Quantum computers open the possibility of performing real-time calculations for quantum field theory scattering processes. We propose to use an index averaging the absolute value of the difference between the accurately calculated Trotter evolution of site occupations and their actual measurements on NISQ machines. The average is over all the qubits for a certain number of Trotter steps. We use this metric to quantify the progress made in successive state-of-the-art machines and error-mitigation techniques. We illustrate the concept with the transverse Ising model in one spatial dimension with four sites using three of IBM's quantum computers (Almaden, Boeblingen, and Melbourne). We discuss the size of the Trotter steps needed to achieve physics goals. Using the proposed metric, we show that readout mitigation methods and Richardson extrapolations of mitigated measurements are very effective for specific numbers of Trotter steps of a chosen size. This specific choice can be applied to other machines and noise mitigation methods. On the other hand, a reliable algorithmic mitigation would require a significantly larger number of smaller Trotter steps.
Benchmarking quantum computers for real-time evolution of a (1+1) field theory with error mitigation
Quantum computers open the possibility of performing real-time calculations for quantum field theory scattering processes. We propose to use an index averaging the absolute value of the difference between the accurately calculated Trotter evolution of site occupations and their actual measurements on NISQ machines. The average is over all the qubits for a certain number of Trotter steps. We use this metric to quantify the progress made in successive state-of-the-art machines and error-mitigation techniques. We illustrate the concept with the transverse Ising model in one spatial dimension with four sites using three of IBM's quantum computers (Almaden, Boeblingen, and Melbourne). We discuss the size of the Trotter steps needed to achieve physics goals. Using the proposed metric, we show that readout mitigation methods and Richardson extrapolations of mitigated measurements are very effective for specific numbers of Trotter steps of a chosen size. This specific choice can be applied to other machines and noise mitigation methods. On the other hand, a reliable algorithmic mitigation would require a significantly larger number of smaller Trotter steps.
We discuss real-time evolution for the quantum Ising model in one spatial dimension with Ns sites. In the limit where the nearest-neighbor interactions J in the spatial directions are small, there is a simple physical picture where qubit states can be interpreted as approximate particle occupations. Using exact diagonalization, for initial states with one or two particles, we show that for small J, discrete Bessel functions provide very accurate expressions for the evolution of the occupancies corresponding to initial states with one and two particles. Boundary conditions play an important role when the evolution time is long enough. We discuss a Trotter procedure to implement the evolution on existing quantum computers and discuss the error associated with the Trotter step size. We discuss the effects of gate and measurement errors on the evolution of one- and two-particle states using four and eight-qubits circuits approximately corresponding to existing or near-term quantum computers.
In this study, we investigate Trotter evolution in the Gross-Neveu and hyperbolic Ising models in two spacetime dimensions, using quantum computers. We identify different sources of errors prevalent in various quantum processing units and discuss challenges to scale up the size of the computation. We present benchmark results obtained on a variety of platforms and employ a range of error mitigation techniques to address coherent and incoherent noise. By comparing these mitigated outcomes with exact diagonalization results and density matrix renormalization group calculations, we assess the effectiveness of our approaches. Moreover, we demonstrate the implementation of an out-of-time-ordered correlator (OTOC) protocol using IBM's quantum computers.
Real-time scattering calculations on a noisy intermediate scale quantum (NISQ) quantum computer are disrupted by errors that accumulate throughout the circuits. To improve the accuracy of such physics simulations, one can supplement the application circuits with a recent error mitigation strategy known as noiseless output extrapolation (NOX). We tested these error mitigation protocols on a transverse field Ising model and improved upon previous phase shift calculations. Our proof-of-concept 4-qubit application circuits were run on several IBM quantum computing hardware architectures. We introduce metrics that show between 22% and 73% error reduction for circuit depths ranging from 13 to 37 hard cycles, confirming that the NOX technique applies to circuits with a broad range of failure rates. We also observed an approximate 28% improvement in the accuracy of the time delay calculation of the scattering phase shift. These observations on different cloud-accessible devices confirm that NOX improves performance even when circuits are executed in substantially time-separated batches. Finally, we provide a heuristic method to obtain systematic error bars on the mitigated results, compare them with empirical errors and discuss their effects on phase shift estimates.
Real-time scattering calculations on a Noisy Intermediate Scale Quantum (NISQ) quantum computer are disrupted by errors that accumulate throughout the circuits. To improve the accuracy of such physics simulations, one can supplement the application circuits with a recent error mitigation strategy known as Noisy Output eXtrapolation (NOX). We tested these error mitigation protocols on a Transverse Field Ising model and improved upon previous calculations of the phase shift. Our proof-of-concept 4-qubit application circuits were run on several IBM quantum computing hardware architectures. Metrics were introduced that show between 21\% and 74\% error reduction for circuit depths ranging from 14 to 37 hard cycles, confirming that the NOX technique applies to circuits with a broad range of failure rates. This observation on different cloud-accessible devices further confirms that NOX provides performance improvements even in the advent where circuits are executed in substantially time-separated batches. Finally, we provide a heuristic method to obtain systematic error bars on the mitigated results, compare them with empirical errors and discuss their effects on phase shift estimates.
Quantum computing gives direct access to the study of the real-time dynamics of quantum many-body systems. In principle, it is possible to directly calculate non-equal-time correlation functions, from which one can detect interesting phenomena, such as the presence of quantum scars or dynamical quantum phase transitions. In practice, these calculations are strongly affected by noise, due to the complexity of the required quantum circuits. As a testbed for the evaluation of the real-time evolution of observables and correlations, the dynamics of the Zn Schwinger model in a one-dimensional lattice is considered. To control the computational cost, we adopt a quantum-classical strategy that reduces the dimensionality of the system by restricting the dynamics to the Dirac vacuum sector and optimizes the embedding into a qubit model by minimizing the number of three-qubit gates. The time evolution of particle-density operators in a non-equilibrium quench protocol is both simulated in a bare noisy condition and implemented on a physical IBM quantum device. In either case, the convergence towards a maximally mixed state is targeted by means of different error mitigation techniques. The evaluation of the particle-density correlation shows a well-performing post-processing error mitigation for properly chosen coupling regimes.
Abstract Quantum computing has recently emerged as a novel paradigm for solving problems otherwise intractable on classical computers, yet the practical progress of quantum computers is severely impacted by noise, decoherence, and imperfect gate operations in Noisy Intermediate-Scale Quantum (NISQ) devices. Specific to IBM Quantum hardware, imperfections due to readout error, gate errors, and device drift, which depends on time, resolves limits for the accuracy of outputs from our algorithms. The mitigation strategies currently used, for example, Measurement Error Mitigation (MEM), Zero Noise Extrapolation (ZNE), and Clifford Data Regression (CDR), offer improvement over raw, unmitigated outputs, but they are static and not dynamic; the reduction of noise in within an NISQ device is temporal and can vary in patterns that are non-zero. In addition to this, using the conventional methods provides inconsistent and suboptimal results.This study will provide enhanced reliability with respect to performing quantum computation on IBM Quantum hardware with a unique mitigation framework that is adaptive and computationally efficient for a high-fidelity output. The problem taken on here is the failure of existing error mitigation strategies to provide adaptive noise compensation, as they assume a statically-distributed error, despite the performance-related characteristics already being documented in regards to calibration drift and variation over time.To achieve this, we propose a Hybrid Adaptive Error Mitigation (HAEM) approach that includes baseline measurement error mitigation and an additional correction layer that utilizes realtime calibration information, along with lightweight machine learning models. The approach can be broken down into three steps: (i) perform standard measurement error mitigation to reduce classical readout noise, (ii) execute compact calibration circuits, such as Bell states, GHZ states and Clifford benchmarks to capture then current error profile of the device, and (iii) use a lightweight machine learning model (having been trained on historical and newest calibration data) to dynamically change the mitigation weights applied for the target quantum algorithm. All implementation is done using Qiskit Runtime to ensure low-latency execution, and we completed experiments on both Qiskit Aer noisy simulators and IBM Quantum devices.Initial results suggest HAEM improved the outputs of quantum algorithms' fidelity compared to the unmitigated runs and the baseline measurement error mitigation (MEM) runs. On the noisy simulators, HAEM increased fidelity from a raw performance of 0.65 to 0.87, nearly a 34% improvement. In fairer hardware-like scenarios, fidelity-on-average was persistently 12% better than MEM, with nearly equal time duration for the additional adaptive measurements. The adaptive aspect of HAEM consistently supported subsequent calibration cycles of the device and was effective to continue providing fidelity improvements despite the static mitigation performance degrading.To sum up, the proposed HAEM framework is a modern and viable alternative for error mitigation which brings together the benefits of baseline approaches with corrections that are driven by fixed-function error-corrective, adaptive learning. As both learning-based and standard baseline approaches can only achieve fixed levels of performance, HAEM, through its use of noise mitigation both at execution time and through correlating it with standard data, provides a route towards reliable quantum computations on current IBM hardware. HAEM also presents a contribution to the NISQ error-resilient landscape, and however it is intended that it will continue to improve future applications of hybrid workflows of quantum and classical computation where error mitigation and resilience is important.