Riemannian quantum circuit

Riemannian Geometry of Quantum Computation

An introduction is given to some recent developments in the differential geometry of quantum computation for which the quantum evolution is described by the special unitary unimodular group SU(2n). Using the Lie algebra su(2n), detailed derivations are given of a useful Riemannian geometry of SU(2n), including the connection, curvature, the geodesic equation for minimal complexity quantum compu...

Riemannian Geometry on Quantum Spaces

An algebraic formulation of Riemannian geometry on quantum spaces is presented, where Riemannian metric, distance, Laplacian, connection, and curvature have their counterparts. This description is also extended ∗email address: [email protected] to complex manifolds. Examples include the quantum sphere, the complex quantum projective spaces and the two-sheeted space.

Riemannian Geometry of Quantum Groups

Riemannian Geometry of Quantum Groups Andfinite

Quantum Photonic Circuit

One promising approach for scalable quantum computing is to use an alloptical architecture, in which the qubits are represented by photons and manipulated by mirrors and beam splitters. So far, researchers have demonstrated this method, called Linear Optical Quantum Computing, on a very small scale by performing operations using just a few photons. In an attempt to scale up this method to large...