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Quantum Magic via Perfect Pauli Sampling of Matrix Product States

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arxiv 2303.05536 v2 pith:RS3FKBD6 submitted 2023-03-09 quant-ph

Guglielmo Lami , Mario Collura This is my paper · ORCID
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keywords quantumsamplingsresachievedmagicmatrixnovelpauli
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abstract

We introduce a novel breakthrough approach to evaluate the nonstabilizerness of an $N$-qubits Matrix Product State (MPS) with bond dimension $\chi$. In particular, we consider the recently introduced Stabilizer R\'enyi Entropies (SREs). We show that the exponentially hard evaluation of the SREs can be achieved by means of a simple perfect sampling of the many-body wave function over the Pauli string configurations. The sampling is achieved with a novel MPS technique, which enables to compute each sample in an efficient way with a computational cost $O(N\chi^3)$. We benchmark our method over randomly generated magic states, as well as in the ground-state of the quantum Ising chain. Exploiting the extremely favourable scaling, we easily have access to the non-equilibrium dynamics of the SREs after a quantum quench.

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Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Magic without a phase: phase-independent stabilizer R\'enyi entropy in gluon scattering

    hep-th 2026-07 conditional novelty 7.0 of 10

    A phase-averaged stabilizer Rényi entropy is introduced for tree-level gluon scattering, with color-independent phase-independent magic that is larger in 3→2 than 2→2 and has a soft-limit lower bound in 2→3.

  2. Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors

    quant-ph 2026-01 conditional novelty 7.0 of 10

    For chaotic all-to-all systems, the stabilizer Rényi entropy of thermofield double states is set by the spectral form factor and saturates through a first-order dynamical transition.

  3. Pauli Spectrum and Stabilizer R\'enyi Entropy in Gapless Symmetry-Protected Topological Phases

    cond-mat.str-el 2026-07 conditional novelty 6.0 of 10

    Stabilizer Rényi entropy signals SPT transitions via extrema, but Pauli-spectrum crossings of string-order operators distinguish the phases via local-unitary or non-invertible dualities.

  4. Sampling two-dimensional isometric tensor network states

    quant-ph 2026-02 conditional novelty 6.0 of 10

    Sampling from 2D isometric tensor network states is made efficient by a row-wise QR sweep and MPO-MPS contraction, with single-sample and top-K variants.

  5. Quantum Non-Local Nonstabilizerness

    quant-ph 2025-02 conditional novelty 6.0 of 10

    Non-local nonstabilizerness is exactly computable for two-qubit pure states and shows power-law scaling and a measurement-induced 'nonstabilizerness swapping' effect in critical systems.

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