On the role of coherence for quantum computational advantage

• URL: http://arxiv.org/abs/2410.07024v1
• Date: Wed, 9 Oct 2024 16:06:07 GMT
• Title: On the role of coherence for quantum computational advantage
• Authors: Hugo Thomas, Pierre-Emmanuel Emeriau, Elham Kashefi, Harold Ollivier, Ulysse Chabaud,
• Abstract summary: We introduce path coherence as a measure of the coherent paths interferences arising in a quantum computation. Our results have practical applications for simulating large classes of quantum computations with classical computers.
• Score: 0.5825410941577593
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantifying the resources available to a quantum computer appears to be necessary to separate quantum from classical computation. Among them, entanglement, magic and coherence are arguably of great significance. We introduce path coherence as a measure of the coherent paths interferences arising in a quantum computation. Leveraging the sum-over-paths formalism, we obtain a classical algorithm for estimating quantum transition amplitudes, the complexity of which scales with path coherence. As path coherence relates to the hardness of classical simulation, it provides a new perspective on the role of coherence in quantum computational advantage. Beyond their fundamental significance, our results have practical applications for simulating large classes of quantum computations with classical computers.

Related papers

• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Character Complexity: A Novel Measure for Quantum Circuit Analysis [0.0]
  This paper introduces Character Complexity, a novel measure that bridges Group-theoretic concepts with practical quantum computing concerns. I prove several key properties of character complexity and establish a surprising connection to the classical simulability of quantum circuits. I present innovative visualization methods for character complexity, providing intuitive insights into the structure of quantum circuits.
  arXiv  Detail & Related papers  (2024-08-19T01:58:54Z)
• Evolution of Quantum Resources in Quantum-walk-based Search Algorithm [3.604186493583444]
  We consider the effects of quantum coherence and quantum entanglement for the quantum walk search on the complete bipartite graph. First, we numerically show the complementary relationship between the success probability and the two quantum resources. At last, we discuss the role played by generalized depolarizing noises and find that it would influence the dynamics of success probability and quantum coherence sharply.
  arXiv  Detail & Related papers  (2023-09-30T12:16:28Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• The Quantum Trellis: A classical algorithm for sampling the parton shower with interference effects [9.690748017851927]
  We present a classical algorithm called the quantum trellis to efficiently compute the un-normalized probability density over N-body phase space. This provides a potential path forward for classical computers and a strong baseline for approaches based on quantum computing.
  arXiv  Detail & Related papers  (2021-12-23T19:00:05Z)
• Efficient criteria of quantumness for a large system of qubits [58.720142291102135]
  We discuss the dimensionless combinations of basic parameters of large, partially quantum coherent systems. Based on analytical and numerical calculations, we suggest one such number for a system of qubits undergoing adiabatic evolution.
  arXiv  Detail & Related papers  (2021-08-30T23:50:05Z)
• 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)
• Resource-efficient encoding algorithm for variational bosonic quantum simulations [0.0]
  In the Noisy Intermediate Scale Quantum (NISQ) era of quantum computing, quantum resources are limited. We present a resource-efficient quantum algorithm for bosonic ground and excited state computations.
  arXiv  Detail & Related papers  (2021-02-23T19:00:05Z)
• A general quantum algorithm for open quantum dynamics demonstrated with the Fenna-Matthews-Olson complex [0.0]
  We develop a quantum algorithm to simulate any dynamical process represented by either the operator sum representation or the Lindblad master equation. We demonstrate the quantum algorithm by simulating the dynamics of the Fenna-Matthews-Olson complex on the IBM QASM quantum simulator.
  arXiv  Detail & Related papers  (2021-01-13T19:00:02Z)
• An Application of Quantum Annealing Computing to Seismic Inversion [55.41644538483948]
  We apply a quantum algorithm to a D-Wave quantum annealer to solve a small scale seismic inversions problem. The accuracy achieved by the quantum computer is at least as good as that of the classical computer.
  arXiv  Detail & Related papers  (2020-05-06T14:18:44Z)

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.