Quantum Path Signatures

Understand

We elucidate physical aspects of path signatures by formulating randomised path developments within the framework of matrix models in quantum field theory.

• Using tools from physics, we introduce a new family of randomised path developments and derive corresponding loop equations.
• We then interpret unitary randomised path developments as time evolution operators on a Hilbert space of qubits.
• This leads to a definition of a quantum path signature feature map and associated quantum signature kernel through a quantum circuit construction.