Dilution of error in digital Hamiltonian simulation

• URL: http://arxiv.org/abs/2409.04254v1
• Date: Fri, 6 Sep 2024 13:04:21 GMT
• Title: Dilution of error in digital Hamiltonian simulation
• Authors: Etienne Granet, Henrik Dreyer,
• Abstract summary: We provide a microscopic explanation of this dilution of errors based on the "relevant string" of operators. We show that this explanation can predict when dilution of errors occurs and when it does not. Our findings imply that digital quantum simulation with noisy devices is in appropriate cases scalable.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We provide analytic, numerical and experimental evidence that the amount of noise in digital quantum simulation of local observables can be independent of system size in a number of situations. We provide a microscopic explanation of this dilution of errors based on the "relevant string length" of operators, which is the length of Pauli strings in the operator at time $s$ that belong to the exponentially small subspace of strings that can give a non-zero expectation value at time $t$. We show that this explanation can predict when dilution of errors occurs and when it does not. We propose an error mitigation method whose efficiency relies on this mechanism. Our findings imply that digital quantum simulation with noisy devices is in appropriate cases scalable in the sense that gate errors do not need to be reduced linearly to simulate larger systems.

Related papers

• Realizing fracton order from long-range quantum entanglement in programmable Rydberg atom arrays [45.19832622389592]
  Storing quantum information requires battling quantum decoherence, which results in a loss of information over time. To achieve error-resistant quantum memory, one would like to store the information in a quantum superposition of degenerate states engineered in such a way that local sources of noise cannot change one state into another. We show that this platform also allows to detect and correct certain types of errors en route to the goal of true error-resistant quantum memory.
  arXiv  Detail & Related papers  (2024-07-08T12:46:08Z)
• Incoherent Approximation of Leakage in Quantum Error Correction [0.03922370499388702]
  Quantum error correcting codes typically do not account for quantum state transitions - leakage - out of the computational subspace. We introduce a Random Phase Approximation (RPA) on quantum channels that preserves the incoherence between the computational and leakage subspaces. We show that RPA yields accurate error correction statistics in the repetition and surface codes with physical error parameters.
  arXiv  Detail & Related papers  (2023-12-16T00:52:23Z)
• Stochastic Error Cancellation in Analog Quantum Simulation [0.6410191755165466]
  We consider an error model in which the actual Hamiltonian of the simulator differs from the target Hamiltonian. We show that, due to error cancellation, the error scales as the square root of the number of qubits instead of linearly. We also show that error cancellation also manifests in the fidelity between the target state at the end of time-evolution and the actual state we obtain in the presence of noise.
  arXiv  Detail & Related papers  (2023-11-24T19:25:08Z)
• Limitations of probabilistic error cancellation for open dynamics beyond sampling overhead [1.1864834557465163]
  Methods such as probabilistic error cancellation rely on discretizing the evolution into finite time steps and applying the mitigation layer after each time step. This may lead to Trotter-like errors in the simulation results even if the error mitigation is implemented ideally. We show that, they are determined by the commutating relations between the superoperators of the unitary part, the device noise part and the noise part of the open dynamics to be simulated.
  arXiv  Detail & Related papers  (2023-08-02T21:45:06Z)
• Study of noise in virtual distillation circuits for quantum error mitigation [0.0]
  We study the effect of uncorrelated, identical noise in the cyclic permutation circuit. We find that the estimation of expectation value of observables are robust against dephasing noise. Our results imply that a broad class of quantum algorithms can be implemented with higher accuracy in the near-term.
  arXiv  Detail & Related papers  (2022-10-27T10:56:35Z)
• Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics [62.997667081978825]
  We show how finite-temperature observables can be obtained with an algorithm motivated from the Jarzynski equality. We show that a finite temperature phase transition in the long-range transverse field Ising model can be characterized in trapped ion quantum simulators.
  arXiv  Detail & Related papers  (2022-06-03T18:00:02Z)
• The Accuracy vs. Sampling Overhead Trade-off in Quantum Error Mitigation Using Monte Carlo-Based Channel Inversion [84.66087478797475]
  Quantum error mitigation (QEM) is a class of promising techniques for reducing the computational error of variational quantum algorithms. We consider a practical channel inversion strategy based on Monte Carlo sampling, which introduces additional computational error. We show that when the computational error is small compared to the dynamic range of the error-free results, it scales with the square root of the number of gates.
  arXiv  Detail & Related papers  (2022-01-20T00:05:01Z)
• Bosonic field digitization for quantum computers [62.997667081978825]
  We address the representation of lattice bosonic fields in a discretized field amplitude basis. We develop methods to predict error scaling and present efficient qubit implementation strategies.
  arXiv  Detail & Related papers  (2021-08-24T15:30:04Z)
• 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)
• Simple Mitigation of Global Depolarizing Errors in Quantum Simulations [0.0]
  We present a simple but effective error mitigation technique based on the assumption that noise in a deep quantum circuit is well described by global depolarizing error channels. By measuring the errors directly on the device, we use an error model ansatz to infer error-free results from noisy data.
  arXiv  Detail & Related papers  (2021-01-05T18:31:28Z)
• The role of boundary conditions in quantum computations of scattering observables [58.720142291102135]
  Quantum computing may offer the opportunity to simulate strongly-interacting field theories, such as quantum chromodynamics, with physical time evolution. As with present-day calculations, quantum computation strategies still require the restriction to a finite system size. We quantify the volume effects for various $1+1$D Minkowski-signature quantities and show that these can be a significant source of systematic uncertainty.
  arXiv  Detail & Related papers  (2020-07-01T17:43:11Z)

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.