Quantum algorithms based on quantum trajectories

• URL: http://arxiv.org/abs/2509.10425v1
• Date: Fri, 12 Sep 2025 17:27:25 GMT
• Title: Quantum algorithms based on quantum trajectories
• Authors: Evan Borras, Milad Marvian,
• Abstract summary: We show that the additive complexity of $O(T + log(1/epsilon))$ is reachable for the simulation of a large class of Lindbladian.<n>In this work we show that the additive complexity of $O(T + log(1/epsilon))$ is reachable for the simulation of a large class of Lindbladian by constructing a novel quantum algorithm based on quantum trajectories.
• Score: 0.4870012761464388
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum simulation has emerged as a key application of quantum computing, with significant progress made in algorithms for simulating both closed and open quantum systems. The simulation of open quantum systems, particularly those governed by the Lindblad master equation, has received attention recently with the current state-of-the-art algorithms having an input model query complexity of $O(T \mathrm{polylog}(T/\epsilon))$, where $T$ and $\epsilon$ are the requested time and precision of the simulation respectively. For the Hamiltonian simulation problem it has been show that the optimal Hamiltonian query complexity is $O(T + \log(1/\epsilon))$, additive in nature between the two parameter, but for Lindbladian simulation this question remains open. In this work we show that the additive complexity of $O(T + \log(1/\epsilon))$ is reachable for the simulation of a large class of Lindbladian by constructing a novel quantum algorithm based on quantum trajectories.

Related papers

• Quantum simulation of massive Thirring and Gross--Neveu models for arbitrary number of flavors [40.72140849821964]
  We consider the massive Thirring and Gross-Neveu models with arbitrary number of fermion flavors, $N_f$, discretized on a spatial one-dimensional lattice of size $L$.<n>We prepare the ground states of both models with excellent fidelity for system sizes up to 20 qubits with $N_f = 1,2,3,4$.<n>Our work is a concrete step towards the quantum simulation of real-time dynamics of large $N_f$ fermionic quantum field theories models.
  arXiv  Detail & Related papers  (2026-02-25T19:00:01Z)
• Quantum simulation of multiscale linear transport equations via Schrödingerization and exponential integrators [26.87128563756398]
  We present two Hamiltonian simulation algorithms for multiscale linear transport equations, combining the Schr"odingerization method.<n>The query complexity of both algorithms, $mathcalO(N_vN_x2log N_x)$, outperforms existing quantum and classical algorithms for solving this equation.
  arXiv  Detail & Related papers  (2025-07-25T05:44:28Z)
• Phase estimation with partially randomized time evolution [36.989845156791525]
  Quantum phase estimation combined with Hamiltonian simulation is the most promising algorithmic framework to computing ground state energies on quantum computers.<n>In this paper we use randomization to speed up product formulas, one of the standard approaches to Hamiltonian simulation.<n>We perform a detailed resource estimate for single-ancilla phase estimation using partially randomized product formulas for benchmark systems in quantum chemistry.
  arXiv  Detail & Related papers  (2025-03-07T18:09:32Z)
• Practical Quantum Circuit Implementation for Simulating Coupled Classical Oscillators [1.3140209441982318]
  We present and implement a detailed quantum circuit construction for simulating one-dimensional spring-mass systems.<n>This circuit-based Hamiltonian simulation approach can substantially reduce computational costs and potentially enable larger-scale many-body studies on future quantum hardware.
  arXiv  Detail & Related papers  (2025-01-10T16:53:56Z)
• Exponentially accurate open quantum simulation via randomized dissipation with minimal ancilla [0.35794129023851595]
  Some quantum algorithms for simulating Lindblad dynamics achieve logarithmically short circuit depth in terms of accuracy $varepsilon$ by coherently encoding all possible jump processes with a large ancilla consumption.<n>We present a quantum algorithm for simulating general Lindblad dynamics with multiple jump operators aimed at an observable estimation, that achieves both a logarithmically short circuit depth and a minimum ancilla size.
  arXiv  Detail & Related papers  (2024-12-27T04:43:19Z)
• Quantum Algorithms for Stochastic Differential Equations: A Schrödingerisation Approach [29.662683446339194]
  We propose quantum algorithms for linear differential equations.<n>The gate complexity of our algorithms exhibits an $mathcalO(dlog(Nd))$ dependence on the dimensions.<n>The algorithms are numerically verified for the Ornstein-Uhlenbeck processes, Brownian motions, and one-dimensional L'evy flights.
  arXiv  Detail & Related papers  (2024-12-19T14:04:11Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [62.46800898243033]
  Recent progress in quantum learning theory prompts a question: can linear properties of a large-qubit circuit be efficiently learned from measurement data generated by varying classical inputs?<n>We prove that the sample complexity scaling linearly in $d$ is required to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d.<n>We propose a kernel-based method leveraging classical shadows and truncated trigonometric expansions, enabling a controllable trade-off between prediction accuracy and computational overhead.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Variational-Cartan Quantum Dynamics Simulations of Excitation Dynamics [7.865137519552981]
  Quantum dynamics simulations (QDSs) are one of the most highly anticipated applications of quantum computing. Quantum circuit depth for implementing Hamiltonian simulation algorithms is commonly time dependent. In this work, we generalize this CD-based Hamiltonian simulation algorithm for studying time-dependent systems by combining it with variational Hamiltonian simulation.
  arXiv  Detail & Related papers  (2024-06-20T09:11:46Z)
• A hybrid quantum-classical algorithm for multichannel quantum scattering of atoms and molecules [62.997667081978825]
  We propose a hybrid quantum-classical algorithm for solving the Schr"odinger equation for atomic and molecular collisions. The algorithm is based on the $S$-matrix version of the Kohn variational principle, which computes the fundamental scattering $S$-matrix. We show how the algorithm could be scaled up to simulate collisions of large polyatomic molecules.
  arXiv  Detail & Related papers  (2023-04-12T18:10:47Z)
• Efficient Fully-Coherent Quantum Signal Processing Algorithms for Real-Time Dynamics Simulation [3.3917542048743865]
  We develop fully-coherent simulation algorithms based on quantum signal processing (QSP) We numerically analyze these algorithms by applying them to the simulation of spin dynamics of the Heisenberg model.
  arXiv  Detail & Related papers  (2021-10-21T17:56:33Z)
• An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian Simulation [55.41644538483948]
  Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in chip size and error rates. We derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions. The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $mathcalO(103)$ spins.
  arXiv  Detail & Related papers  (2021-08-06T19:38:03Z)
• Parallel Quantum Algorithm for Hamiltonian Simulation [9.680246554758343]
  A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians. The running time of our parallel quantum simulation algorithm measured by the quantum circuit depth has a doubly (poly-)logarithmic dependence. We show that the total gate depth of our algorithm has a $operatornamepolyloglog (1/epsilon)$ dependence in the parallel setting.
  arXiv  Detail & Related papers  (2021-05-25T12:46:33Z)
• 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)
• Quantum Algorithms for Simulating the Lattice Schwinger Model [63.18141027763459]
  We give scalable, explicit digital quantum algorithms to simulate the lattice Schwinger model in both NISQ and fault-tolerant settings. In lattice units, we find a Schwinger model on $N/2$ physical sites with coupling constant $x-1/2$ and electric field cutoff $x-1/2Lambda$. We estimate observables which we cost in both the NISQ and fault-tolerant settings by assuming a simple target observable---the mean pair density.
  arXiv  Detail & Related papers  (2020-02-25T19:18:36Z)

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.