Preparation Circuits for Matrix Product States by Classical Variational Disentanglement

• URL: http://arxiv.org/abs/2504.21298v1
• Date: Wed, 30 Apr 2025 04:13:01 GMT
• Title: Preparation Circuits for Matrix Product States by Classical Variational Disentanglement
• Authors: Refik Mansuroglu, Norbert Schuch,
• Abstract summary: We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS)<n>Our algorithm represents a near-term alternative to previous sequential approaches by reverse application of a disentangler.<n>We show numerical results for ground states of one-dimensional, local Hamiltonians as well as artificially spread out entanglement among multiple qubits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the classical compilation of quantum circuits for the preparation of matrix product states (MPS), which are quantum states of low entanglement with an efficient classical description. Our algorithm represents a near-term alternative to previous sequential approaches by reverse application of a disentangler, which can be found by minimizing bipartite entanglement measures after the application of a layer of parameterized disentangling gates. Since a successful disentangler is expected to decrease the bond dimension on average, such a layer-by-layer optimization remains classically efficient even for deep circuits. Additionally, as the Schmidt coefficients of all bonds are locally accessible through the canonical $\Gamma$-$\Lambda$ form of an MPS, the optimization algorithm can be heavily parallelized. We discuss guarantees and limitations to trainability and show numerical results for ground states of one-dimensional, local Hamiltonians as well as artificially spread out entanglement among multiple qubits using error correcting codes.

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