Considering Decoherence Errors in the Simulation of Quantum Circuits Using Decision Diagrams

• URL: http://arxiv.org/abs/2012.05629v1
• Date: Thu, 10 Dec 2020 12:29:24 GMT
• Title: Considering Decoherence Errors in the Simulation of Quantum Circuits Using Decision Diagrams
• Authors: Thomas Grurl, J\"urgen Fu{\ss}, Robert Wille
• Abstract summary: We investigate how the consideration of decoherence errors affects the simulation performance of approaches based on decision diagrams. Experiments confirm that this yields improvements of several orders of magnitudes compared to a naive consideration of errors.
• Score: 2.450250748409888
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: By using quantum mechanical effects, quantum computers promise significant speedups in solving problems intractable for conventional computers. However, despite recent progress they remain limited in scaling and availability-making quantum software and hardware development heavily reliant on quantum simulators running on conventional hardware. However, most of those simulators mimic perfect quantum computers and, hence, ignore the fragile nature of quantum mechanical effects which frequently yield to decoherence errors in real quantum devices. Considering those errors during the simulation is complex, but necessary in order to tailor quantum algorithms for specific devices. Thus far, most state-of-the-art simulators considering decoherence errors rely on (exponentially) large array representations. As an alternative, simulators based on decision diagrams have been shown very promising for simulation of quantum circuits in general, but have not supported decoherence errors yet. In this work, we are closing this gap. We investigate how the consideration of decoherence errors affects the simulation performance of approaches based on decision diagrams and propose advanced solutions to mitigate negative effects. Experiments confirm that this yields improvements of several orders of magnitudes compared to a naive consideration of errors.

Related papers

• The curse of random quantum data [62.24825255497622]
  We quantify the performances of quantum machine learning in the landscape of quantum data. We find that the training efficiency and generalization capabilities in quantum machine learning will be exponentially suppressed with the increase in qubits. Our findings apply to both the quantum kernel method and the large-width limit of quantum neural networks.
  arXiv  Detail & Related papers  (2024-08-19T12:18:07Z)
• Quantum Tunneling: From Theory to Error-Mitigated Quantum Simulation [49.1574468325115]
  This study presents the theoretical background and the hardware aware circuit implementation of a quantum tunneling simulation. We use error mitigation techniques (ZNE and REM) and multiprogramming of the quantum chip for solving the hardware under-utilization problem.
  arXiv  Detail & Related papers  (2024-04-10T14:27:07Z)
• 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)
• Machine Learning for Practical Quantum Error Mitigation [0.0]
  We show that machine learning for quantum error mitigation can drastically reduce overheads, maintain or even surpass the accuracy of conventional methods. Our results highlight the potential of classical machine learning for practical quantum computation.
  arXiv  Detail & Related papers  (2023-09-29T16:17:12Z)
• Multi-mode Cavity Centric Architectures for Quantum Simulation [12.40374538847457]
  Near-term quantum computing technologies grapple with huge complexity overheads, hindering their ability to induce algorithms. One class of problems of interest is Quantum Simulation, whereby quantum systems are simulated using a quantum computer. One technology of particular interest is the multi-mode superconducting resonator capable of storing multiple qubits in one device.
  arXiv  Detail & Related papers  (2023-09-27T20:16:44Z)
• Measuring NISQ Gate-Based Qubit Stability Using a 1+1 Field Theory and Cycle Benchmarking [50.8020641352841]
  We study coherent errors on a quantum hardware platform using a transverse field Ising model Hamiltonian as a sample user application. We identify inter-day and intra-day qubit calibration drift and the impacts of quantum circuit placement on groups of qubits in different physical locations on the processor. This paper also discusses how these measurements can provide a better understanding of these types of errors and how they may improve efforts to validate the accuracy of quantum computations.
  arXiv  Detail & Related papers  (2022-01-08T23:12:55Z)
• 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)
• Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
  Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard. We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware. The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
  arXiv  Detail & Related papers  (2021-07-08T17:59:55Z)
• Hardware-Efficient, Fault-Tolerant Quantum Computation with Rydberg Atoms [55.41644538483948]
  We provide the first complete characterization of sources of error in a neutral-atom quantum computer. We develop a novel and distinctly efficient method to address the most important errors associated with the decay of atomic qubits to states outside of the computational subspace. Our protocols can be implemented in the near-term using state-of-the-art neutral atom platforms with qubits encoded in both alkali and alkaline-earth atoms.
  arXiv  Detail & Related papers  (2021-05-27T23:29:53Z)
• Stochastic Quantum Circuit Simulation Using Decision Diagrams [3.9006434061597877]
  A substantial amount of quantum algorithms research still relies on simulating quantum circuits on classical hardware. We propose to use decision diagrams, as well as concurrent executions, to substantially reduce resource-requirements. Backed up by rigorous theory, empirical studies show that this approach allows for a substantially faster and much more scalable simulation for certain quantum circuits.
  arXiv  Detail & Related papers  (2020-12-10T12:10:18Z)
• Just Like the Real Thing: Fast Weak Simulation of Quantum Computation [3.871968228840823]
  We focus on weak simulation that aims to produce outputs which are statistically indistinguishable from those of error-free quantum computers. We develop algorithms for weak simulation based on quantum state representation in terms of decision diagrams. Empirical validation shows, for the first time, that this enables mimicking of physical quantum computers of significant scale.
  arXiv  Detail & Related papers  (2020-07-30T08:00:06Z)

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.