The adiabatic theorem in the presence of noise

Abstract

We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian, coupling to low-energy quantum systems, and decoherent time-dependent perturbations in the Hamiltonian. For decoherent perturbations, we find both upper and lower bounds on the evolution time to guarantee the adiabatic approximation performs within a prescribed tolerance. Our new results include explicit definitions of constants, and we apply them to the spin-1/2 particle in a rotating magnetic field, and to the superconducting flux qubit. We compare the theoretical bounds on the superconducting flux qubit to simulation results.

arXiv comment40 pages, 4 figures

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Cited by in corpus (12)

• Adiabatic Quantum Computing
• Quantum Adiabatic Markovian Master Equations
• Experimental Investigation of an Eight Qubit Unit Cell in a Superconducting Optimization Processor
• Consistency of the Adiabatic Theorem
• Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
• The quantitative condition is necessary in guaranteeing the validity of the adiabatic approximation
• Accuracy vs run time in adiabatic quantum search
• Role of Non-stoquastic Catalysts in Quantum Adiabatic Optimization
• Adiabatic theorems for linear and nonlinear Hamiltonians
• Born-Oppenheimer approximation in open systems
• Quantum adiabatic theorem for unbounded Hamiltonians with a cutoff and its application to superconducting circuits
• Quadratic fermionic interactions yield effective Hamiltonians for adiabatic quantum computing