Quantum-Inspired Algorithms beyond Unitary Circuits: the Laplace Transform
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866912971782881280 |
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| author | Jaseem, Noufal Ramos-Calderer, Sergi S., Gauthameshwar Wang, Dingzu Latorre, José Ignacio Poletti, Dario |
| author_facet | Jaseem, Noufal Ramos-Calderer, Sergi S., Gauthameshwar Wang, Dingzu Latorre, José Ignacio Poletti, Dario |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_17724 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum-Inspired Algorithms beyond Unitary Circuits: the Laplace Transform Jaseem, Noufal Ramos-Calderer, Sergi S., Gauthameshwar Wang, Dingzu Latorre, José Ignacio Poletti, Dario Quantum Physics Mathematical Physics Data Analysis, Statistics and Probability 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. |
| title | Quantum-Inspired Algorithms beyond Unitary Circuits: the Laplace Transform |
| topic | Quantum Physics Mathematical Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2601.17724 |