Terminal iterative learning control(TILC) is developed to reduce the error between system output and a fixed desired point at the terminal end of operation interval over iterations under strictly identical initial con...Terminal iterative learning control(TILC) is developed to reduce the error between system output and a fixed desired point at the terminal end of operation interval over iterations under strictly identical initial conditions. In this work, the initial states are not required to be identical further but can be varying from iteration to iteration. In addition, the desired terminal point is not fixed any more but is allowed to change run-to-run. Consequently, a new adaptive TILC is proposed with a neural network initial state learning mechanism to achieve the learning objective over iterations. The neural network is used to approximate the effect of iteration-varying initial states on the terminal output and the neural network weights are identified iteratively along the iteration axis.A dead-zone scheme is developed such that both learning and adaptation are performed only if the terminal tracking error is outside a designated error bound. It is shown that the proposed approach is able to track run-varying terminal desired points fast with a specified tracking accuracy beyond the initial state variance.展开更多
Human experts cannot efficiently access physical information of a quantum many-body states by simply "reading"its coefficients, but have to reply on the previous knowledge such as order parameters and quantu...Human experts cannot efficiently access physical information of a quantum many-body states by simply "reading"its coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements.We demonstrate that convolutional neural network(CNN) can learn from coefficients of many-body states or reduced density matrices to estimate the physical parameters of the interacting Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states(or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. By assuming certain constraints on the training set for the sake of balance, QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately estimate the parameters of the states beyond such training regions. For instance, our results show that QubismNet can estimate the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work provides a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.展开更多
The shadow tomography problem introduced by[1]is an important problem in quantum computing.Given an unknown-qubit quantum state,the goal is to estimate tr■,...,tr■using as least copies of■as possible,within an addi...The shadow tomography problem introduced by[1]is an important problem in quantum computing.Given an unknown-qubit quantum state,the goal is to estimate tr■,...,tr■using as least copies of■as possible,within an additive error of,whereF1,...,FM are known-outcome measurements.In this paper,we consider the shadow tomography problem with a potentially inaccurate prediction■of the true state■.This corresponds to practical cases where we possess prior knowledge of the unknown state.For example,in quantum verification or calibration,we may be aware of the quantum state that the quantum device is expected to generate.However,the actual state it generates may have deviations.We introduce an algorithm with sample complexity■(nmax{■ε}log2M/ε4.In the generic case,even if the prediction can be arbitrarily bad,our algorithm has the same complexity as the best algorithm without prediction[2].At the same time,as the prediction quality improves,the sample complexity can be reduced smoothly to■(nlog2M/ε3)when the trace distance between the prediction and the unknown state is■(ε).Furthermore,we conduct numerical experiments to validate our theoretical analysis.The experiments are constructed to simulate noisy quantum circuits that reflect possible real scenarios in quantum verification or calibration.Notably,our algorithm outperforms the previous work without prediction in most settings.展开更多
基金supported by National Natural Science Foundation of China(Nos.61374102,61433002 and 61120106009)High Education Science&Technology Fund Planning Project of Shandong Province of China(No.J14LN30)
文摘Terminal iterative learning control(TILC) is developed to reduce the error between system output and a fixed desired point at the terminal end of operation interval over iterations under strictly identical initial conditions. In this work, the initial states are not required to be identical further but can be varying from iteration to iteration. In addition, the desired terminal point is not fixed any more but is allowed to change run-to-run. Consequently, a new adaptive TILC is proposed with a neural network initial state learning mechanism to achieve the learning objective over iterations. The neural network is used to approximate the effect of iteration-varying initial states on the terminal output and the neural network weights are identified iteratively along the iteration axis.A dead-zone scheme is developed such that both learning and adaptation are performed only if the terminal tracking error is outside a designated error bound. It is shown that the proposed approach is able to track run-varying terminal desired points fast with a specified tracking accuracy beyond the initial state variance.
基金Supported by the National Natural Science Foundation of China (Grant Nos. 12004266, 11834014 and 11975050)the Beijing Natural Science Foundation (Grant Nos. 1192005 and Z180013)+1 种基金the Foundation of Beijing Education Committees (Grant No.KM202010028013)the Academy for Multidisciplinary Studies,Capital Normal University。
文摘Human experts cannot efficiently access physical information of a quantum many-body states by simply "reading"its coefficients, but have to reply on the previous knowledge such as order parameters and quantum measurements.We demonstrate that convolutional neural network(CNN) can learn from coefficients of many-body states or reduced density matrices to estimate the physical parameters of the interacting Hamiltonians, such as coupling strengths and magnetic fields, provided the states as the ground states. We propose QubismNet that consists of two main parts: the Qubism map that visualizes the ground states(or the purified reduced density matrices) as images, and a CNN that maps the images to the target physical parameters. By assuming certain constraints on the training set for the sake of balance, QubismNet exhibits impressive powers of learning and generalization on several quantum spin models. While the training samples are restricted to the states from certain ranges of the parameters, QubismNet can accurately estimate the parameters of the states beyond such training regions. For instance, our results show that QubismNet can estimate the magnetic fields near the critical point by learning from the states away from the critical vicinity. Our work provides a data-driven way to infer the Hamiltonians that give the designed ground states, and therefore would benefit the existing and future generations of quantum technologies such as Hamiltonian-based quantum simulations and state tomography.
基金supported by the National Natural Science Foundation of China(Grant Nos.62325210,and 62272441)the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDB28000000)+1 种基金supported by the National Natural Science Foundation of China(Grant Nos.62372006,92365117)the Fundamental Research Funds for the Central Universities,Peking University.
文摘The shadow tomography problem introduced by[1]is an important problem in quantum computing.Given an unknown-qubit quantum state,the goal is to estimate tr■,...,tr■using as least copies of■as possible,within an additive error of,whereF1,...,FM are known-outcome measurements.In this paper,we consider the shadow tomography problem with a potentially inaccurate prediction■of the true state■.This corresponds to practical cases where we possess prior knowledge of the unknown state.For example,in quantum verification or calibration,we may be aware of the quantum state that the quantum device is expected to generate.However,the actual state it generates may have deviations.We introduce an algorithm with sample complexity■(nmax{■ε}log2M/ε4.In the generic case,even if the prediction can be arbitrarily bad,our algorithm has the same complexity as the best algorithm without prediction[2].At the same time,as the prediction quality improves,the sample complexity can be reduced smoothly to■(nlog2M/ε3)when the trace distance between the prediction and the unknown state is■(ε).Furthermore,we conduct numerical experiments to validate our theoretical analysis.The experiments are constructed to simulate noisy quantum circuits that reflect possible real scenarios in quantum verification or calibration.Notably,our algorithm outperforms the previous work without prediction in most settings.
