Quantum computers can tackle problems that would take classical systems thousands of years to solve, but that leads to a critical question: how do we verify the results of a quantum computation when we can’t feasibly check them using traditional methods?
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In a recent study, researchers from Swinburne University have developed a method to validate a Gaussian Boson Sampling experiment, a quantum problem previously estimated to require 9,000 years of classical computation, in just a few minutes on a laptop.
Quantum Supremacy and the Black Box Problem
In October 2019, Google reported achieving “quantum supremacy” by using its 54-qubit processor, Sycamore, to perform a computation in 200 seconds that it estimated would require 10,000 years on the world’s fastest classical supercomputer. This feat marked the first demonstration of a fully programmable quantum device solving a problem beyond practical classical computation.1
However, it was met with excitement and skepticism, particularly after an IBM preprint suggested the same task could be completed in two-and-a-half days on a classical system, raising debate over the legitimacy of quantum supremacy and whether the chosen problem demonstrated true quantum advantage.
Despite the controversies, the experiment illustrated a clear distinction between the computational effort required by classical versus quantum devices, as even IBM’s approach demanded the full resources of the Oak Ridge supercomputer for multiple days.2
This performance gap underscored the urgent need for new verification methods, prompting researchers to develop techniques capable of validating quantum computations without relying on infeasible classical simulations. However, the intrinsic nature of quantum systems poses significant challenges, as they are often described as “black boxes” due to the fragility of qubits, which are highly sensitive to environmental disturbances and cannot be directly replicated or observed without altering their state.
The no-cloning theorem further complicates verification, as quantum states cannot be copied like classical bits. This limits the current validation techniques to relatively simple computations, highlighting the continuing challenge of verifying the correctness of complex quantum solutions.3
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The Swinburne Study: A Classical Validation of Quantum Computation
Recently, Swinburne University researchers developed a novel quantum verification method capable of validating quantum computation results within minutes using a standard laptop. Their study focuses on Gaussian Boson Samplers (GBS), a class of quantum computers that employ photons to calculate probability distributions that would take classical supercomputers thousands of years to reproduce.4
The team implemented a phase-space simulation technique based on the positive-P representation, a probabilistic framework capable of accurately modeling nonclassical quantum states. By combining this approach with grouped count probability (GCP) analysis and an extended form of Mandel’s binning method, they achieved efficient statistical validation of photon-count data without simulating the entire quantum computation.
This method effectively bypasses the computational intractability of calculating full probability distributions, allowing verification that scales exponentially faster, up to 10¹8 times, than direct classical simulation.5
Results and Findings
The Swinburne team validated their approach using data from the 2022 Borealis Gaussian Boson Sampling (GBS) experiment conducted by Xanadu, which demonstrated quantum advantage with up to 288 optical modes.
The experimental data from Borealis deviated from ideal theoretical predictions, revealing inconsistencies between the experimental outputs and the intended quantum model. When thermal noise and transmission-matrix corrections were introduced, the simulations showed strong agreement with the data for one-dimensional grouped count probabilities. However, discrepancies persisted in higher-order correlations, suggesting the presence of additional unmodeled errors.
Further statistical analyses using chi-square and Z-tests revealed that Borealis results were consistent with the corrected quantum models, confirming the framework’s effectiveness in detecting and characterizing imperfections in complex quantum systems.
The positive-P simulations achieved these results with negligible sampling errors and substantially reduced computational cost compared to classical methods, establishing a scalable diagnostic approach for large-scale quantum verification.5
Implications for Quantum Industry and Research
The proposed framework offers a computationally efficient way to validate quantum outputs without needing to fully replicate the results using classical systems. This allows developers and researchers to assess the accuracy and reliability of large-scale quantum systems, while also providing diagnostic insights to pinpoint sources of noise, uncover model mismatches, and fine-tune experimental setups.
Commercial platforms such as IBM, IonQ, and Rigetti could adopt this verification approach to strengthen technical transparency and operational reliability as they advance into the quantum advantage regime. Independent validation will be critical for establishing user confidence, ensuring compliance with emerging regulatory standards, and supporting trust in quantum computations.
This framework also extends verification capabilities across diverse architectures, offering diagnostic precision beyond conventional benchmarking. In high-stakes fields such as cryptography, pharmaceutical modeling, and defense, such verification methods will be essential for maintaining computational integrity and defining certification protocols for next-generation quantum technologies.5
What Comes Next?
The study establishes a practical and scalable framework for validating large-scale quantum experiments, addressing one of the fundamental challenges in the field.
Despite its effectiveness, the framework remains statistical rather than exhaustive, as it does not reproduce full quantum outputs or verify correctness across all correlations. Its precision decreases when experimental data are limited, and systematic errors such as phase noise, optical loss, and imperfect calibration remain unresolved. The Borealis experiment exemplified these limitations, where deviations from theoretical predictions revealed unmodeled noise sources.
Overcoming these constraints is essential for realizing error-resilient, commercially deployable quantum computers capable of delivering fully verifiable results, as emphasized by the study’s lead author, Alexander Dellios:
“Developing large-scale, error-free quantum computers is a herculean task that, if achieved, will revolutionize fields such as drug development, AI, cybersecurity, and deepen our understanding of the physical universe.4”
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References and Further Reading
- Martinis, J. (2019). Quantum Supremacy Using a Programmable Superconducting Processor. https://research.google/blog/quantum-supremacy-using-a-programmable-superconducting-processor/
- Erica K. Brockmeier. (2019). Google’s claims of quantum supremacy: Groundbreaking, overhyped, or both? https://penntoday.upenn.edu/news/googles-claims-quantum-supremacy-groundbreaking-overhyped-or-both
- Resonance. (2024). Quantum Error Correction – The Key to Realizing Quantum Computing’s Potentialhttps://thequantuminsider.com/2023/09/08/guest-post-quantum-error-correction-the-key-to-realizing-quantum-computings-potential/
- Swinburne University of Technology. (2025). If quantum computing is answering unknowable questions, how do we know they’re right? https://www.swinburne.edu.au/news/2025/09/if-quantum-computing-is-answering-unknowable-questions-how-do-we-know-theyre-right/
- Dellios, A. S., Reid, M. D., & Drummond, P. D. (2025). Validation tests of Gaussian boson samplers with photon-number resolving detectors. Quantum Science and Technology, 10(4), 045030. https://doi.org/10.1088/2058-9565/adfe16
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