Dimensional Quantum Research Articles

Digital twin of the atmospheric turbulence channel based on self-supervised deep learning algorithm

High dimensional quantum entanglement based on orbital angular momentum (OAM) can provide infinite freedom theoretically, providing a significant improvement on the capacity of the quantum communication. However, the vortex beam that carries OAM signal can be easily distorted by atmospheric turbulence and can degrade the performance of the system. Consequently, for the operation, administration and maintenance of quantum system, an accurate digital twin model of the turbulent channel is necessary. Digital twin model is a mathematical model which can reflect the influence of atmospheric channel on quantum system by theoretical analysis. Nevertheless, it is challenging to achieve for the complex mechanism of atmospheric turbulence. To address this problem, deep learning (DL) techniques have been studied recently. Whereas, for the training of DL, a massive number of labeled samples are needed, i.e., the actual free-space channel, which are hard to be obtained in practical systems. The pool generalization also hinders the use of these DL-based algorithms in practice. To overcome the above challenges, we propose a self-supervised DL algorithm, which does not need any labeled samples in advance, meaning the training of the algorithm can be restarted any time once the environment changes. Compared with previous studies, the proposed algorithm can better suite as the digital twin of the turbulent channel. To verify the performance of the proposed algorithm, we perform extensive verification, whose results demonstrate the superior performance of the proposed method.

Effect of shallow doping on performance parameters of single heterojunction solar cell

Abstract Fill factor and conversion efficiency of single heterojunction solar cell is analytically computed based on the shallow doping at GaAs quantum well region. Poisson’s equation is solved with suitable boundary condition applied at hetero-interface for both dark and illuminated conditions, corresponding to which open-circuit voltage and short-circuit current are computed. Realistic dependence of minority carrier distribution on material layers and diffusion widths are taken into account for simulation purpose. Result exhibits that variation of acceptor density leads to better outcome in terms of both efficiency and fill factor, which is also critically depends on length of quantum well region. Doping of AlGaAs barrier layer has negligible influence on fill factor and conversion efficiency. Optimized dimension of quantum well layer width is the critical parameter for design of efficient solar cell, as revealed from the analysis.

On an intercritical log-modified nonlinear Schrödinger equation in two spatial dimensions

We consider a dispersive equation of Schrödinger type with a nonlinearity slightly larger than cubic by a logarithmic factor. This equation is supposed to be an effective model for stable two dimensional quantum droplets with Lee-Huang-Yang correction. Mathematically, it is seen to be mass supercritical and energy subcritical with a sign-indefinite nonlinearity. For the corresponding initial value problem, we prove global in-time existence of strong solutions in the energy space. Furthermore, we prove the existence and uniqueness (up to symmetries) of nonlinear ground states and the orbital stability of the set of energy minimizers. We also show that for the corresponding model in 1D a stronger stability result is available.

Convex Optimization for Nonequilibrium Steady States on a Hybrid Quantum Processor.

Finding the transient and steady state properties of open quantum systems is a central problem in various fields of quantum technologies. Here, we present a quantum-assisted algorithm to determine the steady states of open system dynamics. By reformulating the problem of finding the fixed point of Lindblad dynamics as a feasibility semidefinite program, we bypass several well-known issues with variational quantum approaches to solving for steady states. We demonstrate that our hybrid approach allows us to estimate the steady states of higher dimensional open quantum systems and discuss how our method can find multiple steady states for systems with symmetries.

Radial wave function of 2D and 3D quantum harmonic oscillator

One dimensional quantum harmonic oscillator is well studied in elementary textbooks of quantum mechanics. The wave function of one-dimensional oscillator harmonic can be written in term of Hermite polynomial. Due to the symmetry of the spring energy, the wave functions of two-dimensional and three-dimensional harmonic oscillators can be written as products of the one-dimensional case. Because of that, the wave functions of two- and three-dimensional cases are focused on cartesian coordinates. In this article, we utilize polar and spherical coordinates to describe the wave function of two- and three-dimensional harmonic oscillators, respectively. The radial part of the wave functions can be written in term of associated Laguerre polynomials.

Directional Activated Exciton Highway via Fractal Electric Field Modulation for Ultrasensitive Carbon Nanotube-Based Sensors.

The electrical vapor sensor based on carbon nanotubes (CNTs) has attracted wide attention due to its excellent conductivity, stable interfacial structure, and low dimensional quantum effects. However, the conductivity and contact interface activity were still limited by the random distribution of coated CNTs, which led to limited performance. We developed a new strategy to unify the CNT directions with image fractal designing of the electrode system. In such a system, directional aligned CNTs were gained under a well-modulated electric field, leading to microscale CNT exciton highways and molecule-scale host-guest site activation. The carrier mobility of the aligned CNT device is 20-fold higher than that of the random network CNT device. With excellent electrical properties, such modulated CNT devices based on fractal electrodes behave as an ultrasensitive vapor sensor for methylphenethylamine, a mimic of illicit drug methamphetamine. The detection limit reached as low as 0.998 ppq, 6 orders of magnitude sensitive than the reported 5 ppb record based on interdigital electrodes with random distributed CNTs. Since the device is easily fabricated in wafer-level and compatible with the CMOS process, such a fractal design strategy for aligned CNT preparation will be widely applied in a variety of wafer-level electrical functional devices.

Anti-site disorder driven short-range order and canted antiferromagnetism in inverse spinel LiNiVO4

Frustration driven short-range magnetic correlations/fluctuations in quantum materials usually host exotic ground states like spin glass, low dimensional magnetism and quantum spin liquid. In this context, different members of spinel (both normal and inverse) family have gained enormous interest and an inverse spinel vanadate, LiNiVO4, seems to be an interesting candidate. Structural investigations reveal that unlike usual cation ordering, Ni and Li ions are randomly distributed at octahedral sites and results in reduced magnetic frustration. Further, an additional anti-site disorder is present, as a small fraction of Ni ions occupies tetrahedral sites. Magnetic susceptibility and heat capacity studies show that short-range magnetic correlations develop below 30 K, followed by a canted antiferromagnetism below 2.2 K. Different competing magnetic interactions due to the presence of disorder and reduced magnetic frustration result in the short-range ordering as well as canted antiferromagnetism in LiNiVO4.

Quantum structured light in high dimensions

Structured light has become topical of late, where controlling light in all its degrees of freedom has offered novel states of light long predicted, enhanced functionality in applications, and a modern toolbox for probing fundamental science. Structuring light as single photons and entangled states allows the spatial modes of light to be used to encode a large alphabet, accessing high dimensional Hilbert spaces for fundamental tests of quantum mechanics and improved quantum information processing tasks. In this tutorial, we outline the basic concepts of high dimensional quantum states expressed in a basis of spatial modes (structured light) and explain how to create, control, and detect such quantum states in the laboratory with a focus on transverse spatial modes such as the orbital angular momentum and pixel (position) modes. Finally, we highlight some example applications of such quantum structured light, from communications to imaging.

On convergence of form factor expansions in the infinite volume quantum Sinh-Gordon model in 1+1 dimensions

This paper develops a technique allowing one to prove the convergence of a class of series of multiple integrals which corresponds to the form factor expansion of space-like separated two-point functions in the 1+1 dimensional massive integrable Sinh-Gordon quantum field theory.

Optimal compression of quantum many-body time evolution operators into brickwall circuits

Near term quantum computers suffer from a degree of decoherence which is prohibitive for high fidelity simulations with deep circuits. An economical use of circuit depth is therefore paramount. For digital quantum simulation of quantum many-body systems, real time evolution is typically achieved by a Trotter decomposition of the time evolution operator into circuits consisting only of two qubit gates. To match the geometry of the physical system and the CNOT connectivity of the quantum processor, additional SWAP gates are needed. We show that optimal fidelity, beyond what is achievable by simple Trotter decompositions for a fixed gate count, can be obtained by compiling the evolution operator into optimal brickwall circuits for the S=1/2S=1/2 quantum Heisenberg model on chains and ladders, when mapped to one dimensional quantum processors without the need of additional SWAP gates.

Efficient calculation of three-dimensional tensor networks

We have proposed an efficient algorithm to calculate physical quantities in the translational invariant three-dimensional tensor networks, which is particularly relevant to the study of the three-dimensional classical statistical models and the ($2+1$)-dimensional quantum lattice models. In the context of a classical model, we determine the partition function by solving the dominant eigenvalue problem of the transfer matrix, whose left and right dominant eigenvectors are represented by two projected entangled simplex states. These two projected entangled simplex states are not Hermitian conjugate to each other but are appropriately arranged so that their inner product can be computed much more efficiently than in the usual prescription. For the three-dimensional Ising model, the calculated internal energy and spontaneous magnetization agree with the published results in the literature. The possible improvement and extension to other models are also discussed.

Regulation on the electrical and optical properties of two-dimensional stacked graphene quantum dots/gold quantum dots/tungsten sulfide heterostructures

Two-dimensional (2D) transition metal dichalcogenides (TMDCs), like WS2, have been particularly promising in the application of solar energy conversion. Nevertheless, how to enhance the absorption capacity and photogenerated dcharge transfer is yet challenging. Herein, 2D stacked heterostructures were firstly constructed by 2D Au quantum dots (QDs), graphene quantum dots (GQDs) and WS2 monolayer. Compared with WS2 monolayer, the absorption abilities of the Au QDs/WS2 heterostructures in visible-near infrared light region of 450–2300 nm increase evidently. Simultaneously, charge redistribution occurs at the WS2–Au interfaces and generates the built-in electric field with the direction from Au QDs to the WS2 monolayer. This built-in electric field is conducive to boosting photo-induced charge separation and transfer. Notably, more obvious charge transfer and stronger built-in electric field can be achieved in WS2–Au6 interface after introducing the GQDs. Therefore, this work provides unique insights for designing new WS2-based heterostructures to improve the solar energy conversion.

Cu2O quantum dots modified α-Ga2O3 nanorod arrays as a heterojunction for improved sensitivity of self-powered photoelectrochemical detectors

Long distance charge transfer will lead to the recombination of carriers, which seriously limits the practical application of photoelectrochemical (PEC) detector. In this work, a self-powered solar-blind photodetector based on a mixed dimensional α-Ga2O3 nanorod arrays and Cu2O quantum dots has been prepared by a simple hydrothermal method and a two-part impregnation method. Cu2O quantum dots can form type Ⅱ heterojunction with α-Ga2O3 and effectively reduce the photoinduced electron and hole recombination due to their short carrier transport distances. Just because of this, α-Ga2O3 photodetectors modified by Cu2O quantum dots present special self-power optical response at 254 nm, with optical flow densities of 13.88 μA/cm2, large responsivity of 4.57 mA/W, high detection sensitivity of 2.107 × 109 Jones and fast photoresponse time of 0.815 s/0.978 s. This kind of thought provides a simple and feasible method for the preparation of α-Ga2O3 and other semiconductor oxides based on PEC photodetectors.

Quantum simulator of link models using spinor dipolar ultracold atoms

We propose a scheme for the quantum simulation of quantum link models in two-dimensional lattices. Our approach considers spinor dipolar gases on a suitably shaped lattice, where the dynamics of particles in the different hyperfine levels of the gas takes place in one-dimensional chains coupled by the dipolar interactions. We show that at least four levels are needed. The present scheme does not require any particular fine-tuning of the parameters. We perform the derivation of the parameters of the quantum link models by means of two different approaches, a non-perturbative one tied to angular momentum conservation, and a perturbative one. A comparison with other schemes for $(2+1)$-dimensional quantum link models present in literature is discussed. Finally, the extension to three-dimensional lattices is presented, and its subtleties are pointed out.

Non-Abelian fusion, shrinking, and quantum dimensions of Abelian gauge fluxes

Braiding and fusion rules of topological excitations are indispensable topological invariants in topological quantum computation and topological orders. While excitations in 2D are always particle-like anyons, those in 3D incorporate not only particles but also loops -- spatially nonlocal objects -- making it novel and challenging to study topological invariants in higher dimensions. While 2D fusion rules have been well understood from bulk Chern-Simons field theory and edge conformal field theory, it is yet to be thoroughly explored for 3D fusion rules from higher dimensional bulk topological field theory. Here, we perform a field-theoretical study on (i) how loops that carry Abelian gauge fluxes fuse and (ii) how loops are shrunk into particles in the path integral, which generates fusion rules, loop-shrinking rules, and descendent invariants, e.g., quantum dimensions. We first assign a gauge-invariant Wilson operator to each excitation and determine the number of distinct excitations through equivalence classes of Wilson operators. Then, we adiabatically shift two Wilson operators together to observe how they fuse and are split in the path integral; despite the Abelian nature of the gauge fluxes carried by loops, their fusions may be of non-Abelian nature. Meanwhile, we adiabatically deform world-sheets of unknotted loops into world-lines and examine the shrinking outcomes; we find that the resulting loop-shrinking rules are algebraically consistent to fusion rules. Interestingly, fusing a pair of loop and anti-loop may generate multiple vacua, but fusing a pair of anyon and anti-anyon in 2D has one vacuum only. By establishing a field-theoretical ground for fusion and shrinking in 3D, this work leaves intriguing directions, e.g., symmetry enrichment, quantum gates, and physics of braided monoidal 2-category of 2-group.

Graphene/III–V Quantum Dot Mixed-Dimensional Heterostructure for Enhanced Radiative Recombinations via Hole Carrier Transfer

Fabrication of high quantum efficiency nanoscale device is challenging due to increased carrier loss at surface. Low dimensional materials such 0D quantum dots and 2D materials have been widely studied to mitigate the loss. Here, we demonstrate a strong photoluminescence enhancement from graphene/III-V quantum dot mixed-dimensional heterostructures. The distance between graphene and quantum dots in the 2D/0D hybrid structure determines the degree of radiative carrier recombination enhancement from 80% to 800% compared to the quantum dot only structure. Time-resolved photoluminescence decay also shows increased carrier lifetimes when the distance decreases from 50 to 10 nm. We propose that the optical enhancement is due to energy band bending and hole carrier transfer, which repair the imbalance of electron and hole carrier densities in quantum dots. This 2D graphene/0D quantum dot heterostructure shows promise for high performance nanoscale optoelectronic devices.

On a charged spinless point particle minimally coupled to a constant magnetic field in a noncommutative plane

In this paper, we provide a mathematically and physically consistent minimal prescription for a charged spinless point particle coupled to a constant magnetic field in a 2-dimensional noncommutative plane. It turns out to be a gauge invariant prescription in contrast to the widely and carelessly used naive minimal prescription in the context of 2-dimensional quantum mechanics in a noncommutative plane. Besides, we explore the noncommutative U(1) gauge theoretic structure of the underlying noncommutative system by explicitly computing the 1-parameter family of Seiberg–Witten maps.

Quantum Machine Learning: A Review

Abstract: Quantum machine learning is an emerging field that aims to leverage the unique properties of quantum computing to accelerate machine learning tasks. In this paper, we review recent advances in quantum machine learning and discuss the potential applications and challenges associated with this technology. Specifically, we examine the current state of quantum machine learning algorithms, including variational quantum algorithms, quantum neural networks, and quantum generative models. We also discuss the challenges associated with practical quantum computing resources, algorithm design, and interdisciplinary collaboration. Furthermore, we highlight the potential applications of quantum machine learning in areas such as drug discovery, speech and image recognition, financial modeling, and many others. We also examine the ethical and societal implications of this technology, including the potential impact on privacy and security. Finally, we discuss future prospects for quantum machine learning, including the potential for quantum-inspired classical algorithms and the development of error correction techniques. We conclude by emphasizing the importance of interdisciplinary collaboration in the continued advancement of this field.

Preparations for quantum simulations of quantum chromodynamics in 1+1 dimensions. I. Axial gauge

Tools necessary for quantum simulations of $1+1$ dimensional quantum chromodynamics are developed. When formulated in axial gauge and with two flavors of quarks, this system requires 12 qubits per spatial site with the gauge fields included via nonlocal interactions. Classical computations and $D$-wave's quantum annealer advantage are used to determine the hadronic spectrum, enabling a decomposition of the masses and a study of quark entanglement. Color ``edge'' states confined within a screening length of the end of the lattice are found. IBM's seven-qubit quantum computers, ibmq_jakarta and ibm_perth, are used to compute dynamics from the trivial vacuum in one-flavor QCD with one spatial site. More generally, the Hamiltonian and quantum circuits for time evolution of $1+1$ dimensional $SU({N}_{c})$ gauge theory with ${N}_{f}$ flavors of quarks are developed, and the resource requirements for large-scale quantum simulations are estimated.

SL2 quantum trace in quantum Teichmüller theory via writhe

Quantization of the Teichm\"uller space of a punctured Riemann surface $S$ is an approach to $3$-dimensional quantum gravity, and is a prototypical example of quantization of cluster varieties. Any simple loop $\gamma$ in $S$ gives rise to a natural trace-of-monodromy function $\mathbb{I}(\gamma)$ on the Teichm\"uller space. For any ideal triangulation $\Delta$ of $S$, this function $\mathbb{I}(\gamma)$ is a Laurent polynomial in the square-roots of the exponentiated shear coordinates for the arcs of $\Delta$. An important problem was to construct a quantization of this function $\mathbb{I}(\gamma)$, namely to replace it by a noncommutative Laurent polynomial in the quantum variables. This problem, which is closely related to the framed protected spin characters in physics, has been solved by Allegretti and Kim using Bonahon and Wong's ${\rm SL}_2$ quantum trace for skein algebras, and by Gabella using Gaiotto, Moore and Neitzke's Seiberg-Witten curves, spectral networks, and writhe of links. We show that these two solutions to the quantization problem coincide. We enhance Gabella's solution and show that it is a twist of the Bonahon-Wong quantum trace.