Abstract The presence of noise in quantum computers hinders their effective operation. Even though quantum error correction can theoretically remedy this problem, its practical realization is still a challenge. Testing and benchmarking noisy, intermediate-scale quantum (NISC) computers is therefore of high importance. Here, we suggest the application of the so-called quantum state matching protocol for testing purposes. This protocol was originally proposed to determine if an unknown quantum state falls in a prescribed neighborhood of a reference state. We decompose the unitary specific to the protocol and construct the quantum circuit implementing one step of the dynamics for different characteristic parameters of the scheme and present test results for two different IBM quantum computers. By comparing the experimentally obtained relative frequencies of success to the ideal success probability with a maximum statistical tolerance, we discriminate statistical errors from device specific ones. For the characterization of noise, we also use the fact that while the output of the ideal protocol is insensitive to the internal phase of the input state, the actual implementation may lead to deviations. For systematically varied inputs we find that the device with the smaller quantum volume performs better on our tests than the one with larger quantum volume, while for random inputs they show a more similar performance.
Abstract The presence of noise in quantum computers hinders their effective operation. Even though quantum error correction can theoretically remedy this problem, its practical realization is still a challenge. Testing and benchmarking noisy, intermediate-scale quantum (NISC) computers is therefore of high importance. Here, we suggest the application of the so-called quantum state matching protocol for testing purposes. This protocol was originally proposed to determine if an unknown quantum state falls in a prescribed neighborhood of a reference state. We decompose the unitary specific to the protocol and construct the quantum circuit implementing one step of the dynamics for different characteristic parameters of the scheme and present test results for two different IBM quantum computers. By comparing the experimentally obtained relative frequencies of success to the ideal success probability with a maximum statistical tolerance, we discriminate statistical errors from device specific ones. For the characterization of noise, we also use the fact that while the output of the ideal protocol is insensitive to the internal phase of the input state, the actual implementation may lead to deviations. For systematically varied inputs we find that the device with the smaller quantum volume performs better on our tests than the one with larger quantum volume, while for random inputs they show a more similar performance.
Applying post selection in each step of an iterated protocol leads to sensitive quantum dynamics that may be utilized to test and benchmark current quantum computers. An example of this type of protocols was originally proposed for the task of matching an unknown quantum state to a reference state. We propose to employ the quantum state matching protocol for the purpose of testing and benchmarking quantum computers. In particular, we implement this scheme on freely available IBM superconducting quantum computers. By comparing measured values with the theoretical conditional probability of the single, final post-selected qubit, which is easy to calculate classically, we define a benchmark metric. Additionally, the standard deviation of the experimental results from their average serves as a secondary benchmark metric, characterizing fluctuations in the given device. A peculiar feature of the considered protocol is that there is a phase parameter of the initially prepared state, on which the resulting conditional probability should not depend. A careful analysis of the measured values indicates that its dependence on the initial phase can reveal useful information about coherent gate errors of the quantum device.
Abstract Applying post selection in each step of an iterated protocol leads to sensitive quantum dynamics that may be utilized to test and benchmark current quantum computers. An example of this type of protocols was originally proposed for the task of matching an unknown quantum state to a reference state. We propose to employ the quantum state matching protocol for the purpose of testing and benchmarking quantum computers. In particular, we implement this scheme on freely available IBM superconducting quantum computers. By comparing measured values with the theoretical conditional probability of the single, final post-selected qubit, which is easy to calculate classically, we define a benchmark metric. Additionally, the standard deviation of the experimental results from their average serves as a secondary benchmark metric, characterizing fluctuations in the given device. A peculiar feature of the considered protocol is that there is a phase parameter of the initially prepared state, on which the resulting conditional probability should not depend. A careful analysis of the measured values indicates that its dependence on the initial phase can reveal useful information about coherent gate errors of the quantum device.
The characterization of noisy quantum circuits is an important step in the development of large-scale quantum computers. As experimental quantum architectures approach the threshold for fault-tolerant quantum computing, obtaining a benchmark of process fidelities is needed to verify the integrity of the system and ensure functionality. Additionally, the ability to successfully implement a quantum code of choice may depend on the type of noise that is present in the system. It is therefore necessary to characterize not only the fidelity of the process, but also the structure of the noise. \n \nRandomized benchmarking is a characterization protocol which extracts partial information from a noisy quantum process. This thesis gives a detailed review of the randomized benchmarking protocol, and presents the results of three collaborative projects which use techniques similar to randomized benchmarking to obtain previously hidden information. The first protocol is designed to obtain a benchmark on loss errors. This protocol also provides information on the detector efficiency and an additional constraint on estimated parameters from randomized benchmarking. The second protocol is an extension of the first, under the special case of coherent leakage errors, for which we obtain an estimate of the leakage rate. The third protocol provides a method of testing for spatial correlations in noisy processes. This test may be used to determine the correlation structure of errors, and the error correcting codes needed for successful experiments in a particular architecture. All protocols presented in this thesis are scalable, platform-independent and insensitive to state preparation and measurement errors. We also provide results of numerical tests of these protocols for simulated noise, which show their accuracy and robustness.
ABSTRACT: Recent research has tackled the problem of mitigating noise present in quantum computers in the Noisy Intermediate-Scale Quantum (NISQ) era to enable precise computations and to benefit from the intrinsic properties of quantum mechanics. For this matter, an important task is the characterization of qubits available in quantum devices so as to provide insights on how to reduce noise on the final output of a quantum circuit. Characterization comprises analysis of noise sources and this information can be used to reduce noise with methods such as Cycle Benchmarking, Quantum Error Mitigation, Quantum Error Correction and others. Here, we study optimization of pulses through Quantum Optimal Control (QOC) to obtain higher gate fidelity. We will explore an algorithm that performs calibration on specific quantum gates by implementing optimized pulse schedules to subsequently use the algorithm for analysis of noise sources. Using calibrated gates as input, several benchmarking protocols, including pulse noise extrapolation, leakage analysis from quantum optimal control, and machine learning based classification of qubit readout, will be tested to extract precise information on how noise influences the analyzed qubits. We will explain and discuss different techniques for obtaining properties of qubits and quantum computers. We will implement state discrimination with a Machine Learning (ML) focus to analyze readout errors caused by factors such as cross-talk and leakage into higher quantum states. We will perform noise fitting of optimized pulses and evaluate the effectiveness of important quantum algorithms at the pulse level.
Context: The main obstacle of quantum computing on its way to scalability is the noisy nature of current hardware. Various types of errors lead to incorrect computational results,and measures such as quantum error mitigation are needed to counteract these errors. Many error mitigation techniques require a thorough understanding of the noise and its impact on computations. Therefore, accurate noise models are indispensable to facilitate meaningful quantum computing in the near future. They also enable realistic simulations of quantum devices. Since these devices are currently limited and quantum computing is expensive, researchers typically rely on simulations for testing their algorithms.Objective: In this thesis, we aim to construct a realistic noise model for quantum computing and optimise its model parameters. The model construction should build on the underlying physical processes, and the number of parameters should scale well with the system size. We also address the evaluation and comparison of different noise models by benchmarks using quantum circuits specific to real-world applications. Finally, we aim to develop useful graphical representations of noise models based on the existing quantum circuit model.Method: We present a benchmarking framework for quantum computing noise models and evaluate it based on benchmarking quality attributes from the literature. Moreover, we construct a quantum computing noise model and develop a training procedure for its parameters. We analyse the parameters of the trained noise model and the impact ofdifferent types of errors on computations. We benchmark the noise model with the above approach and compare it to a noise model provided by IBM’s software development kit Qiskit. Finally, we develop an extension of the quantum circuit model to represent noise channels.Result: The benchmarks performed in this thesis show that our noise model predicts noisy hardware behaviour of IBM’s ibmq_manila quantum device equally well as the Qiskit model, if not better, based on quantum circuits commonly used for variational quantum algorithms. Within the trained noise model, readout error has the most detrimental impact on computations. Our benchmarking approach satisfies relevant quality criteria by choosing suitable quantum circuits and objective functions to compare model predictionsto hardware data. Moreover, the quantum circuit model can be extended meaningfully by noise channels.Conclusion: Our benchmarking approach is suitable for evaluating and comparing quantum computing noise models. In future work, volumetric benchmarks should be performed for various noise models and application contexts. The parameter optimisation based on learning with training circuits yields accurate noise models and shows the importance of mitigating measurement error. Different optimisation algorithms and quantum circuits should be explored, and more types of noise should be incorporated into the noise model.
While fundamental scientific researchers are eagerly anticipating the breakthroughs of quantum computing both in theory and technology, the current quantum computer, i.e. noisy intermediate-scale quantum (NISQ) computer encounters a bottleneck in how to deal with the noisy situation of the quantum machine. It is still urgently required to construct more efficient and reliable benchmarking protocols through which one can assess the noise level of a quantum circuit that is designed for a quantum computing task. The existing methods that are mainly constructed based on a sequence of random circuits, such as randomized benchmarking (RB), have been commonly adopted as the conventional approach owning to its reasonable resource consumption and relatively acceptable reliability, compared with the average gate fidelity. To more deeply understand the performances of the above different randomized-framed benchmarking protocols, we design special random circuit sequences to test the performances of the three selected standard randomized-frame protocols under T1, T2, and coherent errors, which are regarded to be more practical for a superconductor quantum computer. The simulations indicate that MRB, DRB, and CRB sequentially overestimate the average error rate in the presence of T1 and T2 noise, compared with the conventional circuit's average error. Moreover, these methods exhibit almost the same level of sensitivity to the coherent error. Furthermore, the DRB loses its reliability when the strengths of T1 grow. More practically, the simulated conclusion is verified by running the designed tasks for three protocols on the Quafu quantum computation cloud platform. We find that MRB produces a more precise assessment of a quantum circuit conditioned on limited resources. However, the DRB provides a more stable estimation at a specific precision while a more resource-consuming.