State-independent geometric quantum gates via nonadiabatic and noncyclic evolution

• URL: http://arxiv.org/abs/2309.01323v3
• Date: Tue, 20 Feb 2024 05:06:27 GMT
• Title: State-independent geometric quantum gates via nonadiabatic and noncyclic evolution
• Authors: Yue Chen, Li-Na Ji, Zheng-Yuan Xue and Yan Liang
• Abstract summary: We propose a scheme for universal quantum gates with pure nonadiabatic and noncyclic geometric phases from smooth evolution paths. We show that the implemented geometric gates have stronger robustness than dynamical gates and the geometric scheme with cyclic path. These high-trivial quantum gates are promising for large-scale fault-tolerant quantum computation.
• Score: 10.356589142632922
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Geometric phases are robust to local noises and the nonadiabatic ones can reduce the evolution time, thus nonadiabatic geometric gates have strong robustness and can approach high fidelity. However, the advantage of geometric phase has not being fully explored in previous investigations. Here, we propose a scheme for universal quantum gates with pure nonadiabatic and noncyclic geometric phases from smooth evolution paths. In our scheme, only geometric phase can be accumulated in a fast way, and thus it not only fully utilizes the local noise resistant property of geometric phase but also reduces the difficulty in experimental realization. Numerical results show that the implemented geometric gates have stronger robustness than dynamical gates and the geometric scheme with cyclic path. Furthermore, we propose to construct universal quantum gate on superconducting circuits, with the fidelities of single-qubit gate and nontrivial two-qubit gate can achieve $99.97\%$ and $99.87\%$, respectively. Therefore, these high-fidelity quantum gates are promising for large-scale fault-tolerant quantum computation.

Related papers

• Geometric Quantum Machine Learning with Horizontal Quantum Gates [41.912613724593875]
  We propose an alternative paradigm for the symmetry-informed construction of variational quantum circuits. We achieve this by introducing horizontal quantum gates, which only transform the state with respect to the directions to those of the symmetry. For a particular subclass of horizontal gates based on symmetric spaces, we can obtain efficient circuit decompositions for our gates through the KAK theorem.
  arXiv  Detail & Related papers  (2024-06-06T18:04:39Z)
• Geometric Phase of a Transmon in a Dissipative Quantum Circuit [44.99833362998488]
  We study the geometric phases acquired by a paradigmatic setup: a transmon coupled to a superconductor resonating cavity. In the dissipative model, the non-unitary effects arise from dephasing, relaxation, and decay of the transmon coupled to its environment. Our approach enables a comparison of the geometric phases obtained in these models, leading to a thorough understanding of the corrections introduced by the presence of the environment.
  arXiv  Detail & Related papers  (2024-01-22T16:41:00Z)
• Dynamical-Corrected Nonadiabatic Geometric Quantum Computation [9.941657239723108]
  We present an effective geometric scheme combined with a general dynamical-corrected technique. Our scheme represents a promising way to explore large-scale fault-tolerant quantum computation.
  arXiv  Detail & Related papers  (2023-02-08T16:18:09Z)
• Gaussian initializations help deep variational quantum circuits escape from the barren plateau [87.04438831673063]
  Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years. However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number. This result leads to a general belief that deep quantum circuits will not be feasible for practical tasks.
  arXiv  Detail & Related papers  (2022-03-17T15:06:40Z)
• Path-optimized nonadiabatic geometric quantum computation on superconducting qubits [3.98625523260655]
  We propose a path-optimized scheme for geometric quantum computation on superconducting transmon qubits. We find that the constructed geometric gates can be superior to their corresponding dynamical ones under different local errors. Our scheme provides a new perspective for geometric quantum computation, making it more promising in the application of large-scale fault-tolerant quantum computation.
  arXiv  Detail & Related papers  (2021-10-12T15:26:26Z)
• 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)
• Quantum control landscape for ultrafast generation of single-qubit phase shift quantum gates [68.8204255655161]
  We consider the problem of ultrafast controlled generation of single-qubit phase shift quantum gates. Globally optimal control is a control which realizes the gate with maximal possible fidelity. Trap is a control which is optimal only locally but not globally.
  arXiv  Detail & Related papers  (2021-04-26T16:38:43Z)
• Nonadiabatic geometric quantum gates that are insensitive to qubit-frequency drifts [8.750801670077806]
  In the current implementation of nonadiabatic geometric phases, operational and/or random errors tend to destruct the conditions that induce geometric phases. Here, we apply the path-design strategy to explain in detail why both configurations can realize universal quantum gates in a single-loop way. Our scheme provides a promising way towards practical realization of high-fidelity and robust nonadiabatic geometric quantum gates.
  arXiv  Detail & Related papers  (2021-03-16T12:05:45Z)
• Noncyclic Geometric Quantum Gates with Smooth Paths via Invariant-based Shortcuts [4.354697470999286]
  We propose a scheme to realize geometric quantum gates with noncyclic and nonadiabatic evolution via invariant-based shortcuts. Our scheme provides a promising way to realize high-fidelity fault-tolerant quantum gates for scalable quantum computation.
  arXiv  Detail & Related papers  (2021-02-01T15:05:29Z)
• Experimental Realization of Nonadiabatic Holonomic Single-Qubit Quantum Gates with Two Dark Paths in a Trapped Ion [41.36300605844117]
  We show nonadiabatic holonomic single-qubit quantum gates on two dark paths in a trapped $171mathrmYb+$ ion based on four-level systems with resonant drives. We find that nontrivial holonomic two-qubit quantum gates can also be realized within current experimental technologies.
  arXiv  Detail & Related papers  (2021-01-19T06:57:50Z)
• 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.