Augmenting Density Matrix Renormalization Group with Clifford Circuits

Abstract

Density Matrix Renormalization Group (DMRG) or Matrix Product States (MPS) are widely acknowledged as highly effective and accurate methods for solving one-dimensional quantum many-body systems. However, the direct application of DMRG to the study two-dimensional systems encounters challenges due to the limited entanglement encoded in the wave-function ansatz. Conversely, Clifford circuits offer a promising avenue for simulating states with substantial entanglement, albeit confined to stabilizer states. In this work, we present the seamless integration of Clifford circuits within the DMRG algorithm, leveraging the advantages of both Clifford circuits and DMRG. This integration leads to a significant enhancement in simulation accuracy with small additional computational cost. Moreover, this framework is useful not only for its current application but also for its potential to be easily adapted to various other numerical approaches

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• Stabilizer Rényi Entropy and Conformal Field Theory
• Bridging Entanglement and Magic Resources within Operator Space
• A nonstabilizerness monotone from stabilizerness asymmetry
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• Fermionic Magic Resources of Quantum Many-Body Systems
• Disentangling magic states with classically simulable quantum circuits
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• Designs from magic-augmented Clifford circuits
• Stabilizer-Accelerated Quantum Many-Body Ground-State Estimation
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• Clifford-Dressed Variational Principles for Precise Loschmidt Echoes
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• Clifford Transformations for Fermionic Quantum Systems: From Paulis to Majoranas to Fermions
• GCAMPS: A Scalable Classical Simulator for Qudit Systems
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