Quantum Computation with Coherent Spin States and the Close Hadamard Problem

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.

RevTeX4, 13 pages with 8 figures. Accepted for publication in Quantum Information Processing. Article number: s11128-015-1229-0

References in corpus (1)

• Gaussian quantum computation with oracle-decision problems

Cited by in corpus (8)

• Qudits and high-dimensional quantum computing
• Performing SU($d$) operations and rudimentary algorithms in a superconducting transmon qudit for $d=3$ and $d=4$
• Asymptotically Improved Circuit for $d$-ary Grover's Algorithm with Advanced Decomposition of $n$-qudit Toffoli Gate
• Hybrid controlled-SUM gate with one superconducting qutrit and one cat-state qutrit and application in hybrid entangled state preparation
• A hybrid-qudit representation of digital RGB images
• QuDiet: A Classical Simulation Platform for Qubit-Qudit Hybrid Quantum Systems
• Circuit Design for $k$-coloring Problem and Its Implementation in Any Dimensional Quantum System
• Moving Quantum States without SWAP via Intermediate Higher Dimensional Qudits