A trapped ion simulates a programmable quantum double well

Why make a quantum potential programmable?

Many quantum systems are not well described by the familiar shape of a harmonic oscillator. Molecular vibrations can be anharmonic, while double-well potentials provide simplified models for studying tunnelling and processes such as proton transfer. Simulating these systems is challenging partly because the nonlinear operations needed to represent them can be difficult to implement in quantum hardware.

Cameron McGarry and colleagues demonstrate a method called trigonometric-gate-implemented Fourier synthesis, or TGIFS. It represents a target potential as a sum of trigonometric functions and compiles those terms into operations available on a hybrid quantum system. The aim is to change the simulated potential through classical control settings, without modifying the underlying device.

A motion mode and a qubit

The experiment used a single trapped ytterbium ion. Its motion in one radial direction served as a continuous-variable system, representing quantities such as position and momentum. Two internal energy levels of the ion acted as a qubit. Laser pulses coupled the motion and qubit through state-dependent displacements and qubit rotations.

Combining these operations produced trigonometric gates acting on the ion’s motion. A sequence of gates approximates evolution under a chosen potential. In principle, additional Fourier terms can represent more elaborate shapes, while smaller time steps can improve the approximation. Both require practical resources: deeper circuits involve more operations and can accumulate errors.

To test the method, the researchers prepared the ion’s motion in chosen states, applied gate sequences, and repeated measurements to reconstruct properties of the resulting motion. In the double-well experiments, they tracked the wavepacket’s average position and measured its position distribution at selected times. They also tested a quartic phase gate, which applies a phase that depends on the fourth power of position.

Tunnelling and a gate test

In a symmetric double well, a wavepacket started in one well and moved coherently across the barrier. The researchers observed four traversals over 16 milliseconds. At an intermediate time, the measured position distribution extended across both wells; at the turning points, it was more localised in one well. The measurements agreed with theoretical predictions that included estimated dephasing and gate-approximation effects.

The team then changed control parameters to make the wells asymmetric, without changing the hardware. The wavepacket’s oscillations were smaller in the asymmetric cases, consistent with reduced tunnelling in the simulated potentials. Separately, they synthesised a quartic phase gate using two trigonometric terms. Measurements on two motional input states were closer to the predicted target when the second term was included. This shows that adding terms improved this particular gate test; it does not mean arbitrary potentials have already been experimentally tested.

What the result does—and does not—show

The experiment is a proof of principle: one trapped-ion device used a shared circuit structure to simulate a tunable family of anharmonic dynamics and implement a quartic phase operation. The paper also compares resource requirements with a qubit-only calculation for the same double-well task at matched error. That comparison depends on the chosen algorithm, system and error measure; it does not establish a general advantage over other quantum or classical methods.

The authors identify three sources of disagreement with ideal evolution: motional dephasing, Trotter error from approximating continuous evolution with finite steps, and measurement imperfections. Their analysis finds substantial contributions from dephasing and Trotter error. The quartic-gate demonstration uses a limited Fourier expansion. More complex potentials and multiple interacting modes would require deeper circuits and further experimental development.

TGIFS therefore points toward reusable quantum simulators, rather than providing a ready-made tool for solving chemistry or materials problems. Extensions to arbitrary potentials and coupled modes are proposed possibilities as circuit depth and control improve, not achievements demonstrated in this single-ion experiment. This account is based on the authors’ arXiv preprint, which may not have undergone peer review; its claims should be considered in light of the methods and limitations described in the paper.