Amortized Stabilizer Rényi Entropy of Quantum Dynamics

• URL: http://arxiv.org/abs/2409.06659v1
• Date: Tue, 10 Sep 2024 17:23:05 GMT
• Title: Amortized Stabilizer Rényi Entropy of Quantum Dynamics
• Authors: Chengkai Zhu, Yu-Ao Chen, Zanqiu Shen, Zhiping Liu, Zhan Yu, Xin Wang,
• Abstract summary: We introduce the amortized $alpha$-stabilizer R'enyi entropy, a magic monotone for unitary operations that quantifies the nonstabilizerness generation capability of quantum dynamics. We demonstrate the versatility of the amortized $alpha$-stabilizer R'enyi entropy in investigating the nonstabilizerness resources of quantum dynamics of computational and fundamental interest.
• Score: 7.064711321804743
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Unraveling the secrets of how much nonstabilizerness a quantum dynamic can generate is crucial for harnessing the power of magic states, the essential resources for achieving quantum advantage and realizing fault-tolerant quantum computation. In this work, we introduce the amortized $\alpha$-stabilizer R\'enyi entropy, a magic monotone for unitary operations that quantifies the nonstabilizerness generation capability of quantum dynamics. Amortization is key in quantifying the magic of quantum dynamics, as we reveal that nonstabilizerness generation can be enhanced by prior nonstabilizerness in input states when considering the $\alpha$-stabilizer R\'enyi entropy, while this is not the case for robustness of magic or stabilizer extent. We demonstrate the versatility of the amortized $\alpha$-stabilizer R\'enyi entropy in investigating the nonstabilizerness resources of quantum dynamics of computational and fundamental interest. In particular, we establish improved lower bounds on the $T$-count of quantum Fourier transforms and the quantum evolutions of one-dimensional Heisenberg Hamiltonians, showcasing the power of this tool in studying quantum advantages and the corresponding cost in fault-tolerant quantum computation.

Related papers

• Mutual information fluctuations and non-stabilizerness in random circuits [0.48212500317840945]
  We show a simple relationship between non-stabilizerness and information scrambling. We explore the role of non-stabilizerness in measurement-induced entanglement phase transitions.
  arXiv  Detail & Related papers  (2024-08-07T15:15:41Z)
• Quantum coarsening and collective dynamics on a programmable quantum simulator [27.84599956781646]
  We experimentally study collective dynamics across a (2+1)D Ising quantum phase transition. By deterministically preparing and following the evolution of ordered domains, we show that the coarsening is driven by the curvature of domain boundaries. We quantitatively explore these phenomena and further observe long-lived oscillations of the order parameter, corresponding to an amplitude (Higgs) mode.
  arXiv  Detail & Related papers  (2024-07-03T16:29:12Z)
• Non-stabilizerness in kinetically-constrained Rydberg atom arrays [0.11060425537315084]
  We show that Rydberg atom arrays provide a natural reservoir of non-stabilizerness that extends beyond single qubits. We explain the origin of Rydberg nonstabilizerness via a quantum circuit decomposition of the wave function.
  arXiv  Detail & Related papers  (2024-06-20T14:17:34Z)
• Hysteresis and Self-Oscillations in an Artificial Memristive Quantum Neuron [79.16635054977068]
  We study an artificial neuron circuit containing a quantum memristor in the presence of relaxation and dephasing. We demonstrate that this physical principle enables hysteretic behavior of the current-voltage characteristics of the quantum device.
  arXiv  Detail & Related papers  (2024-05-01T16:47:23Z)
• Enhancement of non-Stabilizerness within Indefinite Causal Order [6.612068248407539]
  The quantum SWITCH allows quantum states to pass through operations in a superposition of different orders, outperforming traditional circuits in numerous tasks. We find that the completely stabilizer-preserving operations, which cannot generate magic states under standard conditions, can be transformed to do so when processed by the quantum SWITCH. These findings reveal the unique properties of the quantum SWITCH and open avenues in research on nonstabilizer resources of general quantum architecture.
  arXiv  Detail & Related papers  (2023-11-27T02:35:48Z)
• Variational quantum simulation using non-Gaussian continuous-variable systems [39.58317527488534]
  We present a continuous-variable variational quantum eigensolver compatible with state-of-the-art photonic technology. The framework we introduce allows us to compare discrete and continuous variable systems without introducing a truncation of the Hilbert space.
  arXiv  Detail & Related papers  (2023-10-24T15:20:07Z)
• Critical behaviors of non-stabilizerness in quantum spin chains [0.0]
  Non-stabilizerness measures the extent to which a quantum state deviates from stabilizer states. In this work, we investigate the behavior of non-stabilizerness around criticality in quantum spin chains.
  arXiv  Detail & Related papers  (2023-09-01T18:00:04Z)
• Measuring nonstabilizerness via multifractal flatness [0.0]
  Universal quantum computing requires nonstabilizer (magic) quantum states. We prove that a quantum state is a stabilizer if and only if all states belonging to its Clifford orbit have a flat probability distribution. We show that the multifractal flatness provides an experimentally and computationally viable nonstabilizerness certification.
  arXiv  Detail & Related papers  (2023-05-19T16:32:59Z)
• Learning in quantum games [41.67943127631515]
  We show that the induced quantum state dynamics decompose into (i) a classical, commutative component which governs the dynamics of the system's eigenvalues. We find that the FTQL dynamics incur no more than constant regret in all quantum games.
  arXiv  Detail & Related papers  (2023-02-05T08:23:04Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.