Exact Solutions of Holonomic Quantum Computation

Abstract

Holonomic quantum computation is analyzed from geometrical viewpoint. We develop an optimization scheme in which an arbitrary unitary gate is implemented with a small circle in a complex projective space. Exact solutions for the Hadamard, CNOT and 2-qubit discrete Fourier transform gates are explicitly constructed.

11 pages, re-organized to be more comprehensive, references added, style file of Physics Letters A is needed

References in corpus (9)

• Holonomic Quantum Computation
• Geometric Manipulation of Trapped Ions for Quantum Computation
• Non-Abelian Berry connections for quantum computation
• Non-Abelian phases, charge pumping, and quantum computation with Josephson junctions
• Realization of Arbitrary Gates in Holonomic Quantum Computation
• Topological Features in Ion Trap Holonomic Computation
• Note on Coherent States and Adiabatic Connections, Curvatures
• Mathematical Foundations of Holonomic Quantum Computer
• Geometrical phases for the G(4,2) Grassmannian manifold

Cited by in corpus (12)

• Geometric phases in quantum information
• Exact solutions of the isoholonomic problem and the optimal control problem in holonomic quantum computation
• Fault-tolerant Holonomic Quantum Computation in Surface Codes
• Control aspects of holonomic quantum computation
• A Fault-Tolerant Scheme of Holonomic Quantum Computation on Stabilizer Codes with Robustness to Low-weight Thermal Noise
• Mixed state non-Abelian holonomy for subsystems
• Demonstrating quantum algorithm acceleration with NMR quantum computer
• Implementation of holonomic quantum gates by an isospectral deformation of an Ising dimer chain
• Exact solutions for a universal set of quantum gates on a family of iso-spectral spin chains
• Generating nonequilibrium stationary state from ground state condensate through an almost-adiabatic cycle
• Application of Geometric Phase in Quantum Computations
• Cyclic Evolution on Grassmann Manifold and Berry Phase