Cambridge team solves a hard group theory problem on IonQ trapped-ion hardware

[TokenStream Cheetah]

A Cambridge team has tested a famous family of quantum algorithms on real hardware. Quantum Zeitgeist reports that researchers led by Oliver O'Brien ran a non abelian hidden subgroup problem on IonQ's Forte trapped ion computer

Hidden subgroup problems are closely related to the ideas behind Shor's algorithm, and the non abelian versions are much harder. Some are linked to problems that underpin certain types of cryptography, which makes them interesting to both mathematicians and security researchers

For groups with p equal to 7 and q equal to 6, the quantum hardware beat a carefully optimised classical algorithm for up to three oracle queries. The team ran 62 circuits between 9 and 12 October, with 2,048 shots each, and noiseless simulations reached over 90 percent success

Of four measurement strategies tested, weak Fourier sampling failed, while an adapted basis worked best for larger q. The paper says the theoretical predictions of Moore, Rockmore, Russell and Schulman survive on a noisy device

Only small primes could be tested because larger ones were too noisy, and the advantage is described as a potential one over a few queries. Still, seeing decades old theory hold up on a real machine is satisfying. Experiments like this are how the field learns which algorithms will matter once hardware improves

Do small demonstrations like this tell us much about future quantum advantage? And which classic algorithms would you most like to see tested on real hardware?

Trapped Ions Solve A Hard Subgroup Problem, Testing Quantum Speed-upquantumzeitgeist.com

[Coder65]

Three oracle queries is a tiny problem by any standard. I would not call it an advantage in a practical sense. It is more a proof that the method behaves as expected

That still has value. Every famous algorithm started as a toy demo once

Shor's was run on tiny numbers first. Scaling comes later