Optimizing quantum circuits with Riemannian gradient flow

Abstract

Variational quantum algorithms are a promising class of algorithms that can be performed on currently available quantum computers. In most settings, the free parameters of a variational circuit are optimized using a classical optimizer that updates parameters in Euclidean geometry. Since quantum circuits are elements of the special unitary group, we can consider an alternative optimization perspective that depends on the structure of this group. In this work, we investigate a Riemannian optimization scheme over the special unitary group and we discuss its implementation on a quantum computer. We illustrate that the resulting Riemannian gradient-flow algorithm has favorable optimization properties for deep circuits and that an approximate version of this algorithm can be performed on near-term hardware.

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• Approximate encoding of quantum states using shallow circuits
• Here comes the SU(N): multivariate quantum gates and gradients
• Double-bracket quantum algorithms for diagonalization
• Randomized adaptive quantum state preparation
• Boundary Treatment for Variational Quantum Simulations of Partial Differential Equations on Quantum Computers
• Equivalence of cost concentration and gradient vanishing for quantum circuits: An elementary proof in the Riemannian formulation
• Efficient Quantum Circuit Compilation for Near-Term Quantum Advantage
• Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states
• Double-bracket quantum algorithms for quantum imaginary-time evolution
• Riemannian quantum circuit optimization based on matrix product operators
• Geometric Quantum Machine Learning with Horizontal Quantum Gates
• Double-bracket algorithm for quantum signal processing without post-selection
• Double-Bracket Master Equations: Phase-Space Representation and Classical Limit
• Global optimization in variational quantum algorithms via dynamic tunneling method
• Role of Riemannian geometry in double-bracket quantum imaginary-time evolution
• Double-bracket quantum algorithms for high-fidelity ground state preparation