ArsoNISQ: Analyzing Quantum Algorithms on Near-Term Architectures

Abstract

While scalable, fully error corrected quantum computing is years or even decades away, there is considerable interest in noisy intermediate-scale quantum computing (NISQ). In this paper, we introduce the ArsoNISQ framework that determines the tolerable error rate of a given quantum algorithm computation, i.e. quantum circuits, and the success probability of the computation given a success criterion and a NISQ computer. ArsoNISQ is based on simulations of quantum circuits subject to errors according to the Pauli error model.ArsoNISQ was evaluated on a set of quantum algorithms that can incur a quantum speedup or are otherwise relevant to NISQ computing. Despite optimistic expectations in recent literature, we did not observe quantum algorithms with intrinsic robustness, i.e. algorithms that tolerate one error on average, in this evaluation. The evaluation demonstrated, however, that the quantum circuit size sets an upper bound for its tolerable error rate and quantified the difference in tolerate error rates for quantum circuits of similar sizes. Thus, the framework can assist quantum algorithm developers in improving their implementation and selecting a suitable NISQ computing platform. Extrapolating the results into the quantum advantage regime suggests that the error rate of larger quantum computers must decrease substantially or active quantum error correction will need to be deployed for most of the evaluated algorithms.

Special Session: Noisy Intermediate-Scale Quantum (NISQ) Computers—How They Work, How They Fail, How to Test Them?

“…For combinations of quantum circuits and Pauli error rate where less than one Pauli error occurs during the quantum circuit computation on average, an exhaustive error simulation was employed. For this exhaustive error simulation, one Pauli X, Z, or Y error was simulated successively at every space-time location in the quantum circuit and the impact of these errors on the target success criterion was scaled according to the specified Pauli error rates [15]. For combinations of quantum circuits and Pauli error rates that incur more than one Pauli error per quantum circuit computation on average, Monte Carlo simulations were conducted to obtain the success probability and tolerable Pauli error rate.…”

“…As with physical interferometers, where a minor misalignment can completely disrupt the interference effect and make the device non-functional, even one error in a quantum algorithm can disrupt the required computational interference effect, resulting in incorrect output. It has been demonstrated for a variety of quantum algorithms that single errors can dramatically reduce the probability of success of generating the correct output [15], [16]. This makes p < 1/Awhich represents the error rate needed such that one error occurs during execution on average-a good bound for the error tolerance of an algorithm.…”

“…A more accurate approach to determine the tolerable error rate of a quantum computation is to conduct simulations subject to errors [15], [16], [25]- [31]. Using Monte Carlo or exhaustive error simulations, the error rate at which the quantum computation starts failing the target success criteria can be determined.…”

“…While simulations subject to errors are a suitable choice to determine the tolerable error rate, they also incur an exponential runtime and space overhead in the number of qubits in general. It is therefore crucial to reduce the simulation effort by a suitable choice of error model and simulation techniques [15].…”

On Structural Identifiability of System with Nonsymmetric Nonlinearities

“…Other approaches to the nonsymmetric Bouc-Wen hysteresis identification consider in [8]. A nonsymmetric switching element used [9] to reduce its own losses in optical waveguides. A phenomenological hysteresis model studies to scribe a magnetostrictive actuator in [11].…”