Quantum simulation of an exciton-transfer Hamiltonian on a silicon photonic circuit

Abstract

An integrated silicon quantum photonic device, capable of implementing non-compiled controlled unitary operations (CUs), is performing a new variational protocol for searching the ground state of an exciton-transfer Hamiltonian in chlorophyll. This protocol only requires single-qubit measurements ―amenable for scalable quantum photonic approaches ― independently from the dimension of the Hamiltonian system. A maximally path-entangled state, |0>C|0>T +|1>C|0>T, is created on chip through the SFWM effect in silicon waveguides. Then, the target qubit state (with subscript “T”) is expanded into a four-dimensional space and evolved according to two separate unitary operations, i.e. I (identity) and an arbitrary U∈SU(2), ended with a path-information erasure process. This yields a non-compiled “CU” operation, controlled by the control qubit (with subscript “C”) as |0>C ⊗I|φ>T +|1>C⊗U|φ>T. In this experiment, an exciton-transfer Hamiltonian in chlorophyll is properly mapped as U onto our circuit’s parameters. Both state preparation and CU operations are implemented using thermo-optic phase shifting heaters. Our new protocol draws on the eigenstate-generation features of the Iterative Phase Estimation Algorithm (IPEA), and relies on 1-qubit state-tomography performed on the C-qubit alone, to infer properties of the Hamiltonian. The protocol proposes a variational search of the ground state in the Hilbert space spanned by U’s eigenstates, combining quantum measurements and a classical update scheme for the trial T-states that are prepared and evolved in the quantum circuit at each step of the algorithm. The search is guided by effectively minimizing an objective function Fobj=-αP+βE. Only when the input T-qubit is an eigenstate of U, the purity (P) of the output C-qubit |0> + eiφ|1>is 1, and in this case, eigenphase φprovides an estimator for |φ>T's eigenvalue (E). The on-chip implementation granted a robust, reconfigurable setup for our variational search algorithm: within less than 10 steps, we were able to achieve 99.8% fidelity of the final T-state with the ground-state of the implemented Hamiltonian. Under reasonable assumptions, these preliminary results may pave the way towards a scalable quantum-simulation approach for the ground-state problem.