Adiabatic Rotation, Quantum Search and Preparation of Superposition States

Abstract

We introduce the idea of using adiabatic rotation to generate superpositions of a large class of quantum states. For quantum computing this is an interesting alternative to the well-studied "straight line" adiabatic evolution. In ways that complement recent results, we show how to efficiently prepare three types of states: Kitaev's toric code state, the cluster state of the measurement-based computation model and the history state used in the adiabatic simulation of quantum circuit. We also show that the method, when adapted for quantum search, provides quadratic speedup as other optimal methods do with the advantages that the problem Hamiltonian is time-independent and that the energy gap above the ground state is strictly nondecreasing with time. Likewise the method can be used for optimization as an alternative to the usual adiabatic algorithm.

arXiv commentExpanded to 6 pages; Accepted by Phys. Rev. A

References in corpus (7)

• Fault-tolerant quantum computation by anyons
• Topological quantum memory
• String-net condensation: A physical mechanism for topological phases
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Quantum Search by Local Adiabatic Evolution
• A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation
• From quantum circuits to adiabatic algorithms

Cited by in corpus (6)

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• Dissipation in adiabatic quantum computers: Lessons from an exactly solvable model
• Adiabatic preparation without Quantum Phase Transitions
• Implementation of many-qubit Grover search with trapped ultracold ions
• Efficient optimization of perturbative gadgets
• Duality in spin systems via the $SU(4)$ algebra