Efficient Quantum Lattice Gas Automata

• URL: http://arxiv.org/abs/2402.16488v2
• Date: Tue, 05 Nov 2024 12:22:46 GMT
• Title: Efficient Quantum Lattice Gas Automata
• Authors: Antonio David Bastida Zamora, Ljubomir Budinski, Ossi Niemimäki, Valtteri Lahtinen,
• Abstract summary: The algorithm is composed of three main steps: collision, mapping, and propagation. Despite the impact of noise, our findings indicate that accurate simulations could be achieved already on current noisy devices.
• Score: 0.0
• License:
• Abstract: This study presents a novel quantum algorithm for lattice gas automata simulation with a single time step, demonstrating logarithmic complexity in terms of $CX$ gates. The algorithm is composed of three main steps: collision, mapping, and propagation. A computational complexity analysis and a comparison using different error rates and number of shots are provided. Despite the impact of noise, our findings indicate that accurate simulations could be achieved already on current noisy devices. This suggests potential for efficient simulation of classical fluid dynamics using quantum lattice gas automata, conditional on advancements to expand the current method to multiple time steps and state preparation.

Related papers

• Compact quantum algorithms for time-dependent differential equations [0.0]
  We build on an idea based on linear combination of unitaries to simulate non-unitary, non-Hermitian quantum systems. We generate hybrid quantum-classical algorithms that efficiently perform iterative matrix-vector multiplication and matrix inversion operations.
  arXiv  Detail & Related papers  (2024-05-16T02:14:58Z)
• Importance sampling for stochastic quantum simulations [68.8204255655161]
  We introduce the qDrift protocol, which builds random product formulas by sampling from the Hamiltonian according to the coefficients. We show that the simulation cost can be reduced while achieving the same accuracy, by considering the individual simulation cost during the sampling stage. Results are confirmed by numerical simulations performed on a lattice nuclear effective field theory.
  arXiv  Detail & Related papers  (2022-12-12T15:06:32Z)
• Hybridized Methods for Quantum Simulation in the Interaction Picture [69.02115180674885]
  We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations. Physical applications of these hybridized methods yield a gate complexity scaling as $log2 Lambda$ in the electric cutoff. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $lambda$ used to impose an energy cost.
  arXiv  Detail & Related papers  (2021-09-07T20:01:22Z)
• 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)
• Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
  We present a constructive algorithm for generating quantum circuits with time-independent depth. We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model. In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
  arXiv  Detail & Related papers  (2021-04-01T19:06:00Z)
• Fast and differentiable simulation of driven quantum systems [58.720142291102135]
  We introduce a semi-analytic method based on the Dyson expansion that allows us to time-evolve driven quantum systems much faster than standard numerical methods. We show results of the optimization of a two-qubit gate using transmon qubits in the circuit QED architecture.
  arXiv  Detail & Related papers  (2020-12-16T21:43:38Z)
• Low-depth Hamiltonian Simulation by Adaptive Product Formula [3.050399782773013]
  Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. Here, we propose an adaptive approach to construct a low-depth time evolution circuit. Our work sheds light on practical Hamiltonian simulation with noisy-intermediate-scale-quantum devices.
  arXiv  Detail & Related papers  (2020-11-10T18:00:42Z)
• Low Rank Density Matrix Evolution for Noisy Quantum Circuits [4.598939257021113]
  We present an efficient rank-compression approach for the classical simulation of Kraus decoherence channels in noisy quantum circuits. We implement this algorithm in an in-house simulator, and show that the low rank algorithm speeds up simulations by more than two orders of magnitude over an existing implementation of full rank simulator.
  arXiv  Detail & Related papers  (2020-09-14T18:00:16Z)
• Efficient calculation of gradients in classical simulations of variational quantum algorithms [0.0]
  We present a novel derivation of an emulation strategy to precisely calculate the gradient in O(P) time. Our strategy is very simple, uses only 'apply gate', 'clone state' and 'inner product' primitives. It is compatible with gate parallelisation schemes, and hardware accelerated and distributed simulators.
  arXiv  Detail & Related papers  (2020-09-06T21:39:44Z)
• Realistic simulation of quantum computation using unitary and measurement channels [1.406995367117218]
  We introduce a new simulation approach that relies on approximating the density matrix evolution by a sum of unitary and measurement channels. This model shows an improvement of at least one order of magnitude in terms of accuracy compared to the best known approaches.
  arXiv  Detail & Related papers  (2020-05-13T14:29:18Z)
• Efficient classical simulation of random shallow 2D quantum circuits [104.50546079040298]
  Random quantum circuits are commonly viewed as hard to simulate classically. We show that approximate simulation of typical instances is almost as hard as exact simulation. We also conjecture that sufficiently shallow random circuits are efficiently simulable more generally.
  arXiv  Detail & Related papers  (2019-12-31T19:00:00Z)

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.