Efficient and fail-safe collisionless quantum Boltzmann method
- URL: http://arxiv.org/abs/2211.14269v1
- Date: Fri, 25 Nov 2022 17:59:09 GMT
- Title: Efficient and fail-safe collisionless quantum Boltzmann method
- Authors: Merel A. Schalkers, Matthias M\"oller
- Abstract summary: We present a scalable algorithm for solving the collisionless Boltzmann equation in two and three spatial dimensions.
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 collisionless Boltzmann
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 collisionless quantum Boltzmann method (CQBM), we describe a
full-circuit start-to-end implementation in Qiskit and present numerical
results for 2D flows. Our CQBM 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
collisionless Boltzmann 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
collisionless Boltzmann 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
- 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) - 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) - Efficient Quantum Circuit Encoding of Object Information in 2D Ray Casting [7.262444673139455]
Quantum computing holds the potential to solve problems that are practically unsolvable by classical computers.
We aim to harness this potential to enhance ray casting, a pivotal technique in computer graphics for simplifying the rendering of 3D objects.
arXiv Detail & Related papers (2024-05-25T08:54:28Z) - 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) - 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) - 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)
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.