Surrogate Quantum Circuit Design for the Lattice Boltzmann Collision Operator

• URL: http://arxiv.org/abs/2507.12256v1
• Date: Wed, 16 Jul 2025 14:02:01 GMT
• Title: Surrogate Quantum Circuit Design for the Lattice Boltzmann Collision Operator
• Authors: Monica Lăcătuş, Matthias Möller,
• Abstract summary: Direct numerical simulation of turbulent flows at high Reynolds numbers remains a major challenge for traditional computational fluid dynamics (CFD) tools.<n>One promising quantum CFD approach is a fully quantum implementation of the lattice Boltzmann method called QLBM.<n>We introduce a framework for learning a surrogate quantum circuit (SQC) that approximates the full Bhatnagar Gross Krook (BGK) collision operator for the D2Q9 lattice.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Direct numerical simulation of turbulent flows at high Reynolds numbers remains a major challenge for traditional computational fluid dynamics (CFD) tools running on classical computer hardware. This has motivated growing interest in quantum algorithms for CFD to enable flow simulations on quantum computers. The reason being that these computers are expected to deliver potential speed-ups for certain problems. One promising quantum CFD approach is a fully quantum implementation of the lattice Boltzmann method called QLBM. Although efficient quantum routines are now available for the streaming step, implementing the nonlinear, irreversible collision step with a low depth circuit that avoids additional ancilla qubits, probabilistic post-selection and repeated executions remains a significant challenge. In this study, we address this challenge by introducing a framework for learning a surrogate quantum circuit (SQC) that approximates the full Bhatnagar Gross Krook (BGK) collision operator for the D2Q9 lattice. The four qubit circuit is trained to respect the physical properties of the BGK collision operator, including mass and momentum conservation, D8 equivariance and scale equivariance. When compiled to the gate set used by IBM Heron processor under the assumption of full qubit connectivity, the 15 block SQC requires only 2,430 native gates and uses neither ancilla qubits nor post-selection or repeated executions. Moreover, its depth is independent of the grid resolution, as collision is a local operation that can exploit quantum parallelism to its full extent. We validate the SQC on two benchmark flows, the Taylor Green vortex decay and the lid driven cavity, demonstrating that it accurately captures vortex dissipation and flow recirculation.

Related papers

• Quantum Wasserstein Compilation: Unitary Compilation using the Quantum Earth Mover's Distance [2.502222151305252]
  quantum circuit compilation (QCC) is a crucial component of any quantum algorithm execution.<n>We present a VQCC-objective function called the quantum Wasserstein compilation (QWC) cost function based on the quantum Wasserstein distance of order 1.<n>An estimation method based on measurements of local Pauli-observable is utilized in a generative adversarial network to learn a given quantum circuit.
  arXiv  Detail & Related papers  (2024-09-09T17:46:40Z)
• Subspace-Based Local Compilation of Variational Quantum Circuits for Large-Scale Quantum Many-Body Simulation [0.0]
  This paper proposes a hybrid quantum-classical algorithm for compiling the time-evolution operator. It achieves a 95% reduction in circuit depth compared to Trotterization while maintaining accuracy. We estimate the gate count needed to execute the quantum simulations using the LSVQC on near-term quantum computing architectures.
  arXiv  Detail & Related papers  (2024-07-19T09:50:01Z)
• Parallel Quantum Computing Simulations via Quantum Accelerator Platform Virtualization [44.99833362998488]
  We present a model for parallelizing simulation of quantum circuit executions. The model can take advantage of its backend-agnostic features, enabling parallel quantum circuit execution over any target backend.
  arXiv  Detail & Related papers  (2024-06-05T17:16:07Z)
• Quantum subspace expansion in the presence of hardware noise [0.0]
  Finding ground state energies on current quantum processing units (QPUs) continues to pose challenges. Hardware noise severely affects both the expressivity and trainability of parametrized quantum circuits. We show how to integrate VQE with a quantum subspace expansion, allowing for an optimal balance between quantum and classical computing capabilities and costs.
  arXiv  Detail & Related papers  (2024-04-14T02:48:42Z)
• 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)
• A multiple-circuit approach to quantum resource reduction with application to the quantum lattice Boltzmann method [39.671915199737846]
  We introduce a multiple-circuit algorithm for a quantum lattice Boltzmann method (QLBM) solve of the incompressible Navier--Stokes equations.<n>The presented method is validated and demonstrated for 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)
• Mitigating crosstalk errors by randomized compiling: Simulation of the BCS model on a superconducting quantum computer [41.94295877935867]
  Crosstalk errors, stemming from CNOT two-qubit gates, are a crucial source of errors on numerous quantum computing platforms. We develop and apply an extension of the randomized compiling protocol that includes a special treatment of neighboring qubits. Our twirling of neighboring qubits is shown to dramatically improve the noise estimation protocol without the need to add new qubits or circuits.
  arXiv  Detail & Related papers  (2023-05-03T18:00:02Z)
• Efficient and fail-safe quantum algorithm for the transport equation [0.0]
  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.
  arXiv  Detail & Related papers  (2022-11-25T17:59:09Z)
• Practical implications of SFQ-based two-qubit gates [3.4982242928569405]
  Scalability of today's superconducting quantum computers is limited due to the huge costs of generating/routing microwave control pulses per qubit from room temperature. One active research area in both industry and academia is to push the classical controllers to the dilution refrigerator in order to increase the scalability of quantum computers. Superconducting Single Flux Quantum (SFQ) is a classical logic technology with low power consumption and ultra-high speed.
  arXiv  Detail & Related papers  (2022-02-03T05:05:24Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)

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.