Realization of Arbitrary Gates in Holonomic Quantum Computation

Abstract

Among the many proposals for the realization of a quantum computer, holonomic quantum computation (HQC) is distinguished from the rest in that it is geometrical in nature and thus expected to be robust against decoherence. Here we analyze the realization of various quantum gates by solving the inverse problem: Given a unitary matrix, we develop a formalism by which we find loops in the parameter space generating this matrix as a holonomy. We demonstrate for the first time that such a one-qubit gate as the Hadamard gate and such two-qubit gates as the CNOT gate, the SWAP gate and the discrete Fourier transformation can be obtained with a single loop.

8 pages, 6 figures

Cited by in corpus (17)

• Geometric phases in quantum information
• Holonomic quantum gates: A semiconductor-based implementation
• Optimal multiqubit operations for Josephson charge qubits
• Non-Abelian holonomic transformation in the presence of classical noise
• Optimized design of universal two-qubit gates
• Geometric quantum gates in liquid-state NMR based on a cancellation of dynamical phases
• Exact solutions of the isoholonomic problem and the optimal control problem in holonomic quantum computation
• Implementing Shor's algorithm on Josephson Charge Qubits
• Scheme for fault-tolerant holonomic computation on stabilizer codes
• Exact Solutions of Holonomic Quantum Computation
• 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 solution of qubit decoherence models by a transfer matrix method
• Exact solutions for a universal set of quantum gates on a family of iso-spectral spin chains
• A possible hypercomputational quantum algorithm
• Application of Geometric Phase in Quantum Computations