Quantum Computation with Coherent Spin States and the Close Hadamard Problem

TL;DR

This paper introduces a quantum computation model based on spin systems and demonstrates its effectiveness by solving the close Hadamard problem with high accuracy in a constant number of queries, highlighting its potential for symmetry-exploiting problems.

Contribution

The paper develops a spin system-based quantum computation model and proves its capability to efficiently solve the close Hadamard problem with minimal error and queries.

Findings

The close Hadamard problem can be solved with arbitrarily small error in a constant number of queries.

The spin system model is suitable for problems exploiting symmetry between information structure and unitary operators.

The model demonstrates potential for solving specific classes of problems efficiently.

Abstract

We study a model of quantum computation based on the continuously-parameterized yet finite-dimensional Hilbert space of a spin system. We explore the computational powers of this model by analyzing a pilot problem we refer to as the close Hadamard problem. We prove that the close Hadamard problem can be solved in the spin system model with arbitrarily small error probability in a constant number of oracle queries. We conclude that this model of quantum computation is suitable for solving certain types of problems. The model is effective for problems where symmetries between the structure of the information associated with the problem and the structure of the unitary operators employed in the quantum algorithm can be exploited.