Quantum circuit compression using qubit logic on qudits

Abstract: We present qubit logic on qudits (QLOQ), a compression scheme in which the qubits from a hardware agnostic circuit are divided into groups of various sizes, and each group is mapped to a physical qudit for computation. QLOQ circuits have qubit-logic inputs, outputs, and gates, making them compatible with existing qubit-based algorithms and Hamiltonians. We show that arbitrary qubit-logic unitaries can in principle be implemented with significantly fewer two-level (qubit) physical entangling gates in QLOQ than in qubit encoding. We achieve this advantage in practice for two applications: variational quantum algorithms, and unitary decomposition. The variational quantum eigensolver (VQE) for LiH took 5 hours using QLOQ on one of Quandela's cloud-accessible photonic quantum computers, whereas it would have taken 4.39 years in qubit encoding. We also provide a QLOQ version of the Quantum Shannon Decomposition, which not only outperforms previous qudit-based proposals, but also beats the theoretical lower bound on the CNOT cost of unitary decomposition in qubit encoding.