Efficient and Fail-Safe Collisionless Quantum Boltzmann Method

Schalkers, Merel; Möller, Matthias

doi:10.2139/ssrn.4353577

Cited by 5 publications

(2 citation statements)

References 10 publications

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“…To leverage quantum computing for multiphysics, quantum LBM (QLBM) has been recently developed for the advection-diffusion and the incompressible Navier-Stokes equations [8,10]. Other approaches can be found in [14][15][16][17][18]. In contrast to macroscale methods, the LBM replaces fluid density with probability distributions of fictive particles.…”

Section: Quantum Lattice Boltzmann Methods (Lbm)mentioning

confidence: 99%

Efficient parallelization of quantum basis state shift

Budinski,

Niemimäki,

Zamora-Zamora

et al. 2023

Quantum Sci. Technol.

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Basis state shift is central to many quantum algorithms, most notably the quantum walk. Efficient implementations are of major importance for achieving the quantum speedup for computational applications. We optimize the state shift algorithm by incorporating the shift in different directions in parallel. This provides a significant reduction in the depth of the quantum circuit in comparison to the currently known methods, giving a linear scaling in the number of gates versus working qubits in contrast to the quadratic scaling of the state-of-the-art method based on the quantum Fourier transform. For a one-dimensional array of size 2n for n > 4, we derive the total number of 15n + 74 two-qubit CX gates in the parallel circuit, using a total of 2n-2 qubits including an ancilla register for the decomposition of multi-controlled gates. We focus on the one-dimensional and periodic shift, but note that the method can be extended to more complex cases.

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Section: Quantum Lattice Boltzmann Methods (Lbm)mentioning

confidence: 99%

Efficient parallelization of quantum basis state shift

Budinski,

Niemimäki,

Zamora-Zamora

et al. 2023

Quantum Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…The hybrid scheme is advantageous because it allows data to be encoded both in qubits and amplitudes; the 'amplitudes' represent the information we are interested in, while the 'qubits' encode the N features. This dual approach makes Qsample encoding particularly useful in probabilistic QML models and quantum Boltzmann machines (QBMs) [89], [90]. In these applications, state preparation for a given probability distribution operates in the same manner, where a qubit-efficient algorithm is polynomial in the input, whereas an amplitude-efficient quantum algorithm is exponential in the input dimension N [83].…”

Section: O Mp U T a T I O N A L B A S I S S T A T E S A Mp L I T U D Ementioning

confidence: 99%

Beyond Bits: A Review of Quantum Embedding Techniques for Efficient Information Processing

Khan,

Aman,

Sikdar

2024

IEEE Access

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The existing body of research on quantum embedding techniques is not only confined in scope but also lacks a comprehensive understanding of the intricacies of the quantum embedding process. To address this critical issue, this article explores quantum encoding schemes, uncovering valuable insights into their encoding algorithms from theoretical foundations to a mathematical perspective, as well as practical applications. Initially, the article briefly overviews classical computing and the limitations associated with classical bits in representing and processing complex information. Next, the article scrutinizes a variety of quantum embedding patterns, including basis encoding, amplitude encoding, Qsample encoding, angle encoding, quantum associative memory encoding, quantum random access memory, superdense encoding, Hamiltonian encoding, and others. In addition, each technique is accompanied by mathematical formulas and examples illustrating how each strategy can be applied. Finally, the article provides a comparative analysis of different quantum embedding/encoding methods, outlining their strengths and limitations. Overall, this insightful article highlights the potential of quantum encoding techniques for efficient information processing beyond classical bits, thereby facilitating scientists and design engineers in selecting the most appropriate encoding technique to develop smart algorithms for revolutionizing the field of quantum computing.INDEX TERMS Encoding patterns, qubits, quantum computing, quantum information processing, quantum circuits.

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Solving transport equations on quantum computers—potential and limitations of physics-informed quantum circuits

Siegl,

Wassing,

Mieth

et al. 2024

CEAS Aeronaut J

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Quantum circuits with trainable parameters, paired with classical optimization routines can be used as machine learning models. The recently popularized physics-informed neural network (PINN) approach is a machine learning algorithm that solves differential equations by incorporating them into a loss function. Being a mesh-free method, it is a promising approach for computational fluid dynamics. The question arises whether the properties of quantum circuits can be leveraged for a quantum physics-informed machine learning model. In this study, we compare the classical PINN-ansatz and its quantum analog, which we name the physics-informed quantum circuit (PIQC). The PIQC simulations are performed on a noise-free quantum computing simulator. Studying various differential equations, we compare expressivity, accuracy and convergence properties. We find that one-dimensional problems, such as the linear transport of a Gaussian-pulse or Burgers’ equation, allow a successful approximation with the classical and the quantum ansatz. For these examples, the PIQC overall performs similarly to PINN and converges more consistently and for Burgers’ equations even faster. While this is promising, the chosen quantum circuit approach struggles to approximate discontinuous solutions which the classical PINN-ansatz can represent. Based on this comparison, we extrapolate that the required number of qubits for solving two-dimensional problems in aerodynamics may already be available in the next few years. However, the acceleration potential is currently unclear and challenges like noisy circuits and approximations of discontinuous solutions have to be overcome.

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Efficient and Fail-Safe Collisionless Quantum Boltzmann Method

Cited by 5 publications

References 10 publications

Efficient parallelization of quantum basis state shift

Efficient parallelization of quantum basis state shift

Beyond Bits: A Review of Quantum Embedding Techniques for Efficient Information Processing

Solving transport equations on quantum computers—potential and limitations of physics-informed quantum circuits

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