Accurate Numerical Simulations of Open Quantum Systems Using Spectral Tensor Trains

• URL: http://arxiv.org/abs/2407.11327v1
• Date: Tue, 16 Jul 2024 02:33:27 GMT
• Title: Accurate Numerical Simulations of Open Quantum Systems Using Spectral Tensor Trains
• Authors: Ryan T. Grimm, Joel D. Eaves,
• Abstract summary: Decoherence between qubits is a major bottleneck in quantum computations. We present a numerical method, Quantum Accelerated Propagator Evaluation (Q-ASPEN) Q-ASPEN is arbitrarily accurate and can be applied to provide estimates for resources needed to error-correct quantum computations.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Decoherence between qubits is a major bottleneck in quantum computations. Decoherence results from intrinsic quantum and thermal fluctuations as well as noise in the external fields that perform the measurement and preparation processes. With prescribed colored noise spectra for intrinsic and extrinsic noise, we present a numerical method, Quantum Accelerated Stochastic Propagator Evaluation (Q-ASPEN), to solve the time-dependent noise-averaged reduced density matrix in the presence of intrinsic and extrinsic noise. Q-ASPEN is arbitrarily accurate and can be applied to provide estimates for the resources needed to error-correct quantum computations. We employ spectral tensor trains, which combine the advantages of tensor networks and pseudospectral methods, as a variational ansatz to the quantum relaxation problem and optimize the ansatz using methods typically used to train neural networks. The spectral tensor trains in Q-ASPEN make accurate calculations with tens of quantum levels feasible. We present benchmarks for Q-ASPEN on the spin-boson model in the presence of intrinsic noise and on a quantum chain of up to 32 sites in the presence of extrinsic noise. In our benchmark, the memory cost of Q-ASPEN scales linearly with the system size once the number of states is larger than the number of basis functions.

Related papers

• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Optimal training of finitely-sampled quantum reservoir computers for forecasting of chaotic dynamics [3.7960472831772765]
  In the current Noisy Intermediate Scale Quantum (NISQ) era, the presence of noise deteriorates the performance of quantum computing algorithms. In this paper, we analyse the effect that finite-sampling noise has on the chaotic time-series prediction capabilities of Quantum Reservoir Computing (QRC) and Recurrence-free Quantum Reservoir Computing (RF-QRC) We show that finite sampling noise degrades the prediction capabilities of both QRC and RF-QRC while affecting QRC more due to the propagation of noise.
  arXiv  Detail & Related papers  (2024-09-02T17:51:48Z)
• Accuracy guarantees and quantum advantage in analogue open quantum simulation with and without noise [0.0]
  We theoretically analyze noisy analogue quantum simulation of geometrically local open quantum systems. We show that the dynamics of local observables can be obtained to a precision of $varepsilon$ in time that is $textpoly(varepsilon-1)$ and uniform in system size.
  arXiv  Detail & Related papers  (2024-04-17T05:40:08Z)
• 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)
• Power Characterization of Noisy Quantum Kernels [52.47151453259434]
  We show that noise may make quantum kernel methods to only have poor prediction capability, even when the generalization error is small. We provide a crucial warning to employ noisy quantum kernel methods for quantum computation.
  arXiv  Detail & Related papers  (2024-01-31T01:02:16Z)
• 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)
• Algorithmic Shadow Spectroscopy [0.0]
  We present a simulator-agnostic quantum algorithm for estimating energy gaps using very few circuit repetitions (shots) and no extra resources (ancilla qubits) We demonstrate that our method is intuitively easy to use in practice, robust against gate noise, to a new type of algorithmic error mitigation technique, and uses orders of magnitude fewer number of shots than typical near-term quantum algorithms -- as low as 10 shots per timestep is sufficient.
  arXiv  Detail & Related papers  (2022-12-21T14:23:48Z)
• Noisy Quantum Kernel Machines [58.09028887465797]
  An emerging class of quantum learning machines is that based on the paradigm of quantum kernels. We study how dissipation and decoherence affect their performance. We show that decoherence and dissipation can be seen as an implicit regularization for the quantum kernel machines.
  arXiv  Detail & Related papers  (2022-04-26T09:52:02Z)
• 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)
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits [58.720142291102135]
  We simulate a noisy quantum Fourier transform processor with up to 21 qubits. We take into account microscopic dissipative processes rather than relying on digital error models. We show that depending on the dissipative mechanisms at play, the choice of input state has a strong impact on the performance of the quantum algorithm.
  arXiv  Detail & Related papers  (2021-02-08T14:55:44Z)
• Quantum reservoir computing with a single nonlinear oscillator [0.0]
  We propose continuous variable quantum reservoir computing in a single nonlinear oscillator. We demonstrate quantum-classical performance improvement, and identify its likely source: the nonlinearity of quantum measurement. We study how the performance of our quantum reservoir depends on Hilbert space dimension, how it is impacted by injected noise, and briefly comment on its experimental implementation.
  arXiv  Detail & Related papers  (2020-04-30T17:14:34Z)

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.