Perturbative Formulation and Non-adiabatic Corrections in Adiabatic Quantum Computing Schemes

Abstract

Adiabatic limit is the presumption of the adiabatic geometric quantum computation and of the adiabatic quantum algorithm. But in reality, the variation speed of the Hamiltonian is finite. Here we develop a general formulation of adiabatic quantum computing, which accurately describes the evolution of the quantum state in a perturbative way, in which the adiabatic limit is the zeroth-order approximation. As an application of this formulation, non-adiabatic correction or error is estimated for several physical implementations of the adiabatic geometric gates. A quantum computing process consisting of many adiabatic gate operations is considered, for which the total non-adiabatic error is found to be about the sum of those of all the gates. This is a useful constraint on the computational power. The formalism is also briefly applied to the adiabatic quantum algorithm.

5 pages, revtex. some references added

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• Quantum Entanglement in Second-quantized Condensed Matter Systems
• Singularity of Berry Connections Inhibits the Accuracy of Adiabatic Approximation
• Circuit-based digital adiabatic quantum simulation and pseudoquantum simulation as new approaches to lattice gauge theory
• Interfacing nuclear spins in quantum dots to cavity or traveling-wave fields
• Geometric vs. Dynamical Gates in Quantum Computing Implementations Using Zeeman and Heisenberg Hamiltonians
• Geometric Phases of Two Ising-interacting Spins in a Rotating Magnetic Field
• Hierarchical Theory of Quantum Adiabatic Evolution
• Quantum Information Aspects on Bulk and Nano Interacting Fermi System: Spin-Space Density Matrix Approach
• Trotter errors in digital adiabatic quantum simulation of quantum ${\mathbb{Z}}_2$ lattice gauge theory
• The Loss of fidelity due to quantum leakage for Josephson charge qubits
• Decoherence of quantum gates based on Aharonov-Anandan phases in a multistep scheme
• Effect of decoherence on the Berry phase of a spin-half in a rotating magnetic field
• Non-adiabatic Arbitary Geometric Gates in 2-qubit NMR Model