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Variational preparation of normal matrix product states on quantum computers

Ben Jaderberg1,*, George Pennington2, Kate V. Marshall1, Lewis W. Anderson1, Abhishek Agarwal3, Lachlan P. Lindoy3, Ivan Rungger3,4, Stefano Mensa2, and Jason Crain5,6

  • *Contact author: benjamin.jaderberg@ibm.com
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Phys. Rev. Research 8, 013081 – Published 26 January, 2026

DOI: https://doi.org/10.1103/m5kb-4f43

Abstract

Preparing matrix product states (MPSs) on quantum computers is an essential routine in the simulation of many-body physics. However, widely used schemes based on staircase circuits are often too deep to execute on current hardware. Here, we demonstrate that MPSs with short-range correlations can be prepared with shallow circuits by leveraging heuristics from approximate quantum compiling (AQC). We achieve this with ADAPT-AQC, an adaptive-ansatz preparation algorithm, and introduce a generalized initialization procedure for the existing AQC-Tensor algorithm. We first compare these methods for the task of preparing a molecular electronic structure ground state. We then use them to prepare an antiferromagnetic (AFM) ground state of the 50-site Heisenberg XXZ spin chain near the AFM-XY phase boundary. Through the execution of circuits with up to 59 cz depth and 1251 cz gates, we perform a global quench and observe the relaxation of magnetic ordering in a parameter regime previously inaccessible due to deep ground-state preparation circuits. Our results demonstrate how the integration of quantum and classical resources can push the boundary of what can be studied on quantum computers.

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Phys. Rev. Research 8, 013081– Published 26 January, 2026
  • Received 28 March 2025
  • Accepted 10 December 2025
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