Quantum Path Signatures

• URL: http://arxiv.org/abs/2508.05103v1
• Date: Thu, 07 Aug 2025 07:39:54 GMT
• Title: Quantum Path Signatures
• Authors: Samuel Crew, Cristopher Salvi, William F. Turner, Thomas Cass, Antoine Jacquier,
• Abstract summary: We introduce a new family of randomised path developments and derive corresponding loop equations.<n>We then interpret unitary randomised path developments as time evolution operators on a Hilbert space of qubits.<n>This leads to a definition of a quantum path signature feature map and associated quantum signature kernel.
• Score: 3.7096216875966115
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. In the case of the Gaussian matrix model, we study a random ensemble of Pauli strings and formulate a quantum algorithm to compute such kernel.

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