself, run on ordinary computers, matched a hybrid quantum solver on payment data in a 2026 central bank study; see Quantum use cases in banking.
Why the label matters
| Quantum or hybrid | Quantum-inspired | |
|---|---|---|
| What it should beat | The best classical method, which may itself be quantum-inspired | The best classical method, including standard solvers and models the bank already uses |
| Where it runs | A quantum processor, usually reached through a cloud service | Classical hardware (CPUs, GPUs, FPGAs or specialised accelerators), on premises or in the cloud |
| Main supplier questions | Access, data location, queueing, hardware roadmap | Licensing, lock-in, portability, whether the speed-up survives on your own hardware |
| How to report it | As quantum exploration | As classical computing, not as quantum-hardware capability or quantum advantage; it can still feed a quantum research programme |
The confusion is easy to make, and it isn't always the buyer's fault. In January 2023, Crédit Agricole CIB announced two experiments with Multiverse Computing and Pasqal. The bank's own release said one used quantum-inspired algorithms that "can run on conventional computer systems"; the other used a quantum processor. A Multiverse article about the same projects was headlined "Study by One of the World's Largest Banks Concludes Quantum Is Useful Today". The headline itself didn't distinguish the quantum-inspired experiment from the one on quantum hardware. The two statements aren't necessarily in conflict, but a steering committee reading only the headline could count classical software as evidence of quantum-hardware capability.
That matters for three reasons. A quantum-inspired product should be judged against the best classical method, not against a quantum computer, because that's what it competes with. It shouldn't be counted as quantum-hardware capability or as a demonstrated quantum advantage, or confused with the separate post-quantum cryptography programme. It can still contribute to a broader quantum research programme: as a strong classical benchmark for quantum results, a way to build skills, and methods the team can reuse. And because it runs on classical hardware, the questions for procurement shift: less about quantum cloud access, more about licensing, lock-in and whether the result holds up on the bank's own infrastructure.
Questions to ask
- Where does each step run? Ask the supplier to name the hardware: a quantum processor, or CPUs, GPUs, FPGAs or specialised classical accelerators. If a quantum processor is involved, ask what share of the work it does.
- Against what was the speed-up measured? A comparison with single-core or standard simulated annealing is a specific baseline. Ask for results against the solver or model the bank would otherwise use, on the same data and time budget.
- Can it run on our hardware? If the method needs a proprietary chip or service, treat that as a supplier dependency. If it runs on standard hardware, ask whether the results reproduce there.
- How is it labelled in our reporting? Agree up front how the work is described: classical computing that may support a quantum research programme, not quantum-hardware capability, so dashboards and board papers stay accurate.
For the wider approval process, including baselines, data and success criteria, see How to evaluate a quantum computing pilot.
What you’ve learned
- Quantum-inspired methods are classical: they execute on classical hardware, whatever the product is called.
- Some work well on specific problems today, but they should be judged against the best classical method, on the same data and time budget.
- Don't report them as quantum-hardware capability or quantum advantage, though they can support a quantum research programme; apply third-party and model risk controls where they're relevant.
Check your understanding optional
A product is labelled quantum-inspired. Does it need a quantum computer?
Show the answer
No. Quantum-inspired methods are classical: they run on ordinary hardware, whatever the product is called.
Written by Muhammad Atif · Reviewed 17 October 2026 · How sources are chosen and checked · Report a correction
Sources and further reading
Tags show what kind of source each one is. A standard or government guidance is an official document; a peer-reviewed paper has been checked by other experts; a preprint has not been peer-reviewed yet; an experiment reports a real-world demonstration; a company announcement is the company's own account; vendor documentation is a supplier's own technical guide; expert commentary is a specialist's published analysis or opinion; a news report is a journalist's account. Dates and figures were checked against these sources on 17 October 2026. Spotted an error? Email hello@plainquantum.com and it will be corrected, with a note.
- Peer-reviewed paperA quantum-inspired classical algorithm for recommendation systemsEwin Tang, ACM Symposium on Theory of Computing (STOC), 2019
- Peer-reviewed paperSampling-based sublinear low-rank matrix arithmetic framework for dequantizing quantum machine learningChia, Gilyén, Li, Lin, Tang and Wang, Journal of the ACM 69(5), 2022
- Peer-reviewed paperQuantum-inspired algorithms in practiceArrazola, Delgado, Bardhan and Lloyd (Xanadu, MIT), Quantum, 2020
- Peer-reviewed paperTensor networks for complex quantum systemsRomán Orús, Nature Reviews Physics, 2019
- Peer-reviewed paperDynamic portfolio optimization with real datasets using quantum processors and quantum-inspired tensor networksMugel et al. (Multiverse Computing, BBVA), Physical Review Research, 2022
- PreprintQuantum-inspired tensor neural networks for option pricingPatel et al. (Multiverse Computing, Crédit Agricole), arXiv, 2022, revised 2024
- Peer-reviewed paperOptimization by simulated annealingKirkpatrick, Gelatt and Vecchi, Science, 1983
- Peer-reviewed paperPhysics-inspired optimization for quadratic unconstrained problems using a digital annealerAramon et al., Frontiers in Physics, 2019
- Company announcementFujitsu quantum-inspired Digital Annealer cloud service to rapidly resolve combinatorial optimization problemsFujitsu press release, 2018
- Peer-reviewed paperCombinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systemsGoto et al. (Toshiba), Science Advances, 2019
- News reportToshiba's optimization algorithm sets speed record for solving combinatorial problemsJohn Boyd, IEEE Spectrum, 2020
- Central bank working paperLiquidity optimization in gross settlement systems with quantum reordering: application to TARGET2 (Staff Working Paper 2026-32)Astuti et al. (Bank of Italy, Bank of Canada), 2026
- Company announcementQuantum computing: two real-world experiments conducted by Crédit Agricole CIB with Pasqal and Multiverse ComputingCrédit Agricole press release, 2023
- Company announcementStudy by one of the world's largest banks concludes quantum is useful todayMultiverse Computing, 2023