A constructive algorithm for the Cartan decomposition of SU(2^N)

Abstract

We present an explicit numerical method to obtain the Cartan-Khaneja-Glaser decomposition of a general element G of SU(2^N) in terms of its `Cartan' and `non-Cartan' components. This effectively factors G in terms of group elements that belong in SU(2^n) with n<N, a procedure that can be iterated down to n=2. We show that every step reduces to solving the zeros of a matrix polynomial, obtained by truncation of the Baker-Campbell-Hausdorff formula, numerically. All computational tasks involved are straightforward and the overall truncation errors are well under control.

15 pages, no figures, matlab file at http://cam.qubit.org/users/jiannis/

Cited by in corpus (14)

• Fixed Depth Hamiltonian Simulation via Cartan Decomposition
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution
• Constructive Quantum Shannon Decomposition from Cartan Involutions
• Optimizing quantum circuits with Riemannian gradient flow
• Time-optimal synthesis of unitary transformations in coupled fast and slow qubit system
• Nearly-optimal state preparation for quantum simulations of lattice gauge theories
• Quantum Geometric Machine Learning for Quantum Circuits and Control
• Finding good quantum codes using the Cartan form
• A General Framework for Recursive Decompositions of Unitary Quantum Evolutions
• Quantum topological data analysis via the estimation of the density of states
• Improving quantum gate fidelities using optimized Euler angles
• Variational LOCC-assisted quantum circuits for long-range entangled states
• Simplified projection on total spin zero for state preparation on quantum computers
• Fast-forwardability of Qubit-mapped Fermion models based on Cartan decomposition