Measuring nonstabilizerness via multifractal flatness

Turkeshi, Xhek; Schirò, Marco; Sierant, Piotr

doi:10.1103/physreva.108.042408

Cited by 14 publications

(6 citation statements)

References 90 publications

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“…The lack of recovery of the OTOC signals a non-Clifford and entangling random quantum circuit dynamics in particular (and non-integrable dynamics in general), as stated in [62] and shown by numerical simulations of reference [63, figure 7, p 29]. As a side note, intriguingly, entanglement and non-stabilizerness are not entirely uncorrelated properties, as it has recently been shown that the flatness of the entanglement spectrum [73,74] can be used to certify non-stabilizerness of quantum states.…”

Section: Scrambling and Quantum Chaosmentioning

confidence: 87%

Non-stabilizerness and entanglement from cat-state injection

Peres,

Wagner,

Galvão

2024

New J. Phys.

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Recently, cat states have been used to heuristically improve the runtime of a classical simulator of quantum circuits based on the diagrammatic ZX-calculus. Here we investigate the use of cat-state injection within the quantum circuit model. We explore a family of cat states, $\left| \mathrm{cat}_m^* \right>$, and describe circuit gadgets using them to concurrently inject non-stabilizerness (also known as magic) and entanglement into any quantum circuit. We provide numerical evidence that cat-state injection does not lead to speed-up in classical simulation. On the other hand, we show that our gadgets can be used to widen the scope of compelling applications of cat states. Specifically, we show how to leverage them to achieve savings in the number of injected qubits, and also to induce scrambling dynamics in otherwise non-entangling Clifford circuits in a controlled manner.

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Section: Scrambling and Quantum Chaosmentioning

confidence: 87%

Non-stabilizerness and entanglement from cat-state injection

Peres,

Wagner,

Galvão

2024

New J. Phys.

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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]. Specifically, the algorithm introduced in [48] is an efficient method for measuring Tsallis stabilizer entropy which has a direct relation to stabilizer Renyi entropy.…”

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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“…Nevertheless, due to the invariance of the considered circuits under local basis rotations, our results remain valid for any basis of

obtained by a unitary transformation

of the computational basis, where

belongs to the unitary group

for a single qudit. For the computational basis,

, which defines the “book” boundary condition for each qudit [ 83 , 84 ]:

where the superscript in

bookkeeps the number of the affected qudit. For later convenience, we recast the problem in the superoperator formalism.…”

Section: Methodsmentioning

confidence: 99%

“…We begin our discussion by reviewing the Hilbert space delocalization of random states [ 21 , 83 ] which correspond to the stationary ensemble of states obtained under the action of sufficiently deep random circuits. Uniformly distributed random states in the Hilbert space

are obtained from a reference state

via a unitary operation U acting globally on the system of N qudits, drawn with the Haar measure from the N qudit unitary group

, where d is the qudit local Hilbert space dimension.…”

Section: Delocalization Properties Of Random Haar Statesmentioning

confidence: 99%

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Hilbert Space Delocalization under Random Unitary Circuits

Turkeshi,

Sierant

2024

Entropy

Self Cite

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The unitary dynamics of a quantum system initialized in a selected basis state yield, generically, a state that is a superposition of all the basis states. This process, associated with the quantum information scrambling and intimately tied to the resource theory of coherence, may be viewed as a gradual delocalization of the system’s state in the Hilbert space. This work analyzes the Hilbert space delocalization under the dynamics of random quantum circuits, which serve as a minimal model of the chaotic dynamics of quantum many-body systems. We employ analytical methods based on the replica trick and Weingarten calculus to investigate the time evolution of the participation entropies which quantify the Hilbert space delocalization. We demonstrate that the participation entropies approach, up to a fixed accuracy, their long-time saturation value in times that scale logarithmically with the system size. Exact numerical simulations and tensor network techniques corroborate our findings.

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Measuring nonstabilizerness via multifractal flatness

Cited by 14 publications

References 90 publications

Non-stabilizerness and entanglement from cat-state injection

Non-stabilizerness and entanglement from cat-state injection

Quantifying non-stabilizerness via information scrambling

Hilbert Space Delocalization under Random Unitary Circuits

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