Overcoming the Matrix-Product-State Encoding Barrier via DMRG-Guided Probabilistic Imaginary-Time Evolution

• URL: http://arxiv.org/abs/2605.30141v1
• Date: Thu, 28 May 2026 16:05:46 GMT
• Title: Overcoming the Matrix-Product-State Encoding Barrier via DMRG-Guided Probabilistic Imaginary-Time Evolution
• Abstract summary: We propose a three-stage framework for ground-state preparation in quantum simulation.<n>The central-bond Schmidt rank of intermediate states during MPS encoding grows logistically with the number of layers.<n>We show that the framework avoids very deep encoding circuits and substantially suppresses the post-selection overhead intrinsic to PITE.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Ground-state preparation is a fundamental task in quantum simulation, because the overlap of the prepared state with the true ground state significantly affects the overall cost of subsequent quantum algorithms. We propose a three-stage framework in which a matrix product state (MPS) of an $N$-site system obtained by the density-matrix renormalization group (DMRG) is loaded onto an $N$-qubit quantum register through an optimization-free matrix product disentangler (MPD) encoding circuit, and the residual error is then reduced by probabilistic imaginary-time evolution (PITE). We demonstrate that the central-bond Schmidt rank of intermediate states during MPS encoding grows logistically with the number of layers. Its inflection point $L^{*}$ marks the boundary of the efficient encoding regime. Beyond this point, the gain in fidelity slows rapidly, and the number of additional MPD layers required to reach a target infidelity $\varepsilon$ empirically scales as $\mathcal{O}(N^5\log(N/\varepsilon))$. To avoid this encoding-only tail, we stop the encoder at $L^{*}$ and suppress the remaining excited-state components by PITE, with the linear PITE schedule fixed deterministically from the ground-state energy, the effective gap, and the reference overlap estimated by DMRG. Numerical experiments on the spin-$1/2$ staggered-field Heisenberg chain show that the framework avoids very deep encoding circuits and substantially suppresses the post-selection overhead intrinsic to PITE. Combining classical preprocessing by DMRG, optimization-free MPS encoding, and deterministically scheduled PITE, the present framework offers a practical hybrid route to ground-state preparation in quantum simulation.

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