Quantifying nonstabilizerness of matrix product states

Haug, Tobias; Piroli, Lorenzo

doi:10.1103/physrevb.107.035148

Cited by 25 publications

(4 citation statements)

References 60 publications

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“…Interesting research direction going forward is to combine our sampling approach with experiment [30] or approximate numerical methods such as tensor networks [32,46] and neural networks [33]. Our method can be used alongside or as a complement to other existing approximation methods [47][48][49][50][51][52].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Quantifying non-stabilizerness via information scrambling

Ahmadi,

Greplova

2024

SciPost Phys.

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The advent of quantum technologies brought forward much attention to the theoretical characterization of the computational resources they provide. A method to quantify quantum resources is to use a class of functions called magic monotones and stabilizer entropies, which are, however, notoriously hard and impractical to evaluate for large system sizes. In recent studies, a fundamental connection between information scrambling, the magic monotone mana and 2-Renyi stabilizer entropy was established. This connection simplified magic monotone calculation, but this class of methods still suffers from exponential scaling with respect to the number of qubits. In this work, we establish a way to sample an out-of-time-order correlator that approximates magic monotones and 2-Renyi stabilizer entropy. We numerically show the relation of these sampled correlators to different non-stabilizerness measures for both qubit and qutrit systems and provide an analytical relation to 2-Renyi stabilizer entropy. Furthermore, we put forward and simulate a protocol to measure the monotonic behaviour of magic for the time evolution of local Hamiltonians.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Quantifying non-stabilizerness via information scrambling

Ahmadi,

Greplova

2024

SciPost Phys.

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“…This feature can also be connected to MPS representations. States that can be represented as translational invariant MPSs, such as the ground state of the unfrustrated Ising model, have extensive SRE [39]. In contrast, the W -state has no efficient representation a translational invariant MPS [13,66], thus a violation of the extensive property of SRE is possible.…”

Section: Analysis Of Some Topologically Frustrated Modelsmentioning

confidence: 99%

“…This picture fails at the quantum critical point, where the correlation length diverges [43,44], and the entanglement shows a logarithmic violation of the area law. Here, the local approximation fails with a large offset error due to entanglement and magic getting a diverging logarithmic correction [39] which cannot be captured by local measures. Therefore, one has to consider very large blocks to get a reasonable approximation of the exact result.…”

Section: Introductionmentioning

confidence: 99%

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Complexity of frustration: A new source of non-local non-stabilizerness

Odavić,

Haug,

Torre

et al. 2023

SciPost Phys.

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We advance the characterization of complexity in quantum many-body systems by examining WW-states embedded in a spin chain. Such states show an amount of non-stabilizerness or “magic”, measured as the Stabilizer Rényi Entropy, that grows logarithmically with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into a WW-state, while in the rest of the phase to which the classical point belongs, it is dressed with local quantum correlations. Topological frustrated quantum spin-chains host phases with the desired phenomenology, and we show that their ground state’s Stabilizer Rényi Entropy is the sum of that of the WW-states plus an extensive local contribution. Our work reveals that WW-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource and has no counterpart in GHZ states/non-frustrated systems.

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