Efficient and fail-safe quantum algorithm for the transport equation

• URL: http://arxiv.org/abs/2211.14269v2
• Date: Tue, 21 Jan 2025 08:51:39 GMT
• Title: Efficient and fail-safe quantum algorithm for the transport equation
• Authors: Merel A. Schalkers, Matthias Möller,
• Abstract summary: We present a scalable algorithm for solving the transport equation in two and three spatial dimensions on a fault-tolerant universal quantum computer.<n>We describe a full-circuit start-to-end implementation in Qiskit and present numerical results for 2D flows.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a scalable algorithm for solving the transport equation in two and three spatial dimensions for variable grid sizes and discrete velocities on a fault-tolerant universal quantum computer. As a proof of concept of our quantum transport method (QTM), we describe a full-circuit start-to-end implementation in Qiskit and present numerical results for 2D flows. Our QTM is based on a novel streaming approach which leads to a reduction in the amount of CNOT gates required in comparison to state-of-the-art quantum streaming methods. As a second highlight we present a novel object encoding method, that reduces the complexity of the amount of CNOT gates required to encode walls, which now becomes independent of the size of the wall. Finally we present a novel quantum encoding of the particles' discrete velocities that enables a linear speed-up in the costs of reflecting the velocity of a particle, which now becomes independent of the amount of velocities encoded. Our main contribution is a detailed description of a fail-safe implementation of a quantum algorithm for the reflection step of the transport equation that can be readily implemented on a physical quantum computer. This fail-safe implementation allows for a variety of initial conditions and particle velocities and leads to physically correct behavior around the walls, edges and corners of obstacles. Combining these results we present a novel and fail-safe start-to-end quantum algorithm for the transport equation that can be used for a multitude of flow configurations. We finally show that our approach is quadratic in the amount of qubits necessary to encode the grid and the amount of qubits necessary to encode the discrete velocities in a single spatial dimension, which makes our approach superior to state-of-the-art approaches known in the literature.

Related papers

• Algorithmic Advances Towards a Realizable Quantum Lattice Boltzmann Method [2.7192829556657774]
  The Quantum Lattice Boltzmann Method (QLBM) is one of the most promising approaches for realizing the potential of quantum computing. We present a series of novel algorithmic advances which allow us to implement the QLBM algorithm, for the first time, on a quantum computer.
  arXiv  Detail & Related papers  (2025-04-15T05:02:41Z)
• Robust Implementation of Discrete-time Quantum Walks in Any Finite-dimensional Quantum System [2.646968944595457]
  discrete-time quantum walk (DTQW) model one of most suitable choices for circuit implementation. In this paper, we have successfully cut down the circuit cost concerning gate count and circuit depth by half. For the engineering excellence of our proposed approach, we implement DTQW in any finite-dimensional quantum system with akin efficiency.
  arXiv  Detail & Related papers  (2024-08-01T13:07:13Z)
• Route-Forcing: Scalable Quantum Circuit Mapping for Scalable Quantum Computing Architectures [41.39072840772559]
  Route-Forcing is a quantum circuit mapping algorithm that shows an average speedup of $3.7times$. We present a quantum circuit mapping algorithm that shows an average speedup of $3.7times$ compared to the state-of-the-art scalable techniques.
  arXiv  Detail & Related papers  (2024-07-24T14:21:41Z)
• Quantum Compiling with Reinforcement Learning on a Superconducting Processor [55.135709564322624]
  We develop a reinforcement learning-based quantum compiler for a superconducting processor. We demonstrate its capability of discovering novel and hardware-amenable circuits with short lengths. Our study exemplifies the codesign of the software with hardware for efficient quantum compilation.
  arXiv  Detail & Related papers  (2024-06-18T01:49:48Z)
• Towards Fault-Tolerant Quantum Deep Learning: Designing and Analyzing Quantum ResNet and Transformer with Quantum Arithmetic and Linear Algebra Primitives [5.89456905230997]
  We introduce a framework to overcome the dual challenges of constructing deep architectures and the prohibitive overhead of data loading and measurement.<n>Our framework enables the design of multi-layer Quantum ResNet and Quantum Transformer models.<n>A cornerstone of our approach is a novel data transfer protocol, Discrete Chebyshev Decomposition (DCD), which facilitates this modularity.
  arXiv  Detail & Related papers  (2024-02-29T08:12:02Z)
• A two-circuit approach to reducing quantum resources for the quantum lattice Boltzmann method [41.66129197681683]
  Current quantum algorithms for solving CFD problems use a single quantum circuit and, in some cases, lattice-based methods. We introduce the a novel multiple circuits algorithm that makes use of a quantum lattice Boltzmann method (QLBM) The problem is cast as a stream function--vorticity formulation of the 2D Navier-Stokes equations and verified and tested on a 2D lid-driven cavity flow.
  arXiv  Detail & Related papers  (2024-01-20T15:32:01Z)
• 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)
• Near-Term Distributed Quantum Computation using Mean-Field Corrections and Auxiliary Qubits [77.04894470683776]
  We propose near-term distributed quantum computing that involve limited information transfer and conservative entanglement production. We build upon these concepts to produce an approximate circuit-cutting technique for the fragmented pre-training of variational quantum algorithms.
  arXiv  Detail & Related papers  (2023-09-11T18:00:00Z)
• Sequential quantum simulation of spin chains with a single circuit QED device [5.841833052422423]
  Quantum simulation of many-body systems in materials science and chemistry are promising application areas for quantum computers. We show how a single-circuit quantum electrodynamics device can be used to simulate the ground state of a highly-entangled quantum many-body spin chain. We demonstrate that the large state space of the cavity can be used to replace multiple qubits in a qubit-only architecture, and could therefore simplify the design of quantum processors for materials simulation.
  arXiv  Detail & Related papers  (2023-08-30T18:00:03Z)
• Robust sparse IQP sampling in constant depth [3.670008893193884]
  NISQ (noisy intermediate scale quantum) approaches without any proof of robust quantum advantage and fully fault-tolerant quantum computation. We propose a scheme to achieve a provable superpolynomial quantum advantage that is robust to noise with minimal error correction requirements.
  arXiv  Detail & Related papers  (2023-07-20T09:41:08Z)
• On the importance of data encoding in quantum Boltzmann methods [0.0]
  We show that for encodings commonly discussed in literature either the collision or the streaming step cannot be unitary. We propose a novel encoding in which the number of qubits used to encode the velocity depends on the number of time steps one wishes to simulate. Our encoding method is to the best of our knowledge the only one currently known that can be used for a start-to-end quantum Boltzmann solver.
  arXiv  Detail & Related papers  (2023-02-10T15:05:33Z)
• An Optimized Quantum Implementation of ISD on Scalable Quantum Resources [2.274915755738124]
  We show that Prange's ISD algorithm can be implemented rather efficiently on a quantum computer. We leverage the idea of classical co-processors to design hybrid classical-quantum trade-offs.
  arXiv  Detail & Related papers  (2021-12-12T06:01:10Z)
• Simulating the Mott transition on a noisy digital quantum computer via Cartan-based fast-forwarding circuits [62.73367618671969]
  Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model. Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models. This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
  arXiv  Detail & Related papers  (2021-12-10T17:32:15Z)
• Quantum amplitude damping for solving homogeneous linear differential equations: A noninterferometric algorithm [0.0]
  This work proposes a novel approach by using the Quantum Amplitude Damping operation as a resource, in order to construct an efficient quantum algorithm for solving homogeneous LDEs. We show that such an open quantum system-inspired circuitry allows for constructing the real exponential terms in the solution in a non-interferometric.
  arXiv  Detail & Related papers  (2021-11-10T11:25:32Z)
• Fast Swapping in a Quantum Multiplier Modelled as a Queuing Network [64.1951227380212]
  We propose that quantum circuits can be modeled as queuing networks. Our method is scalable and has the potential speed and precision necessary for large scale quantum circuit compilation.
  arXiv  Detail & Related papers  (2021-06-26T10:55:52Z)
• Space-efficient binary optimization for variational computing [68.8204255655161]
  We show that it is possible to greatly reduce the number of qubits needed for the Traveling Salesman Problem. We also propose encoding schemes which smoothly interpolate between the qubit-efficient and the circuit depth-efficient models.
  arXiv  Detail & Related papers  (2020-09-15T18:17:27Z)
• Boundaries of quantum supremacy via random circuit sampling [69.16452769334367]
  Google's recent quantum supremacy experiment heralded a transition point where quantum computing performed a computational task, random circuit sampling. We examine the constraints of the observed quantum runtime advantage in a larger number of qubits and gates.
  arXiv  Detail & Related papers  (2020-05-05T20:11:53Z)

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.