Adiabatic Computation - A Toy Model

Abstract

We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter $s$ and the $\alpha$ parameter which emulates many-variables constrains in the classical computational problem. The proposed model presents, in the $s-\alpha$ plane, a line of first order quantum phase transition that ends at a second order point. The relation between computation complexity and the occurrence of quantum phase transitions is discussed. We analyze the behavior of the ground and first excited states near the quantum phase transition, the gap and the entanglement content of the ground state.

7 pages, 8 figures

References in corpus (10)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Robustness of adiabatic quantum computation
• Entanglement in a second order quantum phase transition
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Concurrence in collective models
• Universality of Entanglement and Quantum Computation Complexity
• Exponential complexity of an adiabatic algorithm for an NP-complete problem
• Adiabatic quantum computation and quantum phase transitions
• Adiabatic quantum search algorithm for structured problems

Cited by in corpus (2)

• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• On quantum mean-field models and their quantum annealing