Quantum simulation of single-server Markovian queues: A dynamic amplification approach

• URL: http://arxiv.org/abs/2410.08252v1
• Date: Thu, 10 Oct 2024 15:55:17 GMT
• Title: Quantum simulation of single-server Markovian queues: A dynamic amplification approach
• Authors: Michal Koren, Or Peretz,
• Abstract summary: This study presents a quantum method for simulating single-server Markovian (M/M/1) queues. We introduce a dynamic amplification approach that adapts to queue traffic, potentially improving simulation efficiency. Our quantum method shows potential advantages over classical simulations, particularly in high-traffic scenarios.
• Score: 1.2277343096128712
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum computing is revolutionizing various fields, including operations research and queueing theory. This study presents a quantum method for simulating single-server Markovian (M/M/1) queues, making quantum computing more accessible to researchers in operations research. We introduce a dynamic amplification approach that adapts to queue traffic, potentially improving simulation efficiency, and design custom-parameterized quantum gates for arrival and service processes. This flexible framework enables modeling of various queueing scenarios while bridging quantum computing and classical queueing theory. Notably, our quantum method shows potential advantages over classical simulations, particularly in high-traffic scenarios. This quantum simulation approach opens new possibilities for analyzing complex queueing systems, potentially outperforming classical methods in challenging scenarios and paving the way for quantum-enhanced operations research. The method was implemented and tested across low-, moderate-, and high-traffic scenarios, comparing quantum simulations with both theoretical formulas and classical simulations. Results demonstrate high agreement between quantum computations and theoretical predictions, with relative errors below 0.002 for effective arrival rates in high-traffic scenarios. As the number of qubits increases, we observe rapid convergence to theoretical values, with relative errors decreasing by up to two orders of magnitude in some cases. Sensitivity analysis reveals optimal parameter regions yielding errors lower than 0.001.

Related papers

• Leveraging Pre-Trained Neural Networks to Enhance Machine Learning with Variational Quantum Circuits [48.33631905972908]
  We introduce an innovative approach that utilizes pre-trained neural networks to enhance Variational Quantum Circuits (VQC) This technique effectively separates approximation error from qubit count and removes the need for restrictive conditions. Our results extend to applications such as human genome analysis, demonstrating the broad applicability of our approach.
  arXiv  Detail & Related papers  (2024-11-13T12:03:39Z)
• Scalable Quantum Simulations of Scattering in Scalar Field Theory on 120 Qubits [0.0]
  Simulations of collisions of fundamental particles on a quantum computer are expected to have an exponential advantage over classical methods. In this paper, scattering of wavepackets in one-dimensional scalar field theory is simulated using 120 qubits of IBM's Heron superconducting quantum computer ibm_fez. A new strategy is introduced to mitigate errors in quantum simulations, which enables the extraction of meaningful results from circuits with up to 4924 two-qubit gates and two-qubit gate depths of 103.
  arXiv  Detail & Related papers  (2024-11-04T19:00:00Z)
• 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)
• Lower bound for simulation cost of open quantum systems: Lipschitz continuity approach [5.193557673127421]
  We present a general framework to calculate the lower bound for simulating a broad class of quantum Markov semigroups. Our framework can be applied to both unital and non-unital quantum dynamics.
  arXiv  Detail & Related papers  (2024-07-22T03:57:41Z)
• Quantum Tunneling: From Theory to Error-Mitigated Quantum Simulation [49.1574468325115]
  This study presents the theoretical background and the hardware aware circuit implementation of a quantum tunneling simulation. We use error mitigation techniques (ZNE and REM) and multiprogramming of the quantum chip for solving the hardware under-utilization problem.
  arXiv  Detail & Related papers  (2024-04-10T14:27:07Z)
• A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity [50.387179833629254]
  We introduce a collaborative classical-quantum architecture called co-TenQu. Co-TenQu enhances a classical deep neural network by up to 41.72% in a fair setting. It outperforms other quantum-based methods by up to 1.9 times and achieves similar accuracy while utilizing 70.59% fewer qubits.
  arXiv  Detail & Related papers  (2024-02-23T14:09:41Z)
• 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)
• Efficient Quantum Simulation of Open Quantum System Dynamics on Noisy Quantum Computers [0.0]
  We show that quantum dissipative dynamics can be simulated efficiently across coherent-to-incoherent regimes. This work provides a new direction for quantum advantage in the NISQ era.
  arXiv  Detail & Related papers  (2021-06-24T10:37:37Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Optimal quantum simulation of open quantum systems [1.9551668880584971]
  Digital quantum simulation on quantum systems require algorithms that can be implemented using finite quantum resources. Recent studies have demonstrated digital quantum simulation of open quantum systems on Noisy Intermediate-Scale Quantum (NISQ) devices. We develop quantum circuits for optimal simulation of Markovian and Non-Markovian open quantum systems.
  arXiv  Detail & Related papers  (2020-12-14T14:00:36Z)
• Autoregressive Transformer Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation [5.668795025564699]
  We present an approach for tackling open quantum system dynamics. We compactly represent quantum states with autoregressive transformer neural networks. Efficient algorithms have been developed to simulate the dynamics of the Liouvillian superoperator.
  arXiv  Detail & Related papers  (2020-09-11T18:00:00Z)

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.