arXiv subjects

Zibo Miao

Publications and source records attributed to Zibo Miao.

18 recordsLinked to original sources

arXiv2026

Robust Parametric Quantum Gate Against Stochastic Time-Varying Noise

The performance of quantum processors in the noisy intermediate-scale quantum (NISQ) era is severely constrained by environmental noise and other uncertainties. While the recently proposed quantum control robustness landscape (QCRL) offers a powerful framework for generating robust control pulses for parametric gate families, its application has been practically restricted to quasi-static noise. To address the spectrally complex, time-varying noise prevalent in reality, we propose filter function-enhanced QCRL (FF-QCRL), which integrates filter function formalism into the QCRL framework. The resulting FF-QCRL algorithm minimizes a generalized robustness metric that faithfully encodes the impact of stochastic processes, enabling robust pulse-family generation for parametric gates under realistic time-varying noise. Numerical validation in a representative single-qubit setting confirms the effectiveness of the proposed method.

quant-ph↗

arXiv2025

Tight bounds of quantum speed limit for noisy dynamics via maximum rotation angles

The laws of quantum physics place a limit on the speed of computation. In particular, the evolution time of a system from an initial state to a final state cannot be arbitrarily short. Bounds on the speed of evolution for unitary dynamics have long been studied. A few bounds on the speed of evolution for noisy dynamics have also been obtained recently, which are, however, not tight. In this paper, we present a new framework for quantum speed limit concerning noisy dynamics. Within this framework, we obtain the exact maximum rotation angle that noisy dynamics can achieve at any given time, which gives rise to a tight bound on the evolution time for noisy dynamics. The bound obtained through semi-definite programming highlights the fundamental differences between noisy dynamics and unitary dynamics. Furthermore, we show that the \textit{orthogonalization} time, defined as the minimum time required to evolve any initial state to a state with zero fidelity with respect to the initial state, is generally not applicable to noisy dynamics.

quant-ph↗

arXiv2025

Meta-learning assisted robust control of universal quantum gates with uncertainties

Achieving high-fidelity quantum gates is crucial for reliable quantum computing. However, decoherence and control pulse imperfections pose significant challenges in realizing the theoretical fidelity of quantum gates in practical systems. To address these challenges, we propose the meta-reinforcement learning quantum control algorithm (metaQctrl), which leverages a two-layer learning framework to enhance robustness and fidelity. The inner reinforcement learning network focuses on decision making for specific optimization problems, while the outer meta-learning network adapts to varying environments and provides feedback to the inner network. Our comparative analysis regarding realization of universal quantum gates demonstrates that metaQctrl achieves higher fidelity with fewer control pulses than conventional methods in the presence of uncertainties. These results can contribute to the exploration of the quantum speed limit and facilitate the implementation of quantum circuits with system imperfections involved.

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arXiv2025

Smolyak algorithm assisted robust control for quantum systems with uncertainties

Efficient and systematic numerical methods for robust control design are crucial in quantum systems due to inevitable uncertainties or disturbances. We propose a novel approach that models uncertainties as random variables and quantifies robustness using the expectation of infidelity by reformulating it as a weighted tensor product quadrature. We employ the Smolyak algorithm to develop a parametric robust quantum control scheme, which balances the reduction of computational cost with the enhancement of estimation accuracy. We demonstrate the effectiveness of our proposed algorithm by incorporating the Smolyak sparse grids into conventional gradient-based quantum optimal control methods such as GRAPE and GOAT. In robust control problems concerning quantum gate realization, low infidelity and strong robustness can be achieved. These results contribute to improving the reliability and security of quantum computing and communication systems in the presence of real-world imperfections.

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arXiv2024

Parallel Ising Annealer via Gradient-based Hamiltonian Monte Carlo

Ising annealer is a promising quantum-inspired computing architecture for combinatorial optimization problems. In this paper, we introduce an Ising annealer based on the Hamiltonian Monte Carlo, which updates the variables of all dimensions in parallel. The main innovation is the fusion of an approximate gradient-based approach into the Ising annealer which introduces significant acceleration and allows a portable and scalable implementation on the commercial FPGA. Comprehensive simulation and hardware experiments show that the proposed Ising annealer has promising performance and scalability on all types of benchmark problems when compared to other Ising annealers including the state-of-the-art hardware. In particular, we have built a prototype annealer which solves Ising problems of both integer and fraction coefficients with up to 200 spins on a single low-cost FPGA board, whose performance is demonstrated to be better than the state-of-the-art quantum hardware D-Wave 2000Q and similar to the expensive coherent Ising machine. The sub-linear scalability of the annealer signifies its potential in solving challenging combinatorial optimization problems and evaluating the advantage of quantum hardware.

quant-ph↗

arXiv2023

Cooperation between coherent control and noises in quantum metrology

In this paper we study the cooperation between coherent control and noises in open spin systems, aiming to demonstrate that such cooperation can provide new possibilities for parametrization in quantum metrology. The cooperative scheme proposed here outperforms the standard scheme, with higher precision achieved. More specifically, we illustrate the effect of cooperative interaction between coherent control and noises in conventional single-spin systems described by Lindblad master equations, with the magnitude of a magnetic field taken as the parameter to be estimated and encoded in the noisy dynamics besides the Hamiltonian. The scenarios of both spontaneous emission and dephasing noise have been analyzed, where the associated quantum Fisher information has been given. Furthermore, it has been demonstrated that in the realm where quantum metrology is mostly applied in practice, the precision limit under the cooperative scheme in the presence of noises can surpass the ultimate precision limit under the unitary dynamics. On the other hand, multiple-spin systems have also been considered. We show that the coupling between different spins can help realize non-local parametrization under the cooperative scheme, with the ground state made entangled. This thus leads to the improvement of precision limit, which has been proved and visualized in our paper.

quant-ph↗

arXiv2021

Bhatia-Davis formula in the quantum speed limit

The Bhatia-Davis theorem provides a useful upper bound for the variance in mathematics, and in quantum mechanics, the variance of a Hamiltonian is naturally connected to the quantum speed limit due to the Mandelstam-Tamm bound. Inspired by this connection, we construct a formula, referred to as the Bhatia-Davis formula, for the characterization of the quantum speed limit in the Bloch representation. We first prove that the Bhatia-Davis formula is an upper bound for a recently proposed operational definition of the quantum speed limit, which means it can be used to reveal the closeness between the timescale of certain chosen states to the systematic minimum timescale. In the case of the largest target angle, the Bhatia-Davis formula is proved to be a valid lower bound for the evolution time to reach the target when the energy structure is symmetric. Regarding few-level systems, it is also proved to be a valid lower bound for any state in two-level systems with any target, and for most mixed states with large target angles in equally spaced three-level systems.

quant-ph↗

arXiv2020

Fluctuation-enhanced quantum metrology

The main obstacle for practical quantum technology is the noise, which can induce the decoherence and destroy the potential quantum advantages. The fluctuation of a field, which induces the dephasing of the system, is one of the most common noises and widely regarded as detrimental to quantum technologies. Here we show, contrary to the conventional belief, the fluctuation can be used to improve the precision limits in quantum metrology for the estimation of various parameters. Specifically, we show that for the estimation of the direction and rotating frequency of a field, the achieved precisions at the presence of the fluctuation can even surpass the highest precision achievable under the unitary dynamics which have been widely taken as the ultimate limit. We provide explicit protocols, which employs the adaptive quantum error correction, to achieve the higher precision limits with the fluctuating fields. Our study provides a completely new perspective on the role of the noises in quantum metrology. It also opens the door for higher precisions beyond the limit that has been believed to be ultimate.

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arXiv2019

Is entanglement necessary in the reservoir input?

In this paper, we continue our investigation on controlling the state of a quantum harmonic oscillator, by coupling it to a reservoir composed of a sequence of qubits. Specifically, we show that sending qubits separable from each other but initialised at different states in pairs can stabilise the oscillator at squeezed states. However, only if entanglement is allowed in the reservoir qubit can we stabilise the oscillator at a wider set of squeezed states. This thus provides a proof for the necessity of involving entanglement in the reservoir qubits input to the oscillator, as regard to the stabilisation of quantum states in the proposed system setting. On the other hand, this system setup can be in turn used to estimate the coupling strength between the oscillator and reservoir qubits. We further demonstrate that entanglement in the reservoir input qubits contributes to the corresponding quantum Fisher information. From this point of view, entanglement is proved to play an indispensable role in the improvement of estimation precision in quantum metrology.

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arXiv2017

Discrete-time reservoir engineering with entangled bath and stabilizing squeezed states

This theoretical proposal investigates how resonant interactions occurring when a harmonic oscillator is fed with a stream of entangled qubits allow us to stabilize squeezed states of the harmonic oscillator. We show that the properties of the squeezed state stabilized by this engineered reservoir, including the squeezing strength, can be tuned at will through the parameters of the "input" qubits, albeit in tradeoff with the convergence rate. We also discuss the influence of the type of entanglement in the input, from a pairwise case to a more widely distributed case. This paper can be read in two ways: either as a proposal to stabilize squeezed states, or as a step towards treating quantum systems with time-entangled reservoir inputs.

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arXiv2016

Reaching Agreement in Quantum Hybrid Networks

We consider a basic quantum hybrid network model consisting of a number of nodes each holding a qubit, for which the aim is to drive the network to a consensus in the sense that all qubits reach a common state. Projective measurements are applied serving as control means, and the measurement results are exchanged among the nodes via classical communication channels. We show how to carry out centralized optimal path planning for this network with all-to-all classical communications, in which case the problem becomes a stochastic optimal control problem with a continuous action space. To overcome the computation and communication obstacles facing the centralized solutions, we also develop a distributed Pairwise Qubit Projection (PQP) algorithm, where pairs of nodes meet at a given time and respectively perform measurements at their geometric average. We show that the qubit states are driven to a consensus almost surely along the proposed PQP algorithm, and that the expected qubit density operators converge to the average of the network's initial values.

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arXiv2015

Interpolation Approach to Hamiltonian-varying Quantum Systems and the Adiabatic Theorem

Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure could be taken as the error of adiabatic approximation. We prove under certain conditions, this error can be precisely estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example on which the applicability of the adiabatic theorem is questionable.

math-ph↗

arXiv2015

Pole placement design for quantum systems via coherent observers

We previously extended Luenberger's approach for observer design to the quantum case, and developed a class of coherent observers which tracks linear quantum stochastic systems in the sense of mean values. In light of the fact that the Luenberger observer is commonly and successfully applied in classical control, it is interesting to investigate the role of coherent observers in quantum feedback. As the first step in exploring observer-based coherent control, in this paper we study pole-placement techniques for quantum systems using coherent observers, and in such a fashion, poles of a closed-loop quantum system can be relocated at any desired locations. In comparison to classical feedback control design incorporating the Luenberger observer, here direct coupling between a quantum plant and the observer-based controller are allowed to enable a greater degree of freedom for the design of controller parameters. A separation principle is presented, and we show how to design the observer and feedback independently to be consistent with the laws of quantum mechanics. The proposed scheme is applicable to coherent feedback control of quantum systems, especially when the transient dynamic response is of interest, and this issue is illustrated in an example.

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arXiv2015

On the generalization of linear least mean squares estimation to quantum systems with non-commutative outputs

The purpose of this paper is to study the problem of generalizing the Belavkin-Kalman filter to the case where the classical measurement signal is replaced by a fully quantum non-commutative output signal. We formulate a least mean squares estimation problem that involves a non-commutative system as the filter processing the non-commutative output signal. We solve this estimation problem within the framework of non-commutative probability. Also, we find the necessary and sufficient conditions which make these non-commutative estimators physically realizable. These conditions are restrictive in practice.

math-ph↗

arXiv2015

Coherently tracking the covariance matrix of an open quantum system

Coherent feedback control of quantum systems has demonstrable advantages over measurement-based control, but so far there has been little work done on coherent estimators and more specifically coherent observers. Coherent observers are input the coherent output of a specified quantum plant, and are designed such that some subset of the observer and plant's expectation values converge in the asymptotic limit. We previously developed a class of mean tracking (MT) observers for open harmonic oscillators that only converged in mean position and momentum; Here we develop a class of covariance matrix tracking (CMT) coherent observers that track both the mean and covariance matrix of a quantum plant. We derive necessary and sufficient conditions for the existence of a CMT observer, and find there are more restrictions on a CMT observer than there are on a MT observer. We give examples where we demonstrate how to design a CMT observer and show it can be used to track properties like the entanglement of a plant. As the CMT observer provides more quantum information than a MT observer, we expect it will have greater application in future coherent feedback schemes mediated by coherent observers. Investigation of coherent quantum estimators and observers is important in the ongoing discussion of quantum measurement; As they provide estimation of a system's quantum state without explicit use of the measurement postulate in their derivation.

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arXiv2014

Heisenberg Picture Approach to the Stability of Quantum Markov Systems

Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.

math-ph↗

arXiv2012

Physical Realizability of Multi-Level Quantum Systems

This paper considers the physical realizability condition for multi-level quantum systems having polynomial Hamiltonian and multiplicative coupling with respect to several interacting boson fields. Specifically, it generalizes a recent result the authors developed for two-level quantum systems. For this purpose, the algebra of SU(n) was incorporated. As a consequence, the obtained condition is given in terms of the structure constants of SU(n).

math.OC↗

arXiv2012

Preservation of Commutation Relations and Physical Realizability of Open Two-Level Quantum Systems

Coherent feedback control considers purely quantum controllers in order to overcome disadvantages such as the acquisition of suitable quantum information, quantum error correction, etc. These approaches lack a systematic characterization of quantum realizability. Recently, a condition characterizing when a system described as a linear stochastic differential equation is quantum was developed. Such condition was named physical realizability, and it was developed for linear quantum systems satisfying the quantum harmonic oscillator canonical commutation relations. In this context, open two-level quantum systems escape the realm of the current known condition. When compared to linear quantum system, the challenges in obtaining such condition for such systems radicate in that the evolution equation is now a bilinear quantum stochastic differential equation and that the commutation relations for such systems are dependent on the system variables. The goal of this paper is to provide a necessary and sufficient condition for the preservation of the Pauli commutation relations, as well as to make explicit the relationship between this condition and physical realizability.

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