Efficient Inversion of Unknown Unitary Operations with Structured Hamiltonians

TL;DR

This paper introduces efficient quantum algorithms for inverting unitaries with structured Hamiltonians, reducing resource requirements and enabling practical implementation on near-term quantum devices.

Contribution

It presents novel algorithms that invert unitaries with specific Hamiltonian structures more efficiently than previous methods, including cases with exponentially many parameters.

Findings

Significant reduction in ancilla qubits needed for inversion.

Ability to invert unitaries with exponentially many parameters using a single query.

Algorithms demonstrated to be robust under realistic noise conditions.

Abstract

Unknown unitary inversion is a fundamental primitive in quantum computing and physics. Although recent work has demonstrated that quantum algorithms can invert arbitrary unknown unitaries without accessing their classical descriptions, improving the efficiency of such protocols remains an open question. In this work, we present efficient quantum algorithms for inverting unitaries with specific Hamiltonian structures, achieving significant reductions in both ancilla qubit requirements and unitary query complexity. We identify cases where unitaries encoding exponentially many parameters can be inverted using only a single query. We further extend our framework to implement unitary complex conjugation and transposition operations, and develop modified protocols capable of inverting more general classes of Hamiltonians. We have also demonstrated the efficacy and robustness of our algorithms via numerical simulations under realistic noise conditions of superconducting quantum hardware. Our results establish more efficient protocols that improve the resources required for quantum unitary inversion when prior information about the quantum system is available, and provide practical methods for implementing these operations on near-term quantum devices.