S. G. Schirmer, I. C. H. Pullen, A. I. Solomon
An overview and synthesis of results and criteria for open-loop controllability of Hamiltonian quantum systems obtained using Lie group and Lie algebra techniques is presented. Negative results for open-loop controllability of dissipative systems are discussed, and the superiority of closed-loop (feedback) control for quantum systems is established.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Manipulation of infinite dimensional quantum systems is important to controlling complex quantum dynamics with many practical physical and chemical backgrounds. In this paper, a general investigation is casted to the controllability problem of quantum systems evolving on infinite dimensional manifolds. Recognizing that such problems are related with infinite dimensional controllability algebras, we introduce an algebraic mathematical framework to describe quantum control systems possessing such controllability algebras. Then we present the concept of smooth controllability on infinite dimensio…
We consider a control scheme where a quantum system S is put in contact with an auxiliary quantum system A and the control can affect A only, while S is the system of interest. The system S is then controlled indirectly through the interaction with A. Complete controllability of S +A means that every unitary state transformation for the system S +A can be achieved with this scheme. Indirect controllability means that every unitary transformation on the system S can be achieved. We prove in this paper, under appropriate conditions and definitions, that these two notions are equivalent in finite…
Complete controllability is a fundamental issue in the field of control of quantum systems, not least because of its implications for dynamical realizability of the kinematical bounds on the optimization of observables. In this paper we investigate the question of complete controllability for finite-level quantum systems subject to a single control field, for which the interaction is of dipole form. Sufficient criteria for complete controllability of a wide range of finite-level quantum systems are established and the question of limits of complete controllability is addressed. Finally, the re…
Precise definitions for different degrees of controllability for quantum systems are given, and necessary and sufficient conditions are discussed. The results are applied to determine the degree of controllability for various atomic systems with degenerate energy levels and transition frequencies.
Complete controllability of degenerate quantum system using quantum accessor modeled as a qubit chain with nearest neighborhood coupling is investigated. Sufficient conditions on the length of accessor and the way of coupling between controlled system and accessor are obtained. General approach to arbitrary finite system is presented and two and three level degenerate systems are investigated in detail.
A quantum mechanical system S is indirectly controlled when the control affects an ancillary system A and the evolution of S is modified through the interaction with A only. A study of indirect controllability gives a description of the set of states that can be obtained for S with this scheme. In this paper, we study the indirect controllability of quantum systems in the finite dimensional case. After discussing the relevant definitions, we give a general necessary condition for controllability in Lie algebraic terms. We present a detailed treatment of the case where both systems, S and A, ar…
Controllability properties for discrete-time, Markovian quantum dynamics are investigated. We find that, while in general the controlled system is not finite-time controllable, feedback control allows for arbitrary asymptotic state-to-state transitions. Under further assumption on the form of the measurement, we show that finite-time controllability can be achieved in a time that scales linearly with the dimension of the system, and we provide an iterative procedure to design the unitary control actions.
The controllability property of the unitary propagator of an N-level quantum mechanical system subject to a single control field is described using the structure theory of semisimple Lie algebras. Sufficient conditions are provided for the vector fields in a generic configuration as well as in a few degenerate cases.
This paper provides a framework for the control of quantum mechanical systems with scattering states, i.e., systems with continuous spectra. We present the concept and prove a criterion of the approximate strong smooth controllability. Our results make non-trivial extensions from quantum systems with finite dimensional control Lie algebras to those with infinite dimensions. It also opens up many interesting problems for future studies.
We give a criterion that is sufficient for controllability of multipartite quantum systems. We generalize the graph infection criterion to the quantum systems that cannot be described with the use of a graph theory. We introduce the notation of hypergraphs and reformulate the infection property in this setting. The introduced criterion has a topological nature and therefore it is not connected to any particular experimental realization of quantum information processing.
We consider the degrees of controllability of multi-partite quantum systems as well as necessary and sufficient criteria for each case. The results are applied to the problem of simultaneous control of an ensemble of quantum dots with a single laser pulse. Finally, we apply optimal control techniques to demonstrate selective excitation of individual dots for a simultaneously controllable ensemble.
This paper discusses the important role of controllability played on the complexity of optimizing quantum mechanical control systems. The study is based on a topology analysis of the corresponding quantum control landscape, which is referred to as the optimization objective as a functional of control fields. We find that the degree of controllability is closely relevant with the ruggedness of the landscape, which determines the search efficiency for global optima. This effect is demonstrated via the gate fidelity control landscape of a system whose controllability is restricted on a SU(2) dyna…
A complete classification of operator controllability for closed three-level quantum systems driven by a single control
本研究针对由单个控制驱动的封闭三能级量子系统，结合李代数结果与已知条件，完成了其算子可控性的完整分类，明确了不同简并、跃迁及受控位移情形下的充要条件。
In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system. We establish the connections among these different notions as well as methods to verify controllability. The paper also contains results on the relation between the controllability in arbitrary small time of a system varying on a compact transformation Lie group and the corresponding system on the associated homogeneous space. As an application, we prove that…
Quantum phenomena of interest in connection with applications to computation and communication almost always involve generating specific transfers between eigenstates, and their linear superpositions. For some quantum systems, such as spin systems, the quantum evolution equation (the Schrödinger equation) is finite-dimensional and old results on controllability of systems defined on on Lie groups and quotient spaces provide most of what is needed insofar as controllability of non-dissipative systems is concerned. However, in an infinite-dimensional setting, controlling the evolution of quantum…
Determining the ability for universal quantum computing: Testing controllability via dimensional expressivity
本文提出一种基于参数化量子电路的混合量子-经典算法，通过维度表达性分析获取独立参数数量，从而高效测试算子可控性，为量子芯片的资源高效设计提供系统方法。
Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and harmonic-oscillator systems, as well as some systems with degenerate energy levels. Morse and harmonic oscillators serve as models for molecular bonds, and the standard control approach of using a sequence of frequency-selective pulses to address a single transition at a time is either not applicable or only of limited utility for such systems.
We show how to control and perform universal three-qubit quantum computation with trapped electron quantum states. The three qubits are the electron spin, and the first two quantum states of the cyclotron and axial harmonic oscillators. We explicitly show how the universal gates can be performed. As an example of a non-trivial quantum algorithm, we outline the implementation of the Deutsch-Jozsa algorithm in this system.
Complete controllability of finite dimensional quantum systems with energy level degeneracy is investigated using two different approaches. One approach is to apply a weak constant field to eliminate the degeneracy and then control it using techniques developed for non-degenerate quantum systems. Conditions for the elimination of degeneracy are found and the issue of influence of relaxation time of constant external field to the target state are addressed through the fidelity. Another approach is to control the degenerate system by a single control field directly. It is found that the system w…
We discuss the use of incoherent light as a resource to control the atomic dynamics and review the proposed in Phys. Rev. A 84, 042106 (2011) method for a controlled transfer between any pure and mixed states of quantum systems using a combination of incoherent and coherent light. Formally, the method provides a constructive proof for an approximate open-loop Markovian state-transfer controllability of quantum system in the space of all density matrices---the strongest possible degree of quantum state control.
The question of controllability is investigated for a quantum control system in which the Hamiltonian operator components carry explicit time dependence which is not under the control of an external agent. We consider the general situation in which the state moves in an infinite-dimensional Hilbert space, a drift term is present, and the operators driving the state evolution may be unbounded. However, considerations are restricted by the assumption that there exists an analytic domain, dense in the state space, on which solutions of the controlled Schrodinger equation may be expressed globally…
We prove complete controllability for rotational states of an asymmetric top molecule belonging to degenerate values of the orientational quantum number M. Based on this insight, we construct a pulse sequence that energetically separates population initially distributed over degenerate M-states, as a precursor for orientational purification. Introducing the concept of enantio-selective controllability, we determine the conditions for complete enantiomer-specific population transfer in chiral molecules and construct pulse sequences realizing this transfer for population initially distributed ov…
In this paper we provide an explicit parameterization of arbitrary unitary transformation acting on n qubits, in terms of one and two qubit quantum gates. The construction is based on successive Cartan decompositions of the semi-simple Lie group, SU(2^n). The decomposition highlights the geometric aspects of building an arbitrary unitary transformation out of quantum gates and makes explicit the choice of pulse sequences for the implementation of arbitrary unitary transformation on $n coupled spins. Finally we make observations on the optimality of the design procedure.
Various notions from geometric control theory are used to characterize the behavior of the Markovian master equation for N-level quantum mechanical systems driven by unitary control and to describe the structure of the sets of reachable states. It is shown that the system can be accessible but neither small-time controllable nor controllable in finite time. In particular, if the generators of quantum dynamical semigroups are unital, then the reachable sets admit easy characterizations as they monotonically grow in time. The two level case is treated in detail.
Resource-bounded controllability benchmarking of open quantum systems
本文提出基于灰箱响应模型的资源受限框架，评估开放量子系统实际可控性，通过实例验证有限控制资源与系统噪声共同制约门性能，为相关基准测试提供方法。
In this paper, we consider discrete time quantum walks on graphs with coin focusing on the decentralized model, where the coin operation is allowed to change with the vertex of the graph. When the coin operations can be modified at every time step, these systems can be looked at as control systems and techniques of geometric control theory can be applied. In particular, the set of states that one can achieve can be described by studying controllability. Extending previous results, we give a characterization of the set of reachable states in terms of an appropriate Lie algebra. We then prove ge…
Extended Controllability Tests for Quantum Decoherence-Free Subspaces
本文提出两个公理化可控性测试，用于验证开放量子系统无消相干子空间中子系统码的可控性，适用于任意Lindbladian模型，并通过囚禁离子系统实例验证了其有效性。
We give a sufficient criterion that guarantees that a many-body quantum system can be controlled by properly manipulating the (local) Hamiltonian of one of its subsystems. The method can be applied to a wide range of systems: it does not depend on the details of the couplings but only on their associated topology. As a special case, we prove that Heisenberg and Affleck-Kennedy-Lieb-Tasaki chains can be controlled by operating on one of the spins at their ends. In principle, arbitrary quantum algorithms can be performed on such chains by acting on a single qubit.
In coherent quantum feedback control schemes, a target quantum system S is put in contact with an auxiliary system A and the coherent control can directly affect only A. The system S is controlled 'indirectly' through the interaction with A. The system S is said to be indirectly controllable if every unitary transformation can be performed on the state of S with this scheme. The indirect controllability of S will depend on the `dynamical Lie algebra' L characterizing the dynamics of the total system S+A and on the initial state of the auxiliary system A. In this paper we describe this characte…
In this paper, we study the control theoretic properties of a couple of interacting spin 1's driven by an electro-magnetic field. In particular, we assume that it is possible to observe the expectation value of the total magnetization and we study controllability, observability and parameter identification of these systems. We give conditions for controllability and observability and characterize the classes of equivalent models which have the same input-output behavior. The analysis is motivated by the recent interest in three level systems in quantum information theory and quantum cryptograp…
Graph test of controllability in qubit arrays: A systematic way to determine the minimum number of external controls
本文提出基于哈密顿量图表示的量子比特阵列可控性检验框架，可避免构造动力学李代数的高成本，并在受 ibmq_quito 启发的五量子比特阵列中将外部控制数由五个分别降至一个或两个。
On the Role of Controllability in Pulse-based Quantum Machine Learning Models
该研究针对基于脉冲的量子机器学习模型中表达能力与可训练性的权衡问题，通过Fliess级数展开提出通用表达能力评估准则，设计低维流形上的有限可控性模型，经数值验证实现了高表达性与可训练性的平衡。
Subspace Controllability in Variational Quantum Circuits: Maximising Expressivity and Increasing Search Efficiency with Dynamical Lie Algebras
该研究通过MNIST-1D多分类任务验证，子空间可控的变分量子电路在超参数搜索中更易达到最低损失，可限制搜索范围以降低计算成本。
The article considers a two-level open quantum system, whose evolution is governed by the Gorini--Kossakowski--Lindblad--Sudarshan master equation with Hamiltonian and dissipation superoperator depending, correspondingly, on piecewise constant coherent and incoherent controls with constrained magnitudes. Additional constraints on controls' variations are also considered. The system is analyzed using Bloch parametrization of the system's density matrix. We adapt the section method for obtaining outer parallelepipedal and pointwise estimations of reachable and controllability sets in the Bloch b…
Indirect controllability of an arbitrary finite dimensional quantum system (N-dimensional qudit) through a quantum accessor is investigated. Here, The qudit is coupled to a quantum accessor which is modeled as a fully controllable spin chain with nearest neighbor (anisotropic) XY-coupling. The complete controllability of such indirect control system is investigated in detail. The general approach is applied to the indirect controllability of two and three dimensional quantum systems. For two and three dimensional systems, a simpler indirect control scheme is also presented.
A closed quantum system is defined as completely controllable if an arbitrary unitary transformation can be executed using the available controls. In practice, control fields are a source of unavoidable noise. Can one design control fields such that the effect of noise is negligible on the time-scale of the transformation? Complete controllability in practice requires that the effect of noise can be suppressed for an arbitrary transformation. The present study considers a paradigm of control, where the Lie-algebraic structure of the control Hamiltonian is fixed, while the size of the system in…
The reachable set for a finite dimensional quantum system is shown to be the orbit of the group corresponding to the internal and control Hamiltonians, even if this group is not compact.
Controllability -- the possibility of performing any target dynamics by applying a set of available operations -- is a fundamental requirement for the practical use of any physical system. For finite-dimensional systems, as for instance spin systems, precise criterions to establish controllability, such as the so called rank criterion, are well known. However most physical systems require a description in terms of an infinite-dimensional Hilbert space whose controllability properties are poorly understood. Here, we investigate infinite-dimensional bosonic quantum systems -- encompassing quantu…
Qualitative differences in the robust controllability of model two-qubit systems
针对哈密顿量参数不确定性导致量子系统难以完全控制的问题，该研究结合理论框架与数值方法分析两模型两量子比特系统的鲁棒可控性差异，并通过在保真度函数中加惩罚项优化控制脉冲以增强鲁棒性。
Quantum gates (unitary gates) on physical systems are usually implemented by controlling the Hamiltonian dynamics. When full descriptions of the Hamiltonians parameters is available, the set of implementable quantum gates is easily characterised by quantum control theory. In many real systems, however, the Hamiltonians may include unknown parameters due to the difficulty of precise measurements or instability of the system. In this paper, we consider the situation that some parameters of the Hamiltonian are unknown, but we still want to perform a robust control of a quantum gate irrespectively…
High-throughput assessment of defect-nuclear spin register controllability for quantum memory applications
针对量子存储中缺陷-核自旋寄存器可控性评估效率低的问题，提出一种高效系统评估方法，量化了SiC中双物种核寄存器的纠缠门性能，可指导高通量筛选适配的量子存储缺陷系统。
We describe quantum controllability under the influences of the quantum decoherence induced by the quantum control itself. It is shown that, when the controller is considered as a quantum system, it will entangle with its controlled system and then cause quantum decoherence in the controlled system. In competition with this induced decoherence, the controllability will be limited by some uncertainty relation in a well-armed quantum control process. In association with the phase uncertainty and the standard quantum limit, a general model is studied to demonstrate the possibility of realizing a …
Local controllability of heralded quantum linear optics
通过分析输出态关于酉电路的雅可比矩阵秩，量化heralding对线性光学网络局部可控性的增强，并确定实现完全局部可控所需的资源。
Enhancing the controllability of quantum systems via a static field
本文提出利用弱锥形连接谱理论，通过静态场增强量子系统可控性，并通过两个实例验证了该方法的有效性。
In this paper we study the controllability problem for a symmetric-top molecule, both for its classical and quantum rotational dynamics. The molecule is controlled through three orthogonal electric fields interacting with its electric dipole. We characterize the controllability in terms of the dipole position: when it lies along the symmetry axis of the molecule neither the classical nor the quantum dynamics are controllable, due to the presence of a conserved quantity, the third component of the total angular momentum; when it lies in the orthogonal plane to the symmetry axis, a quantum symme…
Quantum Chaos as an Essential Resource for Full Quantum State Controllability
量子混沌通过遍历性和对弱扰动的敏感性，实现全量子态可控性，优于经典方法。
We study the dynamics of systems on networks from a linear algebraic perspective. The control theoretic concept of controllability describes the set of states that can be reached for these systems. Under appropriate conditions, there is a connection between the quantum (Lie theoretic) property of controllability and the linear systems (Kalman) controllability condition. We investigate how the graph theoretic concept of a zero forcing set impacts the controllability property. In particular, we prove that if a set of vertices is a zero forcing set, the associated dynamical system is controllable…
Any Quantum Network is Structurally Controllable by a Single Driving Signal
本文证明Lin结构可控性定理不限制量子网络，并指出通过局域操作和经典通信可将任意量子网络改造为仅需单一驱动信号即可结构可控的系统。
A new notion of controllability, eigenstate controllability, is defined for finite-dimensional bilinear quantum mechanical systems which are neither strongly completely controllably nor completely controllable. And a quantum control algorithm based on Grover iteration is designed to perform a quantum control task of steering a system, which is eigenstate controllable but may not be (strongly) completely controllable, from an arbitrary state to a target state.
In this paper, we study the controllability properties and the Lie algebra structure of networks of particles with spin immersed in an electro-magnetic field. We relate the Lie algebra structure to the properties of a graph whose nodes represent the particles and an edge connects two nodes if and only if the interaction between the two corresponding particles is active. For networks with different gyromagnetic ratios, we provide a necessary and sufficient condition of controllability in terms of the properties of the above mentioned graph and describe the Lie algebra structure in every case. F…
Beyond bilinear controllability : applications to quantum control
本文针对量子控制中双线性模型的一阶近似不足的问题，提出了适用于演化算子表示为控制函数的非线性泛函与时间无关耦合算子乘积之和的可控性判据。
This work addresses a fundamental problem of controllability of open quantum systems, meaning the ability to steer arbitrary initial system density matrix into any final density matrix. We show that under certain general conditions open quantum systems are completely controllable and propose the first, to the best of our knowledge, deterministic method for a laboratory realization of such controllability which allows for a practical engineering of arbitrary pure and mixed quantum states. The method exploits manipulation by the system with a laser field and a tailored nonequilibrium and time-de…
This paper presents a constructive proof of complete kinematic state controllability of finite-dimensional open quantum systems whose dynamics are represented by Kraus maps. For any pair of states (pure or mixed) on the Hilbert space of the system, we explicitly show how to construct a Kraus map that transforms one state into another. Moreover, we prove by construction the existence of a Kraus map that transforms all initial states into a predefined target state (such a process may be used, for example, in quantum information dilution). Thus, in sharp contrast to unitary control, Kraus-map dyn…
Scalable modular architecture for universal quantum computation
本文提出了一种可扩展的模块化架构，通过连接两个可控的量子比特数组，利用单一纠缠门实现大规模量子比特数组的可控性，从而减少资源消耗。
The periodic changes in the physical and chemical properties of the chemical elements are caused by the periodic change of the ionization energies, which are constant for each element that manifested in the Periodic Table. However, as has been recently shown the modification of the electromagnetic field in the photonic crystals gives rise to the modification of the electron electromagnetic mass. We show that the effect can significantly change the ionization energy of atoms placed in voids of photonic crystals consisting of metamaterials with a highly tunable refractive index and voids. The co…
This is an overview of the state of the art for practical quantum key distribution (QKD) as of March 2015. It is written by a non-expert for non-experts. Additions and corrections are welcome.
An incoherent control scheme for state control of locally controllable quantum systems is proposed. This scheme includes three steps: (1) amplitude amplification of the initial state by a suitable unitary transformation, (2) projective measurement on the amplified state, and (3) final optimization by a unitary controlled transformation. The first step increases the amplitudes of some desired eigenstates and the corresponding probability of observing these eigenstates, the second step projects, with high probability, the amplified state into a desired eigenstate, and the last step steers this e…
Quantum controllability on graph-like manifolds through magnetic potentials and boundary conditions
该研究针对厚量子图上的量子粒子这一无穷维系统，证明通过边界条件控制或含时磁场两种方案，均可实现全局近似可控性，为类图流形上的量子控制提供了理论依据。
On global approximate controllability of a quantum particle in a box by moving walls
本文研究壁位置可变的盒中自由量子粒子系统，利用含时 Schrödinger 方程弱解及其稳定性定理，证明了在预定盒终位下的全局近似能控性。
We investigate accessibility and controllability of a quantum system S coupled to a quantum probe P, both described by two-dimensional Hilbert spaces, under the hypothesis that the external control affects only P. In this context accessibility and controllability properties describe to what extent it is possible to drive the state of the system S by acting on P and using the interaction between the two systems. We give necessary and sufficient conditions for these properties and we discuss the relation with the entangling capability of the interaction between S and P. In particular, we show th…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。