Creating and manipulating a Laughlin-type $\nu=1/3$ fractional quantum Hall state on a quantum computer with linear depth circuits

• URL: http://arxiv.org/abs/2005.02399v2
• Date: Sat, 7 Nov 2020 18:07:18 GMT
• Title: Creating and manipulating a Laughlin-type $\nu=1/3$ fractional quantum Hall state on a quantum computer with linear depth circuits
• Authors: Armin Rahmani, Kevin J. Sung, Harald Putterman, Pedram Roushan, Pouyan Ghaemi, Zhang Jiang
• Abstract summary: We present an efficient quantum algorithm to generate an equivalent many-body state to Laughlin's $nu=1/3$ fractional quantum Hall state. Our algorithm only uses quantum gates acting on neighboring qubits in a quasi-one-dimensional setting.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Here we present an efficient quantum algorithm to generate an equivalent many-body state to Laughlin's $\nu=1/3$ fractional quantum Hall state on a digitized quantum computer. Our algorithm only uses quantum gates acting on neighboring qubits in a quasi-one-dimensional setting, and its circuit depth is linear in the number of qubits, i.e., the number of Landau orbitals in the second quantized picture. We identify correlation functions that serve as signatures of the Laughlin state and discuss how to obtain them on a quantum computer. We also discuss a generalization of the algorithm for creating quasiparticles in the Laughlin state. This paves the way for several important studies, including quantum simulation of nonequilibrium dynamics and braiding of quasiparticles in quantum Hall states.

Related papers

• QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum Circuits [82.50620782471485]
  QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits. It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness. Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
  arXiv  Detail & Related papers  (2024-01-10T22:33:00Z)
• A vertical gate-defined double quantum dot in a strained germanium double quantum well [48.7576911714538]
  Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation. We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well. We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
  arXiv  Detail & Related papers  (2023-05-23T13:42:36Z)
• Digital Quantum Simulation and Circuit Learning for the Generation of Coherent States [1.4153418423656923]
  Two ways to digitally prepare coherent states in quantum circuits are introduced. The high fidelity of the digitally generated coherent states is verified. The simulation results show that quantum circuit learning can provide high fidelity on learning coherent states by choosing appropriate ansatzes.
  arXiv  Detail & Related papers  (2022-10-30T09:06:21Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• Separation of gates in quantum parallel programming [1.4821822452801385]
  Ying conceived of using two or more small-capacity quantum computers to produce a larger-capacity quantum computing system by quantum parallel programming. Main obstacle is separating the quantum gates in the whole circuit to produce a tensor product of the local gates. We theoretically analyse the (sufficient and necessary) separability conditions of multipartite quantum gates in finite or infinite dimensional systems.
  arXiv  Detail & Related papers  (2021-10-28T09:11:41Z)
• Stochastic emulation of quantum algorithms [0.0]
  We introduce higher-order partial derivatives of a probability distribution of particle positions as a new object that shares basic properties of quantum mechanical states needed for a quantum algorithm. We prove that the propagation via the map built from those universal maps reproduces up to a prefactor exactly the evolution of the quantum mechanical state. We implement several well-known quantum algorithms, analyse the scaling of the needed number of realizations with the number of qubits, and highlight the role of destructive interference for the cost of emulation.
  arXiv  Detail & Related papers  (2021-09-16T07:54:31Z)
• Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
  Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems. We propose an algorithm to implement imaginary time propagation on a quantum computer.
  arXiv  Detail & Related papers  (2021-02-24T12:48:00Z)
• Quantum walk processes in quantum devices [55.41644538483948]
  We study how to represent quantum walk on a graph as a quantum circuit. Our approach paves way for the efficient implementation of quantum walks algorithms on quantum computers.
  arXiv  Detail & Related papers  (2020-12-28T18:04:16Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)
• Roadmap for quantum simulation of the fractional quantum Hall effect [0.0]
  A major motivation for building a quantum computer is that it provides a tool to efficiently simulate strongly correlated quantum systems. In this work, we present a detailed roadmap on how to simulate a two-dimensional electron gas---cooled to absolute zero and pierced by a strong magnetic field---on a quantum computer.
  arXiv  Detail & Related papers  (2020-03-05T10:17:21Z)

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.