Low-temperature environments for quantum computation and quantum simulation

This review summarizes the requirement of low temperature conditions in existing experimental approaches to quantum computation and quantum simulation.     

Ballistic Aharonov–Bohm quantum bits and quantum gates

We propose an architecture to perform quantum computation, using ballistic electrons as qubits and coupled quantum rings as quantum gates. In the proposed architecture two adjacent one-dimensional wires, creating a single qubit, are connected to two coupled quantum rings, where the required magnetic flux is provided by enclosed nano-sized magnets. The phase modulation of the wave function of the ballistic electrons under the Aharonov–Bohm effect is carefully designed to facilitate reprogrammable and dynamically controllable quantum gates. Arbitrary single-qubit quantum gates with high fidelity can be constructed on the basis of this architecture.     

Excitons in quantum—dot quantum—well nanoparticles

A variational calculation is presented for the ground-state properties of excitons confined in spherical core-shell quantum-dot quantum-well (QDQW) nanoparticles. The relationship between the exciton states and structure parameters of QDQW nanoparticles is investigated, in which both the heavy-hole and the light-hole exciton states are considered. The results show that the confinement energies of the electron and hole states and the exciton binding energies depend sensitively on the well width and core radius of the QDQW structure. A detailed comparison between the heavy-hole and light-hole exciton states is given. Excellent agreement is found between experimental results and our calculated 1s_e－1s_h transition energies.     

Kullback–Leibler quantum divergence as an indicator of quantum chaos

We discuss a system of a nonlinear Kerr-like oscillator externally pumped by ultra-short, coherent pulses. For such a system, we analyse the application of the Kullback–Leibler quantum divergence K[ρ||σ]$K[\rho ||\sigma ]$ to the detection of quantum chaotic behaviour. Defining linear and nonlinear quantum divergences, and calculating their power spectra, we show that these parameters are more suitable indicators of quantum chaos than the fidelity commonly discussed in the literature, and are useful for dealing with short time series. Moreover, the nonlinear divergence is more sensitive to chaotic bands and to boundaries of chaotic regions, compared to its linear counterpart.     

Electron–phonon interaction in fan-shaped quantum dot and quantum wire

The optical phonon modes and electron–optical-phonon interaction in fan-shaped quantum dot and quantum wire are studied with the dielectric continuum (DC) model and separation of variables. The explicit expressions for the longitudinal optical (LO) and interface optical (IO) phonon eigenmodes are deduced. It is found that there exist two types of IO phonon modes: top interface optical (TIO) phonon mode and arc interface optical (AIO) phonon mode, in a fan-shaped quantum dot. After having quantized the eigenmodes, we derive the Hamiltonian operators describing the LO and IO phonon modes as well as the corresponding Fröhlich electron–phonon interaction. The potential applications of these results are also discussed.     

The quantum Hall＇s effect： A quantum electrodynamic phenomenon

<正>We have applied Maxwell’s equations to study the physics of quantum Hall’s effect.The electromagnetic properties of this system are obtained.The Hall’s voltage,V_H = 2πh²n_s/em,where n_s is the electron number density,for a 2- dimensional system,and h = 2πh is the Planck’s constant,is found to coincide with the voltage drop across the quantum capacitor.Consideration of the cyclotronic motion of electrons is found to give rise to Hall’s resistance. Ohmic resistances in the horizontal and vertical directions have been found to exist before equilibrium state is reached. At a fundamental level,the Hall’s effect is found to be equivalent to a resonant LCR circuit with L_H = 2πm/e²n_s and C_H = me²/2πh²n_s satisfying the resonance condition with resonant frequency equal to the inverse of the scattering （relaxation） time,τ_s.The Hall’s resistance is found to be R_H =（（L_H）/C_H）^1/2.The Hall’s resistance may be connected with the impedance that the electron wave experiences when it propagates in the 2-dimensional gas.     

Efficient universal quantum channel simulation in IBM’s cloud quantum computer

The study of quantum channels is an important field and promises a wide range of applications, because any physical process can be represented as a quantum channel that transforms an initial state into a final state. Inspired by the method of performing non-unitary operators by the linear combination of unitary operations, we proposed a quantum algorithm for the simulation of the universal single-qubit channel, described by a convex combination of “quasi-extreme” channels corresponding to four Kraus operators, and is scalable to arbitrary higher dimension. We demonstrated the whole algorithm experimentally using the universal IBM cloud-based quantum computer and studied the properties of different qubit quantum channels. We illustrated the quantum capacity of the general qubit quantum channels, which quantifies the amount of quantum information that can be protected. The behavior of quantum capacity in different channels revealed which types of noise processes can support information transmission, and which types are too destructive to protect information. There was a general agreement between the theoretical predictions and the experiments, which strongly supports our method. By realizing the arbitrary qubit channel, this work provides a universally- accepted way to explore various properties of quantum channels and novel prospect for quantum communication.     

On the relation of Manin’s quantum plane and quantum Clifford algebras

In a recent work we have shown that quantum Clifford algebras — i.e. Clifford algebras of an arbitrary bilinear form — are closely related to the deformed structures asq-spin groups, Hecke algebras,q-Young operators and deformed tensor products. The question to relate Manin’s approach to quantum Clifford algebras is addressed here. Explicit computations using the CLIFFORD Maple package are exhibited. The meaning of non-commutative geometry is reexamined and interpreted in Clifford algebraic terms. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Theoretical study of quantum confined Stark shift in InAs／GaAs quantum dots

The quantum confined Stark effect (QCSE) of the self-assembled InAs/GaAs quantum dots has been investigated theoretically. The ground-state transition energies for quantum dots in the shape of a cube, pyramid or “truncated pyramid” are calculated and analysed. We use a method based on the Green function technique for calculating thestrain in quantum dots and an efficient plane-wave envelope-function technique to determine the ground-state electronic structure of them with different shapes. The symmetry of quantum dots is broken by the effect of strain. So the properties of carriers show different behaviours from the traditional quantum device. Based on these results, we also calculate permanent built-in dipole moments and compare them with recent experimental data. Our results demonstrate that the measured Stark effect in self-assembled InAs/GaAs quantum dot structures can be explained by including linear grading.     

Circular threshold quantum secret sharing

This paper proposes a circular threshold quantum secret sharing （TQSS） scheme with polarized single photons. A polarized single photon sequence runs circularly among any t or more of n parties and any t or more of n parties can reconstruct the secret key when they collaborate. It shows that entanglement is not necessary for quantum secret sharing. Moreover, the theoretic efficiency is improved to approach 100% as the single photons carrying the secret key are deterministically forwarded among any t or more of n parties, and each photon can carry one bit of information without quantum storage. This protocol is feasible with current technology.     

Recent advances for quantum classifiers

Machine learning has achieved dramatic success in a broad spectrum of applications.Its interplay with quantum physics may lead to unprecedented perspectives for both fundamental research and commercial applications,giving rise to an emergent research frontier of quantum machine learning.Along this line,quantum classifiers,which are quantum devices that aim to solve classification problems in machine learning,have attracted tremendous attention recently.In this review,we give a relatively comprehensive overview for the studies of quantum classifiers,with a focus on recent advances.First,we will review a number of quantum classification algorithms,including quantum support vector machines,quantum kernel methods,quantum decision tree classifiers,quantum nearest neighbor algorithms,and quantum annealing based classifiers.Then,we move on to introduce the variational quantum classifiers,which are essentially variational quantum circuits for classifications.We will review different architectures for constructing variational quantum classifiers and introduce the barren plateau problem,where the training of quantum classifiers might be hindered by the exponentially vanishing gradient.In addition,the vulnerability aspect of quantum classifiers in the setting of adversarial learning and the recent experimental progress on different quantum classifiers will also be discussed.     

CT-MQC – a coupled-trajectory mixed quantum/classical method including nonadiabatic quantum coherence effects

Upon photoexcitation by a short light pulse, molecules can reach regions of the configuration space characterized by strong nonadiabaticity, where the motion of the nuclei is strongly coupled to the motion of the electrons. The subtle interplay between the nuclear and electronic degrees of freedom in such situations is rather challenging to capture by state-of-the-art nonadiabatic dynamics approaches, limiting therefore their predictive power. The Exact Factorization of the molecular wavefunction, though, offers new perspectives in the solution of this longstanding issue. Here, we investigate the performance of a mixed quantum/classical (MQC) limit of this theory, named Coupled Trajectory-MQC, which was shown to reproduce the excited-state dynamics of small systems accurately. The method is applied to the study of the photoinduced ring opening of oxirane and the results are compared with two other nonadiabatic approaches based on different Ansätze for the molecular wavefunction, namely Ehrenfest dynamics and Ab Initio Multiple Spawning (AIMS). All simulations were performed using linear-response time-dependent density functional theory. We show that the CT-MQC method can capture the (de)coherence effects resulting from the dynamics through conical intersections, in good agreement with the results obtained with AIMS and in contrast with ensemble Ehrenfest dynamics.     

Controlled teleportation of multi-qudit quantum information

We propose a scheme for realizing a controlled teleportation of random M-qudit quantum information under the control of N agents. The resource consumption includes a prearranged （2M ＋ N ＋ 1）-qudit entangled quantum channel and （2M ＋ N ＋1） log2 d-bit classical communication. And the quantum operations used in the teleportation process are a series of generalized Bell-state measurements, single-qudit measurements, qudit H-gates, qudit-Pauli gates and qudit phase gates. It is shown that the original state can be restored by the receiver only on condition that all the agents work in collaboration with each others. If one agent does not cooperate with the other, the original state cannot be fully recovered.     

How adiabatic is quantum tunneling?

We consider the coupling between collective and intrinsic degrees of freedom of a many-dimensional quantum system. We give a criterion for the validity of the adiabatic approximation in tunneling processes and derive an equation for the “lag” of the intrinsic wave function with respect to the adiabatic groundstate. Solutions for several simple cases are presented.     

Superrenormalizable quantum electrodynamics inn⩾4

In order to formulate a satisfactory QFT it is not sufficient to secure renormaliz-ability, but rather superrenormalizability. On the other hand, it is not necessary to search for a formalism completely free of infinities. A Superrenormalizable QED inn4 dimensions may be formulated by introducing a relativistic form factor preserving gauge invariance. This formalism is characterized by a running coupling constant and is asymptotically free. A relation between the bare and the dressed coupling constant is discussed anew.     

A potential application in quantum networks—Deterministic quantum operation sharing schemes with Bell states

In this paper, we propose certain different design ideas on a novel topic in quantum cryptography — quantum operation sharing(QOS). Following these unique ideas, three QOS schemes, the "HIEC"(The scheme whose messages are hidden in the entanglement correlation), "HIAO"(The scheme whose messages are hidden with the assistant operations) and "HIMB"(The scheme whose messages are hidden in the selected measurement basis), have been presented to share the single-qubit operations determinately on target states in a remote node. These schemes only require Bell states as quantum resources. Therefore, they can be directly applied in quantum networks, since Bell states are considered the basic quantum channels in quantum networks. Furthermore, after analyse on the security and resource consumptions, the task of QOS can be achieved securely and effectively in these schemes.     

How to avoid “quantum paradoxes”

The theorems showing the impossibility of ascribing to individual quantum systems a definite value of a set of observables, not necessarily commuting,^1–4 are based on the tacit assumption that eachindividual spin component has a discrete dichotomic value. We show explicitly that it is possible to introduce continuous hidden variables for individual spins which avoid these quantum paradoxes without changing any of the observed quantum mechanical results.     

From where do quantum groups come?

The phase space realizations of quantum groups are discussed using *-products. We show that on phase space, quantum groups appear necessarily as two-parameter deformation structures, one parameter (v) being concerned with the quantization in phase space, the other () expressing the quantum groups as deformation of their Lie counterparts. Introducing a strong invariance condition, we show the uniqueness of the -deformation. This suggests that the strong invariance condition is a possible origin of the quantum groups.Dedicated to Asim Barut with all our friendship.     

When is quantum decoherence dynamics classical?

A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong decoherence theory, showing a strong dependence on the nature of the system-environment coupling. For example, for the traditionally assumed linear coupling, the classical and quantum results are shown to be in exact agreement.