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

TL;DR

This paper introduces a co-designed family of quantum eigenvalue transformation oracles optimized for hybrid qubit/qumode hardware, enabling efficient spectral filtering and eigenstate preparation with minimal discretization errors.

Contribution

It develops a novel spectral transformation oracle framework that leverages continuous-variable qumodes for efficient encoding and compilation on hybrid quantum processors.

Findings

Efficient encoding of spectral functions without discretization errors.

Scalable algorithms for eigenstate preparation in spin models.

Analysis of physical error effects and open research directions.

Abstract

We co-design a family of quantum eigenvalue transformation oracles that can be efficiently implemented on hybrid discrete/continuous-variable (qubit/qumode) hardware. To illustrate the oracle's representation-theoretic power and near-term experimental accessibility, we encode a Gaussian imaginary time evolution spectral filter. As a result, we define a continuous linear combination of unitaries block-encoding. Due to the ancillary qumode's infinite-dimensional nature, continuous variable qumodes constitute a powerful compilation tool for encoding continuous spectral functions without discretization errors while minimizing resource requirements. We then focus on the ubiquitous task of preparing eigenstates in quantum spin models. For completeness, we provide an end-to-end compilation which expresses high-level oracles in terms of an experimentally realizable instruction set architecture in both 1D and 2D. Finally, we examine the leading-order effects of physical errors and highlight open research directions. Our algorithms scale linearly with the spatial extent of the target system and are applicable to both near-term and large-scale quantum processors.