Operator Learning for efficient Quantum Computation

2026-06-18

AI Summary

This work addresses the challenge of achieving practical quantum advantage under current hardware constraints, which stem from the lack of efficient operator and state-preparation primitives. The authors propose an end-to-end variational framework that unifies arbitrary unitary and non-unitary operators—including both sparse and dense cases—into compact quantum circuits tailored to hardware connectivity, using a block-encoding strategy requiring only a single ancilla qubit. By integrating a custom cost function, a novel regularization term, and backpropagation-based optimization, the method substantially reduces approximation errors. It efficiently learns propagators in quantum simulation and quantum chemistry with lower resource overhead than Suzuki–Trotter decomposition, and successfully implements dense non-unitary operators such as finite-difference Laplacians and inviscid potential flow around airfoils, demonstrating its generality and high accuracy.

Abstract

An efficient implementation of quantum algorithms is often hindered by the lack of efficient primitives for operators and state preparation. This limits both the ability of near-term quantum hardware to simulate complex problems and the potential of fault-tolerant algorithms to achieve practical quantum advantage. To address this, we propose a full-stack variational framework that transforms arbitrary operators to compact quantum circuits. The resulting variational circuits can be tailored to the connectivity and long-range interaction of the target hardware. The learning process employs backpropagation together with a cost function that efficiently optimizes unitary operators and non-unitary -- dense or sparse -- operators using only a single ancilla qubit for block encoding. Additionally, we introduce a regularization term that reduces the approximation error. The approach is validated for both quantum mechanical and engineering applications. In the former case, we learn propagators that arise in native quantum problems -- such as quantum simulation and quantum chemistry -- and achieve improved resource scaling in comparison to standard Suzuki-Trotter expansions. In the latter case, we demonstrate the approach's ability to implement the second-order central finite difference approximation of the Laplace operator -- relevant for solving partial differential equations -- while improving upon current error metrics. The final example deals with learning a dense, non-unitary operator that arises in the analysis of inviscid potential flow around an airfoil. This universality of the framework opens the door for solving general problems beyond prototypical engineering and quantum applications.

Problem

• quantum computation
• operator learning
• state preparation
• quantum advantage
• efficient primitives

Innovation

• operator learning
• variational quantum circuits
• block encoding
• quantum algorithm compilation
• non-unitary operator