A PARTICLE COLLIDER INSIDE A QUANTUM COMPUTER

Collisions have long been one of physics’ main tools for probing the inner structure of matter. Quantum simulators now make it possible to run collisions on quantum hardware, where the strength of the interactions can be tuned at will, from weak to very strong.

In real materials where electrons interact strongly, collisions between quasiparticles — collective excitations that behave like particles — govern how charge and energy move. Yet they are usually studied only indirectly, through spectroscopy. A quantum simulator can create individual quasiparticles, launch them, and watch them collide in space and time.

Two opposite projectiles

Chan Bin Bark, Moon Jip Park and colleagues at Hanyang University in Seoul, Ajou University in Korea and Ohio State University in the United States, chose a textbook model of interacting electrons, the Fermi-Hubbard model. Electrons hop from site to site along a chain, and two electrons on the same site repel each other with an energy U. With exactly one electron per site, the chain becomes a so-called Mott insulator.

On that background, two kinds of excitations can carry charge:

• a doublon, a site with two electrons;
• a holon, an empty site.

They behave like a particle and its antiparticle. Collisions between identical quasiparticles had been studied before; a collision between two different ones, each prepared individually, had not.

Building the collider

The team encoded a chain of 21 sites on 42 qubits of IBM’s superconducting quantum processor ibm_boston, two qubits per site. They placed a doublon on one side and a holon on the other.

To launch them, they first switched off the hopping toward the outer edges for a short time, so each excitation could only move toward the centre — like a starting gate. Then they restored all hopping and let the two packets meet near the middle.

Running such circuits on today’s noisy hardware took care: they picked the best qubits with preliminary tests, ran 70,000 measurements per data point, and used the fact that the total number of particles must stay constant to correct for errors. They compared everything with an exact theoretical solution of the model, known as the Bethe ansatz, and with classical computer simulations.

Pass through, bounce, or both

• With weak repulsion (U = 1), the doublon and the holon pass through each other and keep going.
• With strong repulsion (U = 7), they bounce back. To swap places, they would have to go through an intermediate arrangement that costs an energy U, so they behave like hard balls.
• In both cases they leave as fast as they came: the collision is elastic.

They measured the probability of passing through for repulsions from 1 to 8. It follows the exact theory without any adjusted parameter — a first for quasiparticles of this model on quantum hardware, according to the authors.

Half through, half back

At an intermediate repulsion (U = 3.5), something unusual happens: the charge almost disappears after the collision. Measuring doublons and holons separately shows why. Neither vanished — the number of doublons does not drop — but each spread to both sides of the chain. The outgoing state looks like a mix of “passed through” and “bounced back” in comparable proportions.

Such a superposition entangles the left and right halves of the chain. The team detected it without a full reconstruction of the quantum state, by measuring how much the number of particles in the left half fluctuates from one run to the next. The fluctuation is largest in the intermediate regime.

As a control, they replaced the holon with a second doublon. Two identical doublons cannot swap places, and indeed their collision looked almost the same at every repulsion, with almost no fluctuation.

What remains to be shown

The authors are careful: their measurements show that the two outcomes are present, and in what proportions, but they do not directly prove that the two are coherently superposed. That interpretation rests on the laws of quantum evolution and on the agreement with theory. An interference experiment could confirm it once longer simulations become possible — beyond the time window studied here, even classical simulations struggle to keep up.