From quantum circuits to adiabatic algorithms

Abstract

This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically, we look for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state. Since this construction requires in general an n-local Hamiltonian, we will study whether approximation is possible using previous results on ground state entanglement and perturbation theory. Finally we will point out how the adiabatic model can be relaxed in various ways to allow for 2-local partially adiabatic algorithms as well as 2-local holonomic quantum algorithms.

Version accepted by and to appear in Phys. Rev. A

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• Adiabatic Theorem without a Gap Condition
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• Adiabatic Quantum Computation in Open Systems
• Realizable Hamiltonians for Universal Adiabatic Quantum Computers
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• Towards Fault Tolerant Adiabatic Quantum Computation
• Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions
• MAX 2-SAT with up to 108 qubits
• Quantum computation in continuous time using dynamic invariants
• Non-Abelian holonomic transformation in the presence of classical noise
• The quantum adiabatic search with decoherence in the instantaneous energy eigenbasis
• A modified quantum adiabatic evolution for the Deutsch-Jozsa problem
• High Fidelity Adiabatic Quantum Computation via Dynamical Decoupling
• Adiabatic Quantum Search in Open Systems
• Quantum and Classical in Adiabatic Computation
• Scheme for fault-tolerant holonomic computation on stabilizer codes
• Fault-tolerant Holonomic Quantum Computation in Surface Codes
• Quantum search by partial adiabatic evolution
• A Fault-Tolerant Scheme of Holonomic Quantum Computation on Stabilizer Codes with Robustness to Low-weight Thermal Noise
• Adiabatic Rotation, Quantum Search and Preparation of Superposition States
• Quantum adiabatic brachistochrone for open systems