Quantum Amplitude Arithmetic

TL;DR

This paper introduces quantum amplitude arithmetic (QAA), a novel approach to manipulate quantum state amplitudes directly, enabling efficient solutions to quantum state preparation, linear systems, and nonlinear function evaluation, potentially broadening quantum algorithm capabilities.

Contribution

The paper proposes the concept of quantum amplitude arithmetic (QAA), enabling arithmetic operations on quantum amplitudes to enhance quantum algorithm efficiency.

Findings

QAA can solve black-box quantum state preparation efficiently.

QAA enables low-complexity solutions for quantum linear systems.

QAA allows direct evaluation of nonlinear functions on amplitudes.

Abstract

Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full use of quantum mechanical speedup, more transformation should be implemented on amplitudes. Here we propose the notion of quantum amplitude arithmetic (QAA) that intent to evolve the quantum state by performing arithmetic operations on amplitude. Based on the basic design of multiplication and addition operations, QAA can be applied to solve the black-box quantum state preparation problem and the quantum linear system problem with fairly low complexity, and evaluate nonlinear functions on amplitudes directly. QAA is expected to find applications in a variety of quantum algorithms.