arXiv:2110.09793 · Physical Review Research

Toward reliability in the NISQ era: Robust interval guarantee for quantum measurements on approximate states

Maurice Weber, Abhinav Anand, Alba Cervera-Lierta, Jakob S. Kottmann, Thi Ha Kyaw, Bo Li, Alán Aspuru‐Guzik, Ce Zhang, Zhikuan Zhao

Published Sep 19, 2022• 6 citations

arXiv HTML PDF

Abstract

Near-term quantum computation holds potential across multiple application domains. However, imperfect preparation and evolution of states due to algorithmic and experimental shortcomings, characteristic in the near-term implementation, would typically result in measurement outcomes deviating from the ideal setting. It is thus crucial for any near-term application to quantify and bound these output errors. We address this need by deriving robustness intervals which are guaranteed to contain the output in the ideal setting. The first type of interval is based on formulating robustness bounds as semidefinite programs, and uses only the first moment and the fidelity to the ideal state. Furthermore, we consider higher statistical moments of the observable and generalize bounds for pure states based on the non-negativity of Gram matrices to mixed states, thus enabling their applicability in the NISQ era where noisy scenarios are prevalent. Finally, we demonstrate our results in the context of the variational quantum eigensolver (VQE) on noisy and noiseless simulations.

DOI: 10.1103/physrevresearch.4.033217

Related papers

Error Analysis of the Variational Quantum Eigensolver Algorithm

Sebastian Brandhofer, Simon J. Devitt, Ilia Polian

Variational quantum algorithms have been one of the most intensively studied applications for near-term quantum computing applications. The noisy intermediate-scale quantum (NISQ) regime, where small enough algorithms can be run successfully on noisy quantum computers expected during the next 5 years, is driving both a large amount of research work and a significant amount of private sector funding. Therefore, it is important to understand whether variational algorithms are effective at successfully converging to the correct answer in presence of noise. We perform a comprehensive study of the variational quantum eigensolver (VQE) and its individual quantum subroutines. Building on asymptotic bounds, we show through explicit simulation that the VQE algorithm effectively collapses already when single errors occur during a quantum processing call. We discuss the significant implications of this result in the context of being able to run any variational type algorithm without resource expensive error correction protocols.

arXiv:2301.07263IEEE/ACM International Symposium on Nanoscale Architectures (NANOARCH)Nov 8, 20212 citations

Optimization Verification and Engineered Reliability of Quantum Computers (OVER-QC).

Mohan Sarovar

Quantumtechnologies, especially quantum computers, show great promise for revolutionizing high-performance computing and simulation.As prototype quantum computers come online, it is becoming clear that obtaining useful output from such devices will require layers of sophisticated classical software that provide interpretation and analysis of the quantum computer's state and output.We will develop critical components in this "software stack" with a particular focus on enabling near-term Noisy Intermediate-Scale Quantum (NISQ) technologies.We have identified three critical needs for near-term quantum computing platforms, and the project is structured around three thrusts that address these needs.Application layer e.g., Abstract algorithms and interfaces with classical software.Thrust 3 Logical layer e.g., Compilation software that translates algorithms to quantum circuits.Thrust 1 Hardware layer e.g., Quantum circuit programs and hardware-level error mitigation.Thrust 2 Verification of correctness of circuit compilations New robust circuit compilations Verification of' correctness of new VHP heuristics Symmetries, influential circuit parameters New VHP heuristicsHow the project thrusts fit into the conventional picture of a quantum computing software stack, and how the outcomes of each thrust inform the other ones. Research HighlightsProveIt theorem proving assistant pv

Jan 24, 20200 citations

Impact of Unreliable Devices on Stability of Quantum Computations

Samudra Dasgupta, Travis S. Humble

Noisy intermediate-scale quantum (NISQ) devices are valuable platforms for testing the tenets of quantum computing, but these devices are susceptible to errors arising from de-coherence, leakage, cross-talk, and other sources of noise. This raises concerns regarding the stability of results when using NISQ devices since strategies for mitigating errors generally require well-characterized and stationary error models. Here, we quantify the reliability of NISQ devices by assessing the necessary conditions for generating stable results within a given tolerance. We use similarity metrics derived from device characterization data to derive and validate bounds on the stability of a 5-qubit implementation of the Bernstein-Vazirani algorithm. Simulation experiments conducted with noise data from IBM washington, spanning January 2022 to April 2023, revealed that the reliability metric fluctuated between 41% and 92%. This variation significantly surpasses the maximum allowable threshold of 2.2% needed for stable outcomes. Consequently, the device proved unreliable for consistently reproducing the statistical mean in the context of the Bernstein-Vazirani circuit.

arXiv:2307.06833ACM Transactions on Quantum ComputingJul 29, 20247 citations

Noise robust detection of quantum phase transitions

Kevin Lively, Tim Bode, Jochen Szangolies +2 more

Quantum computing allows for the manipulation of highly correlated states whose properties quickly go beyond the capacity of any classical method to calculate. Thus one natural problem which could lend itself to quantum advantage is the study of ground-states of condensed matter models, and the transitions between them. However, current levels of hardware noise can require extensive application of error-mitigation techniques to achieve reliable computations. In this work, we use several IBM devices to explore a finite-size spin model with multiple “phaselike” regions characterized by distinct ground-state configurations. Using preoptimized Variational Quantum Eigensolver (VQE) solutions, we demonstrate that in contrast to calculating the energy, where zero-noise extrapolation is required in order to obtain qualitatively accurate yet still unreliable results, calculations of the energy derivative, two-site spin correlation functions, and the fidelity susceptibility yield accurate behavior across multiple regions, even with minimal or no application of error-mitigation approaches. Taken together, these sets of observables could be used to identify level crossings in a simple, noise-robust manner which is agnostic to the method of ground state preparation. This work shows promising potential for near-term application to identifying quantum phase transitions, including avoided crossings and nonadiabatic conical intersections in electronic structure calculations. Published by the American Physical Society 2024

arXiv:2402.18953Physical Review ResearchDec 10, 20248 citations

Noise Resilience and Robust Convergence Guarantees for the Variational Quantum Eigensolver

Mirko Legnini, Julian Berberich

Variational Quantum Algorithms (VQAs) are a class of hybrid quantum-classical algorithms that leverage on classical optimization tools to find the optimal parameters for a parameterized quantum circuit. One relevant application of VQAs is the Variational Quantum Eigensolver (VQE), which aims at steering the output of the quantum circuit to the ground state of a certain Hamiltonian. Recent works have provided global convergence guarantees for VQEs under suitable local surjectivity and smoothness hypotheses, but little has been done in characterizing convergence of these algorithms when the underlying quantum circuit is affected by noise. In this work, we derive an upper bound on the error on the optimal parameters of a VQE under the effect of different coherent and incoherent noise processes. We then procced to show robust convergence guarantees of the algorithm to the perturbed optimal parameters. Our work provides novel theoretical insight into the behavior of VQAs subject to noise. Furthermore, we accompany our results with numerical simulations implemented via Pennylane.

quant-pharXiv:2601.16758Jan 26, 20260 citations

Reducing runtime and error in VQE using deeper and noisier quantum circuits

Amara Katabarwa, Alexander A. Kunitsa, Borja Peropadre +1 more

The rapid development of noisy intermediate-scale quantum (NISQ) devices has raised the question of whether or not these devices will find commercial use. Unfortunately, a major shortcoming of many proposed NISQ-amenable algorithms, such as the variational quantum eigensolver (VQE), is coming into view: the algorithms require too many independent quantum measurements to solve practical problems in a reasonable amount of time. This motivates the central question of our work: how might we speed up such algorithms in spite of the impact of error on NISQ computations? We demonstrate on quantum hardware that the estimation of expectation values, a core subroutine of many quantum algorithms including VQE, can be improved in terms of precision and accuracy by using a technique we call Robust Amplitude Estimation. Consequently, this method reduces the runtime to achieve the same mean-squared error compared to the standard prepare-and-measure estimation method. The surprising result is that by using deeper, and therefore more error-prone, quantum circuits, we realize more accurate quantum computations in less time. As the quality of quantum devices improves, this method will provide a proportional reduction in estimation runtime. This technique may be used to speed up quantum computations into the regime of early fault-tolerant quantum computation and aid in the realization of quantum advantage.

arXiv:2110.10664Oct 20, 20216 citations