Quantum Dissipative Search via Lindbladians

• URL: http://arxiv.org/abs/2407.11782v2
• Date: Mon, 18 Nov 2024 12:21:11 GMT
• Title: Quantum Dissipative Search via Lindbladians
• Authors: Peter J. Eder, Jernej Rudi Finžgar, Sarah Braun, Christian B. Mendl,
• Abstract summary: We analyze a purely dissipative quantum random walk on an unstructured classical search space. We show that certain jump operators make the quantum process replicate a classical one, while others yield differences between open quantum (OQRW) and classical random walks. We also clarify a previously observed quadratic speedup, demonstrating that OQRWs are no more efficient than classical search.
• Score: 0.0
• License:
• Abstract: Closed quantum systems follow a unitary time evolution that can be simulated on quantum computers. By incorporating non-unitary effects via, e.g., measurements on ancilla qubits, these algorithms can be extended to open-system dynamics, such as Markovian processes described by the Lindblad master equation. In this paper, we analyze the convergence criteria and speed of a Markovian, purely dissipative quantum random walk on an unstructured classical search space. Notably, we show that certain jump operators make the quantum process replicate a classical one, while others yield differences between open quantum (OQRW) and classical random walks. We also clarify a previously observed quadratic speedup, demonstrating that OQRWs are no more efficient than classical search. Finally, we analyze a dissipative discrete-time ground-state preparation algorithm with a lower implementation cost. This allows us to interpolate between the dissipative and the unitary domain and thereby illustrate the important role of coherence for the quadratic speedup.

Related papers

• An Exponential Separation Between Quantum and Quantum-Inspired Classical Algorithms for Machine Learning [14.955338558971787]
  A provable exponential quantum speedup has been a central research goal since the seminal HHL quantum algorithm for solving linear systems. We present the first such provable exponential separation between quantum and quantum-inspired classical algorithms.
  arXiv  Detail & Related papers  (2024-11-04T13:49:26Z)
• Efficient Quantum Pseudorandomness from Hamiltonian Phase States [41.94295877935867]
  We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem. We show that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We show that our assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives.
  arXiv  Detail & Related papers  (2024-10-10T16:10:10Z)
• Hybrid quantum gap estimation algorithm using a filtered time series [0.0]
  We prove that classical post-processing, i.e., long-time filtering of an offline time series, exponentially improves the circuit depth needed for quantum time evolution. We apply the filtering method to the construction of a hybrid quantum-classical algorithm to estimate energy gap. Our findings set the stage for unbiased quantum simulation to offer memory advantage in the near term.
  arXiv  Detail & Related papers  (2022-12-28T18:59:59Z)
• Classical simulation of short-time quantum dynamics [0.0]
  We present classical algorithms for approximating the dynamics of local observables and nonlocal quantities. We establish a novel quantum speed limit, a bound on dynamical phase transitions, and a concentration bound for product states evolved for short times.
  arXiv  Detail & Related papers  (2022-10-20T18:00:04Z)
• Anticipative measurements in hybrid quantum-classical computation [68.8204255655161]
  We present an approach where the quantum computation is supplemented by a classical result. Taking advantage of its anticipation also leads to a new type of quantum measurements, which we call anticipative. In an anticipative quantum measurement the combination of the results from classical and quantum computations happens only in the end.
  arXiv  Detail & Related papers  (2022-09-12T15:47:44Z)
• 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)
• Interactive Protocols for Classically-Verifiable Quantum Advantage [46.093185827838035]
  "Interactions" between a prover and a verifier can bridge the gap between verifiability and implementation. We demonstrate the first implementation of an interactive quantum advantage protocol, using an ion trap quantum computer.
  arXiv  Detail & Related papers  (2021-12-09T19:00:00Z)
• 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)
• Sampling, rates, and reaction currents through reverse stochastic quantization on quantum computers [0.0]
  We show how to tackle the problem using a suitably quantum computer. We propose a hybrid quantum-classical sampling scheme to escape local minima.
  arXiv  Detail & Related papers  (2021-08-25T18:04:52Z)
• Quantum algorithms for quantum dynamics: A performance study on the spin-boson model [68.8204255655161]
  Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator. variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware. We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
  arXiv  Detail & Related papers  (2021-08-09T18:00:05Z)
• Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
  We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
  arXiv  Detail & Related papers  (2021-01-21T22:18:49Z)

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.