Quantum-Inspired Algorithms beyond Unitary Circuits: the Laplace Transform

• URL: http://arxiv.org/abs/2601.17724v1
• Date: Sun, 25 Jan 2026 07:19:56 GMT
• Title: Quantum-Inspired Algorithms beyond Unitary Circuits: the Laplace Transform
• Authors: Noufal Jaseem, Sergi Ramos-Calderer, Gauthameshwar S., Dingzu Wang, José Ignacio Latorre, Dario Poletti,
• Abstract summary: Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods.<n>We introduce a tensor-network approach to compute the discrete Laplace transform, a non-unitary, aperiodic transform.<n>We demonstrate simulations up to $N=230$ input data points, with up to $260$ output data points, and quantify how bond dimension controls runtime and accuracy.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor networks naturally accommodate non-unitary maps. This flexibility lets us design quantum-inspired methods that start from a quantum algorithmic structure, yet go beyond unitarity to achieve speedups. Here we introduce a tensor-network approach to compute the discrete Laplace transform, a non-unitary, aperiodic transform (in contrast to the Fourier transform). We encode a length-$N$ signal on two paired $n$-qubit registers and decompose the overall map into a non-unitary exponential Damping Transform followed by a Quantum Fourier Transform, both compressed in a single matrix-product operator. This decomposition admits strong MPO compression to low bond dimension resulting in significant acceleration. We demonstrate simulations up to $N=2^{30}$ input data points, with up to $2^{60}$ output data points, and quantify how bond dimension controls runtime and accuracy, including precise and efficient pole identification.

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