Topics in matrix analysis
Nonlinear partial differential equations: for scientists and engineers
Nonlinear partial differential equations: for scientists and engineers
Topological methods in hydrodynamics
Topological methods in hydrodynamics
Quantum computation and quantum information
Quantum computation and quantum information
Problems And Solutions in Quantum Computing And Quantum Information
Problems And Solutions in Quantum Computing And Quantum Information
A geometric approach to quantum circuit lower bounds
Quantum Information & Computation
The geometry of quantum computation
Quantum Information & Computation
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An introduction is first given of recent developments in the Riemannian geometry of quantum computation in which the quantum evolution is represented in the tangent space manifold of the special unitary unimodular group for n qubits. The Riemannian right-invariant metric, connection, curvature, geodesic equation for minimal complexity quantum circuits, Jacobi equation, and the lifted Jacobi equation for varying penalty parameter are reviewed. Sharpened tools for calculating the geodesic derivative are presented. The geodesic derivative may facilitate the numerical investigation of conjugate points and the global characteristics of geodesic paths in the group manifold, the determination of optimal quantum circuits for carrying out a quantum computation, and the determination of the complexity of particular quantum algorithms.