Quantifying nonstabilizerness through entanglement spectrum flatness

Tirrito, Emanuele; Tarabunga, Poetri Sonya; Lami, Gugliemo; Chanda, Titas; Leone, Lorenzo; Oliviero, Salvatore F. E.; Dalmonte, Marcello; Collura, Mario; Hamma, Alioscia

doi:10.1103/physreva.109.l040401

Cited by 14 publications

(1 citation statement)

References 64 publications

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“…Properties of the dynamics of participation entropies under higher dimensional circuits are another unresolved problem. Moreover, stabilizer Rényi entropies [ 103 , 104 , 105 , 106 , 107 ], which determine the number of beyond-classical (non-Clifford) operations needed to perform a quantum task, are related to participation entropies [ 83 ]. The long-time limit of stabilizer Rényi entropies under local unitary dynamics has been recently understood [ 108 ].…”

Section: Discussion and Conclusionmentioning

confidence: 99%

Hilbert Space Delocalization under Random Unitary Circuits

Turkeshi,

Sierant

2024

Entropy

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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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Section: Discussion and Conclusionmentioning

confidence: 99%

Hilbert Space Delocalization under Random Unitary Circuits

Turkeshi,

Sierant

2024

Entropy

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Quantifying magic resource via quantum Jensen–Shannon divergence

Tian,

Sun

2024

J. Phys. A: Math. Theor.

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Magic is a precious resource necessary for achieving universal fault-tolerant quantum computation. Therefore, it is of vital importance to study the detection and quantification of the magic resource encompassed in quantum states and quantum gates both theoretically and experimentally. In this work, we adopt the quantum Jensen-Shannon divergence to quantify the magic resource of quantum states and quantum gates. On the one hand, we determine the magic resource of a pure state as the minimal and average distance between this state and the set of pure stabilizer states via the quantum Jensen-Shannon divergence, respectively, and extend them to the general mixed states through the method of convex roof construction. We investigate the basic properties of these two magic quantifiers and utilize them to evaluate the magic resource for some typical qubit and qutrit states. By comparing the magic quantifier via the quantum Jensen-Shannon divergence with the min-relative entropy of magic and the stabilizer α-Rényi entropies, we find that the min-relative entropy of magic provides both an upper bound and a lower bound for the magic quantifier via the quantum Jensen-Shannon divergence, and the stabilizer α-Rényi entropies provide a series of lower bounds for the magic quantifier via the quantum Jensen-Shannon divergence. On the other hand, based on the magic quantifier via the quantum Jensen-Shannon divergence for quantum states, we further propose two quantifiers for the magic-resource-generating power of quantum gates and demonstrate that the T-gate is the optimal diagonal unitary gate in creating magic resource for both qubit and qutrit systems in the sense of Clifford equivalence.

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