Berry's phase on photonic quantum computers

TL;DR

This paper develops a CVQC-based protocol to observe Berry's phase for orbital angular momentum in a time-dependent magnetic field, implemented entirely with passive Gaussian operations. By simulating the Hamiltonian $H=\frac{1}{2}\sum_i(p_i^2+q_i^2)-\mu\vec{B}\cdot\vec{L}$ using Strang-Trotter-Suzuki gadgets and a four-mode interferometer, the authors demonstrate that the geometric Berry phase $\gamma(C)$ can be extracted from interferometric readout. They extend the framework to the non-adiabatic regime via the Aharonov-Anandan phase, showing that the averaged phase $\tfrac{1}{2}(\xi_+ + \xi_-)$ tracks $\gamma(C)$ even when dynamical and leading non-geometric contributions are large. The framework is validated both in a quantum emulator (Quandela Perceval) and on the Ascella QPU, confirming experimental feasibility on current photonic hardware and highlighting potential for holonomic and geometric-gate applications in CVQC.

Abstract

We formulate a continuous-variable quantum computing (CVQC) algorithm to study Berry's phase on photonic quantum computers. We demonstrate that CVQC allows the simulation of charged particles with orbital angular momentum under the influence of an adiabatically changing $\vec{B}$ field. Although formulated entirely in the CVQC setting, our construction uses only passive linear-optical operations (beam splitters and phase shifts), which act identically in single-photon photonic architectures. This enables experimental realisation on the Quandella Ascella platform, where we observe the Berry's phase phenomenon with interferometric measurement. We also generalise the framework to more rapid non-adiabatic evolution. By concatenating Aharonov-Anandan cycles for opposing magnetic fields we demonstrate that one can engineer a circuit in which dynamical phases and leading non-geometric errors cancel by symmetry, leaving the intrinsically robust geometric phase contribution.

Figures (10)

• Figure 1: Isosurface of the density $|\phi_{0,1,1}|^2$ (at $|\phi_{0,1,1}|^2=1/8$) of the "donut state" when $\vec{B}$ is pointing in the $\hat{z}$ direction.
• Figure 2: Wigner function $W(r_+)$ of $\phi_{0,1,1}$, where the radius in phase space is $r_+ = \sqrt{q^2_++p^2_+}$, where the quadrature variables are $q_\pm$ and $p_\mp$ are as in Eq. \ref{['eq:quadpm']}.
• Figure 3: Inducing Berry phase with state $\phi_{0,1,1}$, with $\vec{B}$ field indicated in green.
• Figure 4: The Trotter-Suzuki "gadget" $G^{(1)}(dt)$ for a single time step through time $dt$, to generate real time evolution under the influence of the Hamiltonian in Eq. \ref{['eq:H_final']}. The second order Strang "gadget" is given by halving the time interval and doubling the gates, $S(dt) = G(\frac{dt}{2}) \cdot (G(\frac{dt}{2}))^T$.
• Figure 5: The Gaussian Trotter-Suzuki "gadget" $G^{(1)}(dt)$ for a single time step through time $dt$, to generate real time evolution under the influence of the Hamiltonian in Eq. \ref{['eq:H_final']}. Here the pairs of CX gates in Fig. \ref{['fig:gates']} that generated $e^{i \delta t \mu B_i L_i }$ are replaced by beam splitters.