Non-adiabatic holonomic quantum operations in continuous variable systems

• URL: http://arxiv.org/abs/2402.02373v3
• Date: Tue, 21 May 2024 03:21:19 GMT
• Title: Non-adiabatic holonomic quantum operations in continuous variable systems
• Authors: Hao-Long Zhang, Yi-Hao Kang, Fan Wu, Zhen-Biao Yang, Shi-Biao Zheng,
• Abstract summary: Quantum operations by utilizing the underlying geometric phases produced in physical systems are favoured due to its potential robustness. Here we propose a feasible scheme to realize non-adiabatic holonomic quantum logic operations in continuous variable systems with cat codes.
• Score: 2.4060220973816144
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum operations by utilizing the underlying geometric phases produced in physical systems are favoured due to its potential robustness. When a system in a non-degenerate eigenstate undergoes an adiabatically cyclic evolution dominated by its Hamiltonian, it will get a geometric phase, referred to as the Berry Phase. While a non-adiabatically cyclic evolution produces an Aharonov-Anandan geometric phase. The two types of Abelian geometric phases are extended to the non-Abelian cases, where the phase factors become matrix-valued and the transformations associated with different loops are non-commutable. Abelian and non-Abelian (holonomic) operations are prevalent in discrete variable systems, whose limited (say, two) energy levels, form the qubit. While their developments in continuous systems have also been investigated, mainly due to that, bosonic modes (in, such as, cat states) with large Hilbert spaces, provide potential advantages in fault-tolerant quantum computation. Here we propose a feasible scheme to realize non-adiabatic holonomic quantum logic operations in continuous variable systems with cat codes. We construct arbitrary single-qubit (two-qubit) gates with the combination of single- and two-photon drivings applied to a Kerr Parametric Oscillator (KPO) (the coupled KPOs). Our scheme relaxes the requirements of the previously proposed quantum geometric operation strategies in continuous variable systems, providing an effective way for quantum control.

Related papers

• Dynamics of a Nonequilibrium Discontinuous Quantum Phase Transition in a Spinor Bose-Einstein Condensate [0.0]
  We show that critical scaling behavior in a first-order quantum phase transition can be understood from generic properties. We predict the onset of the decay of the metastable state on short times scales and the number of resulting phase-separated ferromagnetic domains at longer times.
  arXiv  Detail & Related papers  (2023-12-27T12:39:23Z)
• Quantum Gate Generation in Two-Level Open Quantum Systems by Coherent and Incoherent Photons Found with Gradient Search [77.34726150561087]
  We consider an environment formed by incoherent photons as a resource for controlling open quantum systems via an incoherent control. We exploit a coherent control in the Hamiltonian and an incoherent control in the dissipator which induces the time-dependent decoherence rates.
  arXiv  Detail & Related papers  (2023-02-28T07:36:02Z)
• 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)
• Geometric phases along quantum trajectories [58.720142291102135]
  We study the distribution function of geometric phases in monitored quantum systems. For the single trajectory exhibiting no quantum jumps, a topological transition in the phase acquired after a cycle. For the same parameters, the density matrix does not show any interference.
  arXiv  Detail & Related papers  (2023-01-10T22:05:18Z)
• On optimization of coherent and incoherent controls for two-level quantum systems [77.34726150561087]
  This article considers some control problems for closed and open two-level quantum systems. The closed system's dynamics is governed by the Schr"odinger equation with coherent control. The open system's dynamics is governed by the Gorini-Kossakowski-Sudarshan-Lindblad master equation.
  arXiv  Detail & Related papers  (2022-05-05T09:08:03Z)
• Chaos in coupled Kerr-nonlinear parametric oscillators [0.0]
  We investigate complex dynamics, i.e., chaos, in two coupled nondissipative KPOs at a few-photon level. We conclude that some of them can be regarded as quantum signatures of chaos, together with energy-level spacing statistics.
  arXiv  Detail & Related papers  (2021-10-08T10:35:12Z)
• Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
  Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. We present an algorithm that compresses the Trotter steps into a single block of quantum gates. This results in a fixed depth time evolution for certain classes of Hamiltonians.
  arXiv  Detail & Related papers  (2021-08-06T19:38:01Z)
• Geometrical Rabi oscillations and Landau-Zener transitions in non-Abelian systems [0.0]
  We propose universal protocols to determine quantum geometric properties in non-Abelian systems. Our schemes suggest a way to prepare eigenstates of the quantum metric.
  arXiv  Detail & Related papers  (2021-05-06T14:09:52Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Approach to realizing nonadiabatic geometric gates with prescribed evolution paths [0.0]
  Nonadiabatic geometric phases are robust against control errors. Quantum computation based on nonadiabatic geometric phases is robust against control errors.
  arXiv  Detail & Related papers  (2020-06-06T10:37:18Z)

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.