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arXiv:2606.12056 · Journal of Chemical Theory and Computation

Clifford disentanglers for entanglement reduction in molecular electronic structure simulations

Longfei Chang, Zibo Wu, Yunzhi Li, Haiqi Liu, Jiajun Ren, Mingpu Qin, Zhendong Li, Wei-Hai Fang

quant-phSubmitted Jun 10, 2026• Announced Jun 11, 2026• 0 citations
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Abstract

Entanglement is a key bottleneck limiting the efficiency of tensor-network and quantum simulations of molecular electronic structures. Here, we systematically assess and extend Clifford disentanglers as a structure-preserving approach to entanglement reduction: they can modify the entanglement structure of qubit wavefunctions while retaining the Pauli-string form of qubit Hamiltonians. To enable a practical search over Clifford transformations, we classify Clifford operators by their action on the Schmidt spectrum across a bipartition, reducing the two- and four-qubit search spaces to 20 and 91392 representatives, respectively. Embedded in an iterative Clifford-augmented matrix product state framework, these transformations reduce the energy errors at fixed bond dimension for the molecular test cases studied and mitigate the dependence on orbital orderings and fermion-to-qubit mappings. We further show that Clifford disentanglers can also benefit quantum simulations such as the shallow-circuit variational quantum eigensolver calculations. Together, these results establish Clifford disentanglers as a useful structure-preserving entanglement-engineering tool for tensor-network and quantum simulations of molecular electronic structure, while also clarifying their correlation dependence and motivating future developments.

Comments
18 pages, 11 figures

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Entanglement is a key bottleneck limiting the efficiency of tensor-network and quantum simulations of molecular electronic structures. Here, we systematically assess and extend Clifford disentanglers as a structure-preserving approach to entanglement reduction: they can modify the entanglement structure of qubit wavefunctions while retaining the Pauli-string form of qubit Hamiltonians. To enable a practical search over Clifford transformations, we classify Clifford operators by their action on the Schmidt spectrum across a bipartition, reducing the two- and four-qubit search spaces to 20 and 91392 representatives, respectively. Embedded in an iterative Clifford-augmented matrix product state framework, these transformations reduce the energy errors at fixed bond dimension for the molecular test cases studied and mitigate the dependence on orbital orderings and fermion-to-qubit mappings. We further show that Clifford disentanglers can also benefit quantum simulations such as the shallow-circuit variational quantum eigensolver calculations. Together, these results establish Clifford disentanglers as a useful structure-preserving entanglement-engineering tool for tensor-network and quantum simulations of molecular electronic structure, while also clarifying their correlation dependence and motivating future developments.
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Recently (Physica Scripta, 100(10):105401, 2025), an algorithm was introduced that deterministically generates a Clifford transformation from the Qubit Coupled Cluster (QCC) algorithm which we call Q-Cliff (QCC+Clifford). There, it was shown that Q-Cliff could be utilized to generate a hardware efficient version of the QCC ansatz. Here, we examine and refine these techniques and show that Q-Cliff can be utilized to generate efficient classical and quantum approximations to the ground states of chemical systems. The algorithm generates an efficient variational method that generally has accuracy between MP2 and CISD with O(N6)O(N^6)O(N6). Furthermore, we show through DMRG calculations that the entanglement between qubits is reduced significantly and therefore the accuracy for a given bond dimension can be vastly improved (up to an order of magnitude). Finally, we refine the previously reported algorithm to generate low-depth and CNOT efficient circuits that can be optimized with a comparable number of energy evaluations to state-of-the-art VQE algorithms. All these results show that this Hamiltonian derived Clifford transformation should be a tool used for many classical and quantum algorithms.
Determining the quantum-classical boundary between quantum circuits that can be efficiently simulated classically and those that cannot remains a fundamental question. One approach to classical simulation is to represent the output of a quantum circuit as a Clifford-augmented matrix product state (CAMPS), which, via a disentangling algorithm, decomposes the wave function into Clifford and MPS components, and from which Pauli expectation values can be computed in time polynomial in the MPS bond dimension. In this work, we develop an optimization-free disentangling (OFD) algorithm for Clifford circuits either doped with T gates or, equivalently, preceded by multiqubit gates of the form α I + β P . We give a simple and easily computed algebraic criterion that characterizes the individual quantum circuits for which OFD generates an efficient CAMPS—the bond dimension is exponential in the null space of a Galois binary field GF(2) matrix induced by a tableau of the twisted Pauli strings P . This significantly increases the number of circuits with rigorous polynomial-time classical simulations. We also give evidence that the typical N qubit random Clifford circuit doped with N uniformly distributed T gates of polylogarithmic depth or greater has a CAMPS with polynomial bond dimension. In addition, we compare OFD against disentangling by optimization. We further explore the representability of CAMPS for random Clifford circuits doped with more than N T gates. We also propose algorithms for sampling, probability, and amplitude estimation of bitstrings, and evaluation of entanglement Rényi entropy from CAMPS, which, though still having exponential complexity, are more efficient than standard MPS simulations. This work establishes a versatile framework for understanding classical simulatability of Clifford + T circuits and explores the interplay between quantum entanglement and quantum magic in quantum systems.