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

Luke Bell1,2,*, Yan Wang3,†, Kevin C. Smith4,5,1,‡, Yuan Liu6,7,8, Eugene Dumitrescu3,§, and S.M. Girvin1,5

  • *Contact author: lukebell@ucsb.edu
  • †Contact author: wangy2@ornl.gov
  • ‡Present address: IBM Quantum, Cambridge, MA, USA.
  • §Contact author: dumitrescuef@ornl.gov
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PRX Quantum 6, 040359 – Published 9 December, 2025

DOI: https://doi.org/10.1103/1496-tlmm

Abstract

We co-design a family of quantum eigenvalue transformation oracles that can be efficiently implemented on hybrid discrete- or continuous-variable (qubit or 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.

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Physics Subject Headings (PhySH)

Corrections

12 January, 2026

Correction: During the production cycle, the parentheses after O and commas between commators were removed in several locations and have been restored. In the seventh paragraph of Sec. II, primes were missing from two occurrences of H^ and have been restored.

Popular Summary

Quantum computers are powerful, but turning theory into useful results is difficult in practice. To make progress, optimizing high-level quantum algorithms for experimental hardware is necessary. In our work, qubits work hand in hand with harmonic oscillator modes that live in a continuous space. The key result is an energy selective continuous filter that can be implemented efficiently on a variety of platforms. This filter boosts the weight of states near a chosen energy and can be straightforwardly compiled on realistic devices with resources that scale linearly in the system size.

How does it work? We couple the spin system to an auxiliary oscillator that we nudge by an amount proportional to the desired filtering. A simple measurement of the oscillator then applies a Gaussian-shaped filter on the energy levels. This can be used as an imaginary time evolution, which suppresses higher energy components while keeping lower energy ones. We provide full hardware-level compilation for one- and two-dimensional spin models using the Heisenberg model as an example. We then outline parallel versions that use multiple oscillators to quadratically speed up filtering and analyze the leading physical errors. Because oscillators handle continuous functions natively, our approach avoids discretization overheads that burden qubit-only techniques.

Looking ahead, our work is far from the end of the story, with straightforward extensions to fermionic models relevant to chemistry and materials. Our work also invites near-term experiments on superconducting and trapped-ion platforms, software development to automate continuous-variable or discrete-variable compilation, and the exploration of richer filters and complex-time dynamics to further accelerate algorithms.

Article Text

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PRX Quantum 6, 040359– Published 9 December, 2025
  • Received 1 May 2025
  • Revised 2 October 2025
  • Accepted 30 October 2025
  • Corrected 12 January 2026
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