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Quantum computers are designed to solve problems beyond the capabilities of human intelligence. That power raises a simple but difficult question: when a quantum device gives us an answer we can't directly check, how do we know that the answer is correct?

A research team at Swinburne University of Technology has proposed a method to test several photonic quantum computers to answer this question.

The team took the idea of ​​comparing easily calculated and measurable statistics, then using them to flag errors and check whether the device is working as expected.

Validation from quantum experiments

This work was led by Alexander Dellios at Swinburne University's Centre for Theoretical Quantum Science and Technology.

His team focused on Gaussian boson sampling (GBS), a photonics approach that uses compressed light to create complex probability patterns. In this setup, a network combines multiple modes of light with detectors that record the number of photons that fall into each output.

 

For photon number resolving detectors, the probabilities for specific detection patterns are calculated using the Hafnian function (a mathematical function used to calculate probabilities in certain quantum systems, especially in Gaussian boson sampling with photon number resolving detectors).

When experiments using threshold detectors only indicate whether light is arriving or not, the associated matrix function changes.

Those results are connected to the Torontonian function (the Torontonian function is a mathematical function used to calculate probabilities in the sampling of Gaussian bosons when using threshold detectors, introduced by researchers in Toronto).

How quantum testing works

The Swinburne method does not attempt to compute any hard probabilities that define the full distribution. It examines lower-dimensional summaries of the data, sometimes called group count probabilities, and compares them to theory across multiple bins in a single run.

Essentially, the 'core' of the simulation is the positive P representation. This phase space technique accurately reproduces the normal ordered moments for any quantum state and is well scalable to many modes.

The team reports a speedup of about 10^18 compared to the direct classical simulation in the 288 mode case. This scaling is important because it turns a near-hopeless calculation into a practical test that can be run on a workstation.

" Some problems take even the fastest supercomputer millions of years to solve. Our method allows us to check in minutes on a laptop whether a GBS experiment is producing the right results and what errors might have occurred ," Dellios said.

 

What did the research team discover?

To demonstrate this method, the team analyzed data from a famous recent boson sampling experiment.

In 2022, the Borealis machine estimated that it would take a leading classical supercomputer more than 9,000 years to generate a single accurate pattern, which the device produced in 36 microseconds. When the Swinburne team ran their quantum experiment, they found that the measured probability distribution did not match the original target model.

The quantum data are better fitted to a modified distribution that accounts for thermal and measurement imperfections.

This result does not imply that the photonic machine lacks a computational advantage. It suggests that the device was solving a slightly different statistical problem than the ideal one the experimenters intended.

The next step is to determine whether sampling from that alternative distribution is still computationally difficult. If it is still computationally difficult, the computational promise remains, but the goal needs to be clearly stated.

Quantum computer tests are important

Verification and computational advantage are related but different.

1. Comparative advantage of running time between the best classical methods and quantum devices for a given task, while validation asks whether the hardware can solve the given task.
2. Scalable validation helps teams locate and fix sources of errors before they cause system mismatches.

Such a workflow could steer photonic hardware to setups where the output retains non-classical features and the stated task remains intact.

Positive results from these tests can also guide parameter tuning. If a small change in compression or transmission tweaks the statistics, engineers get a direct tuning knob to improve fidelity without weeks of trial and error.

As the number of detected modes and photons increases, the full distribution becomes too sparse to estimate or calculate.

This is where group statistics shine, as they can still be estimated on limited samples and still carry the high-order correlations that define non-classical behavior.

Quantum testing and the future

The team plans to test whether the alternative model discovered by their experiments remains in the category of difficult to simulate using classical methods.

That answer will clarify whether the photonic device maintained its quantum properties throughout the run or entered a regime that classical algorithms can simulate.

' Developing a large-scale, error-free quantum computer is an incredibly difficult task, but if successful, it would revolutionize areas such as drug development, AI, cybersecurity, and allow us to gain a deeper understanding of the physical universe, ' said Dellios .

The research was published in the journal Quantum Science and Technology.