Co-Designing Spectral Transformation Oracles with Hybrid Oscillator-Qubit Quantum Processors: From Algorithms to Compilation

Experimental and algorithmic challenges limit the near-term utility of quantum computers. First, from a computer science perspective, one desires optimal compilation of broad classes of oracles. Second, from an experimental hardware perspective, one wishes to maximize a physical platform's computational reach by judiciously leveraging physical features. In this work, we unify these seemingly disparate compilation challenges by co-designing algorithms alongside general hardware architectures that comprise a lattice of continuous variable (CV) oscillators and a dual lattice of discrete variable (DV) qubits. Using the features of this hybrid CV-DV hardware, we co-design a block-encoding algorithm for achieving a linear combination of unitaries that applies a Gaussian energy filter, for example, to project the qubits into a low-energy eigenstate of the paradigmatic Heisenberg model. We show how these algorithms can be directly implemented as a block-encoded imaginary time evolution accessible via measurement of the CV register and provide an end-to-end compilation with the circuit depth scaling linearly with the number of spin sites in the 1D and 2D models. Our work demonstrates how complex oracular functions can be efficiently encoded by a judicious selection of physical degrees of freedom and Gaussian CV-DV gates. Future work may also generalize the class of integral-based, block-encoded oracles to perform generalized quantum state transformations or filtering for arbitrary Hamiltonians.