Cross-entropy benchmarking and random circuit sampling

Short answer: Cross-entropy benchmarking, or XEB, is used with random circuit sampling to estimate how well a quantum processor runs a circuit, and it has been proposed as a way to certify quantum advantage. A 2024 PRX Quantum paper examines its limits and presents a classical algorithm that reaches 5-12% of the XEB values of state-of-the-art experiments, while a 2024 Nature paper reports two phase transitions seen with XEB and a 67-qubit, 32-cycle experiment that its authors say is beyond existing classical supercomputers.

What the benchmark is for

The PRX Quantum abstract explains that demonstrating quantum advantage needs a task that is hard for state-of-the-art classical systems. One approach samples from the distribution of a highly entangled many-body state, and it has been suggested that the linear cross-entropy benchmark can certify such advantage.

2024: a critical look at linear XEB

The authors examine this notion in two settings. In a benign setting with an honest noisy circuit, they characterize when the XEB approximates the fidelity of the dynamics. In an adversarial setting, they show that a relatively high XEB does not imply faithful simulation. They present an efficient classical algorithm that reaches 5-12% of the XEB values of state-of-the-art experiments within seconds on a single GPU machine, by exploiting vulnerabilities of the XEB without simulating the full circuit. They say its scaling with system size is better than that of a noisy quantum device for commonly studied random circuit ensembles. This is the authors' claim about their own algorithm.

2024: phase transitions in random circuit sampling

The Nature abstract notes that noise can trivialize algorithm outputs and make them susceptible to classical spoofing. By implementing random circuit sampling, the authors report observing two phase transitions with XEB. The first is a dynamical transition as a function of the number of cycles, continuing the anti-concentration point of the noiseless case. The second is a quantum phase transition controlled by the error per cycle, studied with a weak-link model. They also present an experiment in the weak-noise phase with 67 qubits at 32 cycles, and say its computational cost is beyond the capabilities of existing classical supercomputers. That is the authors' claim, and the first paper above shows why such claims about XEB are debated.

Limits

The two papers address different questions and should not be merged into one verdict. One shows a spoofing route against high XEB values at a fraction of the experimental level, and the other reports a regime the authors say resists classical simulation. A third paper on Fourier expansion and statistics of random circuit sampling was listed as a source but only its title and not an abstract could be read, so it is not described.

FAQ

What is XEB?

The linear cross-entropy benchmark, used with random circuit sampling and proposed as a certificate of quantum advantage.

Can XEB be fooled?

The 2024 PRX Quantum paper presents a classical algorithm reaching 5-12% of experimental XEB values in seconds on one GPU machine.

What did the Nature paper report?

Two phase transitions observable with XEB, and a 67-qubit, 32-cycle experiment the authors say is beyond existing classical supercomputers.

Do the papers contradict each other?

They study different things. The first limits what XEB proves, the second reports an experiment in a low-noise phase.

Is this practical quantum computing?

No. It concerns benchmarking and sampling tasks, not useful applications.