Random circuit sampling on a 56-qubit trapped-ion machine

Short answer: A 2024 arXiv preprint by Quantinuum and collaborators reports random circuit sampling on its H2 trapped-ion machine, upgraded to operate on up to 56 qubits with arbitrary connectivity and a reported 99.843(5)% two-qubit gate fidelity. The authors say the data are at a scale that appears to be beyond state-of-the-art classical algorithms. This is a vendor-authored preprint, and the claim about classical simulation is the authors' own and unverified here.

What the paper says

The abstract starts from the point that experiments sampling the output distributions of two-dimensional quantum circuits have provided empirical evidence of a gap between classical and quantum computers. Many attempts to close that gap use classical simulation with tensor network techniques, and the authors say their limitations point to the hardware improvements needed to frustrate classical simulation. In particular, they say quantum computers with more than about 50 qubits are primarily vulnerable to classical simulation because of limits on gate fidelity and connectivity, the latter setting how many gates, and so how much infidelity, are needed to generate highly entangled states.

The reported hardware and result

The authors describe recent hardware upgrades to Quantinuum's H2 quantum computer that let it operate on up to 56 qubits with arbitrary connectivity and a two-qubit gate fidelity of 99.843(5)%. Using the flexible connectivity, they present data from random circuit sampling in highly connected geometries, at what they call unprecedented fidelities and at a scale that appears to be beyond the capabilities of state-of-the-art classical algorithms. They add that the considerable difficulty of classically simulating H2 is likely limited only by qubit number, and describe this as showing the promise and scalability of the QCCD architecture as progress continues toward larger machines.

Context

Random circuit sampling is a benchmark task with no stated practical application in the paper's abstract. A related post on this site covers the 2019 superconducting experiment and the disputes around it. The abstract's wording is hedged ("appears to be", "likely"), and a classical simulation result could change the picture, as it did for earlier claims.

Limits

The authors are the company's own researchers together with collaborators, and this is a preprint. The company also published a press release about the machine, which makes further comparative claims; those are company statements and are not repeated or checked here. The quoted fidelity is the authors' measurement for their system.

FAQ

How many qubits did the experiment use?

Up to 56, with arbitrary connectivity, according to the authors.

What two-qubit gate fidelity was reported?

99.843(5)%.

Does this prove classical computers cannot simulate it?

No. The authors say it appears to be beyond state-of-the-art classical algorithms, which is a claim open to later challenge.

Why does connectivity matter?

The abstract says it determines how many gates are needed to generate highly entangled states, and therefore how much infidelity is suffered.

Is this a useful calculation?

The abstract describes a sampling benchmark and states no practical application.