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Variational Optical Phase Learning on a Continuous-Variable Quantum Compiler

Matthew A. Feldman1,2,*, Tyler Volkoff3,†, Seongjin Hong2, Claire E. Marvinney1,2, Zoë Holmes4, Raphael C. Pooser1,2, Andrew Sornborger5,2, and Alberto M. Marino1,2,‡

  • *Contact author: feldmanma@ornl.gov
  • †Contact author: volkoff@lanl.gov
  • ‡Contact author: marinoa@ornl.gov
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PRX Quantum 7, 010358 – Published 23 March, 2026

DOI: https://doi.org/10.1103/7l8z-zn2m

Abstract

Quantum process learning is a fundamental primitive that draws inspiration from machine learning with the goal of better studying the dynamics of quantum systems. One approach to quantum process learning is quantum compilation, whereby an analog quantum operation is digitized by compiling it into a series of basic gates. While there has been significant focus on quantum compiling for discrete-variable systems, the continuous-variable (CV) framework has received comparatively less attention. We present an experimental implementation of a CV quantum compiler that uses two-mode squeezed light to learn a Gaussian unitary operation. We demonstrate the compiler by learning a parameterized linear phase unitary through the use of target and control phase unitaries to demonstrate a factor of 5.4 increase in the precision of the phase estimation and a 3.6-fold acceleration in the time-to-solution metric when leveraging quantum resources. We further show how our approach can be extended to higher-dimensional compilation tasks. Our results are enabled by the tunable control of our cost landscape via variable squeezing, thus providing a critical framework to simultaneously increase precision and reduce time-to-solution.

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Popular Summary

Inspired by the techniques of machine learning, we have developed a novel experimental approach for learning quantum optical operations. Our research introduces a continuous-variable (CV) quantum compiler that uses squeezed light to learn phase operations with remarkable precision and efficiency. In quantum technologies, compilation focuses on learning a quantum digital twin for a complex quantum process. Our approach is particularly unique because it uses CV systems—quantum systems that rely on smoothly varying properties like the amplitude and phase of an electromagnetic field—rather than the more familiar discrete systems used to implement qubits.

In our study, we successfully compiled an optical phase operation by employing light in a two-mode squeezed state, an entangled state of light. This type of light, where the quantum fluctuations in two beams are correlated, serves as a valuable quantum resource for the learning process. By tuning the strength of the quantum correlations through the squeezing parameter, we were able to significantly improve the precision with which the system learns, achieving a factor of 5.4 increase in phase precision, while also accelerating the training process by 3.6 times.

One of the most interesting outcomes of this work is how the tunable squeezing capability impacts the landscape of the cost function, a mathematical measure of how close we are to our target operation. By adjusting the level of squeezing, we show that we can make the cost function more favorable for learning, resulting in faster convergence and higher accuracy. Overall, our work provides an important advance in using quantum light to learn quantum processes. The results demonstrate a practical framework to achieve both high precision and fast learning in quantum compilation, potentially enabling more efficient quantum algorithms and operations for future quantum technologies.

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PRX Quantum 7, 010358– Published 23 March, 2026
  • Received 13 February 2025
  • Revised 20 November 2025
  • Accepted 26 January 2026
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