An overview of quantum error mitigation formulas

Minimizing the effect of noise is essential for quantum computers.The conventional method to protect qubits against noise is through quantum error correction.However,for current quantum hardware in the so-called noisy intermediate-scale quantum(NISQ)era,noise presents in these systems and is too high for error correction to be beneficial.Quantum error mitigation is a set of alternative methods for minimizing errors,including error extrapolation,probabilistic error cancella-tion,measurement error mitigation,subspace expansion,symmetry verification,virtual distillation,etc.The requirement for these methods is usually less demanding than error correction.Quantum error mitigation is a promising way of reduc-ing errors on NISQ quantum computers.This paper gives a comprehensive introduction to quantum error mitigation.The state-of-art error mitigation methods are covered and formulated in a general form,which provides a basis for comparing,combining and optimizing different methods in future work.

NLOS error mitigation with information fusion algorithm for UWB ranging systems

This article puts forward a scalar weighting information fusion （IF） smoother with modified biased Kalman filter （BKF） and maximum likelihood estimation （MLE） to mitigate the ranging errors in ultra wide band （UWB） systems. The information fusion algorithm uses both the time of arrival （TOA） and received signal strength （RSS） measurement data to improve the ranging accuracy. At first, the ranging protocol of IEEE 802.15.4a acts as a multi-sensor system with multi-scale sampling. Then the scalar-based IF smoother accurately estimates the range measurement in the line of sight （LOS） and non-line of sight （NLOS） condition of UWB sensor network, during which the effectiveness of the IF in mitigating errors is especially focused during the LOS/NLOS transitions. Simulation results show that the proposed hybrid TOA-RSS fusion approach indicates a performance improvement compared with the usual TOA-only and other IF method, and the estimated ranging metrics can be used for achieving higher accuracy in location estimation and target tracking.

Near-term quantum computing techniques: Variational quantum algorithms, error mitigation, circuit compilation, benchmarking and classical simulation

Quantum computing is a game-changing technology for global academia,research centers and industries including computational science,mathematics,finance,pharmaceutical,materials science,chemistry and cryptography.Although it has seen a major boost in the last decade,we are still a long way from reaching the maturity of a full-fledged quantum computer.That said,we will be in the noisy-intermediate scale quantum(NISQ)era for a long time,working on dozens or even thousands of qubits quantum computing systems.An outstanding challenge,then,is to come up with an application that can reliably carry out a nontrivial task of interest on the near-term quantum devices with non-negligible quantum noise.To address this challenge,several near-term quantum computing techniques,including variational quantum algorithms,error mitigation,quantum circuit compilation and benchmarking protocols,have been proposed to characterize and mitigate errors,and to implement algorithms with a certain resistance to noise,so as to enhance the capabilities of near-term quantum devices and explore the boundaries of their ability to realize useful applications.Besides,the development of near-term quantum devices is inseparable from the efficient classical sim-ulation,which plays a vital role in quantum algorithm design and verification,error-tolerant verification and other applications.This review will provide a thorough introduction of these near-term quantum computing techniques,report on their progress,and finally discuss the future prospect of these techniques,which we hope will motivate researchers to undertake additional studies in this field.

Simple Mitigation Strategy for a Systematic Gate Error in IBMQ

In this paper, we report the observation and characterisation of a systematic error in the implementation of U3 gates in the IBM quantum computers. By measuring the effect of this gate for various rotation angles the error appears as an over-rotation, whose magnitude does not correlate with IBM’s cited errors calculated using Clifford randomized benchmarking. We propose a simple mitigation procedure to limit the effects of this error. We show that using a simple mitigation strategy one can obtain improved results in the observed value for the CHSH inequality, measured in a cloud-based quantum computer. This work highlights the utility of simple mitigation strategies for short-depth quantum circuits.

Analysis and mitigation of bump magnetic field tracking errors in a multiturn injection system

Purpose The Space Environment Simulation and Research Infrastructure(SESRI)is a cluster of accelerators designed to simulate the cosmic radiation environment by generating particles of various types and energies.Among these accelerators,a synchrotron in the 300 MeV proton and heavy ion accelerator complex utilizes a multiturn injection scheme with four bump magnets to accumulate proton and heavy ion beams effectively.However,the bump magnetic field experiences a rapid drop rate of up to 1000 T/s,inevitably leading to a deviation(field tracking error)from the ideal magnetic field.The injection efficiency and particle distribution are significantly affected by this field tracking error,as evaluated by the ACCSIM code.Method During the device testing stage,the sources of field tracking errors were identified by analysis of the bump power supplies and the field of the magnets.Mitigation techniques were then implemented to reduce the field tracking error from[Math Processing Error]to[Math Processing Error]throughout the entire power supply,transmission cable,and magnet chain.Results Moreover,the successful injection and accumulation of beams during the operational phase of the synchrotron confirmed the effectiveness of the proposed mitigation methods.Additionally,a magnetic field measurement system was developed to monitor the magnetic field tracking error online.Conclusion The combination of the field tracking error mitigation methods and the measurement system provides valuable guidance for optimizing the magnetic fields with rapid drop rates.

HUID:DBN-Based Fingerprint Localization and Tracking System with Hybrid UWB and IMU

High-precision localization technology is attracting widespread attention in harsh indoor environments.In this paper,we present a fingerprint localization and tracking system to estimate the locations of the tag based on a deep belief network(DBN).In this system,we propose using coefficients as fingerprints to combine the ultra-wideband(UWB)and inertial measurement unit(IMU)estimation linearly,termed as a HUID system.In particular,the fingerprints are trained by a DBN and estimated by a radial basis function(RBF).However,UWB-based estimation via a trilateral method is severely affected by the non-line-of-sight(NLoS)problem,which limits the localization precision.To tackle this problem,we adopt the random forest classifier to identify line-of-sight(LoS)and NLoS conditions.Then,we adopt the random forest regressor to mitigate ranging errors based on the identification results for improving UWB localization precision.The experimental results show that the mean square error(MSE)of the localization error for the proposed HUID system reduces by 12.96%,50.16%,and 64.92%compared with that of the existing extended Kalman filter(EKF),single UWB,and single IMU estimation methods,respectively.

Noise-resistant quantum state compression readout

Qubit measurement is generally the most error-prone operation that degrades the performance of near-term quantum devices,and the exponential decay of readout fidelity severely impedes the development of large-scale quantum information processing.Given these disadvantages, we present a quantum state readout method, named compression readout, that naturally avoids large multi-qubit measurement errors by compressing the quantum state into a single qubit for measurement. Our method generally outperforms direct measurements in terms of accuracy, and the advantage grows with the system size. Moreover, because only one-qubit measurements are performed, our method requires solely a fine readout calibration on one qubit and is free of correlated measurement error, which drastically diminishes the demand for device calibration. These advantages suggest that our method can immediately boost the readout performance of near-term quantum devices and will greatly benefit the development of large-scale quantum computing.

Algorithm for simulating ocean circulation on a quantum computer

The accurate and efficient simulation of ocean circulation is a fundamental topic in marine science;however,it is also a well-known and dauntingly difficult problem that requires solving nonlinear partial differential equations with multiple variables.In this paper,we present for the first time an algorithm for simulating ocean circulation on a quantum computer to achieve a computational speedup.Our approach begins with using primitive equations describing the ocean dynamics and then discretizing these equations in time and space.It results in several linear system of equations(LSE)with sparse coefficient matrices.We solve these sparse LSE using the variational quantum linear solver that enables the present algorithm to run easily on near-term quantum computers.Additionally,we develop a scheme for manipulating the data flow in the algorithm based on the quantum random access memory and l∞norm tomography technique.The efficiency of our algorithm is verified using multiple platforms,including MATLAB,a quantum virtual simulator,and a real quantum computer.The impact of the number of shots and the noise of quantum gates on the solution accuracy is also discussed.Our findings demonstrate that error mitigation techniques can efficiently improve the solution accuracy.With the rapid advancements in quantum computing,this work represents an important first step toward solving the challenging problem of simulating ocean circulation using quantum computers.