Binary Quantum Research Articles

Self-Orthogonal Codes Constructed from Posets and Their Applications in Quantum Communication

It is an important issue to search for self-orthogonal codes for construction of quantum codes by CSS construction (Calderbank-Sho-Steane codes); in quantum error correction, CSS codes are a special type of stabilizer codes constructed from classical codes with some special properties, and the CSS construction of quantum codes is a well-known construction. First, we employ hierarchical posets with two levels for construction of binary linear codes. Second, we find some necessary and sufficient conditions for these linear codes constructed using posets to be self-orthogonal, and we use these self-orthogonal codes for obtaining binary quantum codes. Finally, we obtain four infinite families of binary quantum codes for which the minimum distances are three or four by CSS construction, which include binary quantum Hamming codes with length n≥7. We also find some (almost) “optimal” quantum codes according to the current database of Grassl. Furthermore, we explicitly determine the weight distributions of these linear codes constructed using posets, and we present two infinite families of some optimal binary linear codes with respect to the Griesmer bound and a class of binary Hamming codes.

A thermal quantum classifier

We find that the additivity of quantum information channels enables one to introduce a quantum classifier or a quantum decision maker. Proper measurement and sensing of temperature are of central importance to the realization of nanoscale quantum devices. Minimal classifiers may constitute the basic units for the physical quantum neural networks. We introduce a binary temperature classifier quantum model that operates in a thermal environment. In the present study, first the mathematical model was introduced through a two-level quantum system weakly coupled to the thermal reservoirs and it was demonstrated that the model faithfully classifies the temperature information of the reservoirs in the thermal steady state limit. A physical model by superconducting circuits composed of transmon qubits was also suggested.

Dual-color plasmonic random lasers for speckle-free imaging

A dual-color plasmonic random laser under single-excitation is achieved in an ultrathin membrane doped with binary quantum dots and gold nanorods. The gold nanorods tune the luminescence lifetime and emission efficiency of quantum dots. Under single excitation, low-threshold random lasing is observed. Green random lasing at 547 nm is ‘turned on’ and red random lasing at 630 nm is greatly enhanced by the transversal and longitudinal surface plasmon resonance of the gold nanorods, respectively. Speckle-free color imaging is achieved by using the proposed dual-color random laser source. These properties would facilitate the development of random lasers in fields of illumination and imaging.

Constructions of quasi-twisted quantum codes

In this work, our main objective is to construct quantum codes from quasi-twisted (QT) codes. At first, a necessary and sufficient condition for Hermitian self-orthogonality of QT codes is introduced by virtue of the Chinese remainder theorem. Then, we utilize these self-orthogonal QT codes to provide quantum codes via the famous Hermitian construction. Moreover, we present a new construction method of q-ary quantum codes, which can be viewed as an effective generalization of the Hermitian construction. General QT codes that are not self-orthogonal are also employed to construct quantum codes. As the computational results, some binary, ternary and quaternary quantum codes are constructed and their parameters are determined, which all cannot be deduced by the quantum Gilbert–Varshamov bound. In the binary case, a small number of quantum codes are derived with strictly improved parameters compared with the current records. In the ternary and quaternary cases, our codes fill some gaps or have better performances than the current results.

Weight enumerators for nonbinary asymmetric quantum codes and their applications

In 1997, Shor and Laflamme defined weight enumerators for quantum error-correcting codes and derived a MacWilliams identity. Recently, we proposed two new notions, the double weight enumerators and complete weight enumerators, for binary quantum codes. Now we will extend these results to nonbinary quantum codes. Based on the MacWilliams identities for these enumerators, we explicitly determine the Singleton-type and Hamming-type bounds for arbitrary nonbinary asymmetric quantum codes.

GaN/AlN multiple quantum wells grown by molecular beam epitaxy: effect of growth kinetics on radiative recombination efficiency

Ultraviolet (UV) optoelectronic devices based on binary GaN quantum wells have been widely reported in the literature. The internal quantum efficiency (IQE) of such structures is relatively low due to the large dislocation densities generated during heteroepitaxial deposition on to non lattice-matched substrates. Enhancement of IQE is possible through the use of expensive lattice-matched substrates or by using complex dislocation density reducing mechanisms. In this paper we have investigated growth mechanisms of GaN/AlN multiple quantum wells (MQWs) using Plasma Assisted Molecular Beam Epitaxy. Specifically the modulation of the surface diffusivity of adatoms has been carried out through choice of appropriate growth parameters, such as the group-III to group-V flux ratio. Our results indicate that this leads to modification of not only the surface morphology, but also the abruptness of the well-barrier interface. Under conditions of growth where surface morphology was atomically flat, the interfaces are relatively diffuse. The IQE for such structures, as measured by the ratio of room temperature photoluminescence intensity to that measured at 4 K, is rather low typically ~10%. Use of near stoichiometric growth conditions however lead to a reduction of the surface diffusivity of adatoms, and the formation of spontaneous nanostructures in the form of nano-dots of about 20 nm in diameter and high levels of uniformity. The IQE for GaN/AlN MQWs grown under such conditions is increased to as high as 28% even for samples with large dislocation densities. Thus, growth under such conditions can mitigate the detrimental effects of non-radiative recombination centers associated with dislocations by spatial localization of electron-hole pairs. These results are important to many applications, including UV light emitting diodes.

Application of Constacyclic Codes Over the Semi Local Ring $${F_{{p^m}}} + v{F_{{p^m}}}$$

In this paper, we study the quantum codes over $${F_{{p^m}}}$$, which are obtained from (λ1 + λ2)-constacyclic codes over the semi local ring $${F_{{p^m}}} + v{F_{{p^m}}}$$, where v2 = 1, p is odd prime. We decompose a (λ1 + λ2)-constacyclic code over $${F_{{p^m}}} + v{F_{{p^m}}}$$ into two constacyclic codes over $${F_{{p^m}}}$$ such as (λ1 + λ2)-constacyclic and (λ1–λ2)-constacyclic. We give the necessary and sufficient condition that the (λ1 + vλ2)-constacyclic codes over $${F_{{p^m}}} + v{F_{{p^m}}}$$ contain their duals. We give some examples of non binary quantum codes.

All-optical control of exciton flow in a colloidal quantum well complex

Excitonics, an alternative to romising for processing information since semiconductor electronics is rapidly approaching the end of Moore’s law. Currently, the development of excitonic devices, where exciton flow is controlled, is mainly focused on electric-field modulation or exciton polaritons in high-Q cavities. Here, we show an all-optical strategy to manipulate the exciton flow in a binary colloidal quantum well complex through mediation of the Förster resonance energy transfer (FRET) by stimulated emission. In the spontaneous emission regime, FRET naturally occurs between a donor and an acceptor. In contrast, upon stronger excitation, the ultrafast consumption of excitons by stimulated emission effectively engineers the excitonic flow from the donors to the acceptors. Specifically, the acceptors’ stimulated emission significantly accelerates the exciton flow, while the donors’ stimulated emission almost stops this process. On this basis, a FRET-coupled rate equation model is derived to understand the controllable exciton flow using the density of the excited donors and the unexcited acceptors. The results will provide an effective all-optical route for realizing excitonic devices under room temperature operation.

Semi-device-independent information processing with spatiotemporal degrees of freedom

Nonlocality, as demonstrated by the violation of Bell inequalities, enables device-independent cryptographic tasks that do not require users to trust their apparatus. In this article, we consider devices whose inputs are spatiotemporal degrees of freedom, e.g. orientations or time durations. Without assuming the validity of quantum theory, we prove that the devices' statistical response must respect their input's symmetries, with profound foundational and technological implications. We exactly characterize the bipartite binary quantum correlations in terms of local symmetries, indicating a fundamental relation between spacetime and quantum theory. For Bell experiments characterized by two input angles, we show that the correlations are accounted for by a local hidden variable model if they contain enough noise, but conversely must be nonlocal if they are pure enough. This allows us to construct a "Bell witness" that certifies nonlocality with fewer measurements than possible without such spatiotemporal symmetries, suggesting a new class of semi-device-independent protocols for quantum technologies.

A New Method of Constructing Binary Quantum Codes From Arbitrary Quaternary Linear Codes

In this letter, a method of constructing Hermitian dual containing quaternary linear codes from general quaternary linear codes is proposed. Based on this result, a construction method of binary linear quantum codes is obtained. Using three cyclic codes and one linear code over $\mathbb {F}_{4}$ that are not Hermitian dual containing, we construct four record breaking binary linear quantum codes. Furthermore, ten new record breaking binary additive quantum codes are derived from these four linear quantum codes by propagation rule.

Efficient design of quaternary quantum comparator with only a single ancillary input

Circuit design with no energy dissipation is possible in the reversible logic. Also, using the quantum multiple-valued logic in the design of circuits due to the reduction of circuit width leads to the smaller chip area and lower power consumption. Quaternary reversible logic potentially has several advantages in comparison to the equivalent ternary and binary quantum technologies. Hence, the quaternary quantum technology is a promising choice for the future digital system design. Here, the authors proposed an efficient design of 1-qudit and n -qudit quantum comparators. The comparator module is widely used in search conditions, such as Grover's quantum search algorithm in quantum computing. The proposed circuits were better than their existing counterparts in terms of quantum cost, the number of constant inputs, the number of garbage outputs, and hardware complexity. To design these circuits, they have used 1-qudit gates and 2-qudit Muthukrishnan-Stroud gates. The efficiency of their proposed circuits was reported.

Quantum Codes Derived from One-Generator Quasi-Cyclic Codes with Hermitian Inner Product

In this paper, we consider a family of one-generator quasi-cyclic codes and their applications in quantum codes construction. We give a sufficient condition for self-orthogonality with respect to Hermitian inner product. By virtue of the well-known MacWilliams equations, some binary and ternary stabilizer quantum codes with good parameters are constructed. Furthermore, we present a lower bound on the Hermitian dual distance of these involved codes. As the computational results, some good stabilizer quantum codes over small finite fields are obtained.

Leaf-like BiVO4 nanostructure decorated by nitrogen-doped carbon quantum dots: Binary heterostructure photocatalyst for enhanced photocatalytic performance

We constructed a binary nitrogen-doped carbon quantum dots (NCDs)/BiVO4 nanoheterostructure in which NCDs coat on the surface of the leaf-like BiVO4 nanostructures. The binary NCDs/BiVO4 nanocomposites showed enhanced photocatalytic performance for rhodamine B (Rh B) and tetracycline (TE) degradation. The NCDs/BiVO4 sample with an NCDs/BiVO4 mass ratio of 0.125% showed the optimal photocatalytic performance. The improved photocatalytic performance of the NCDs/BiVO4 nanocomposites was due to the efficient separation and transport of photogenerated charge carriers induced by fabricated binary nanoheterostructures.

Identifying Clusters and/or Small-Size Quantum Dots in Colloidal CdSe Ensembles with Optical Spectroscopy.

It is well-known that optical absorption and photoluminescence (PL) provide information that is sensitive to the size and size distribution of colloidal binary semiconductor quantum dots (QDs). To explore the nature of reaction products, clusters, and/or small-size QDs, we show that it is important to perform as well photoluminescence excitation (PLE) spectroscopy. For two non-hot-injection reactions of cadmium oleate (Cd(OA)2) and selenium (Se) in 1-octadecene (ODE), we show that sequentially extracted products displayed a similar apparent red shift in both absorption and PL with a full width at half-maximum (fwhm) of ∼30 nm. We demonstrate that one reaction (with the presence of diphenyl phosphine (HPPh2)) produced multiple types of clusters (with slightly different optical properties) in one ensemble, while the other reaction (without HPPh2) yielded primarily small-size QDs. Our findings provide evidence for the probable existence of clusters within small-size CdSe QD products, the existence of which complicates the size determination of small-size CdSe QDs.

New construction of binary and nonbinary quantum stabilizer codes based on symmetric matrices

In this paper, we propose two construction methods for binary and nonbinary quantum stabilizer codes based on symmetric matrices. In the first construction, we use the identity and symmetric matrices to generate parity-check matrices that satisfy the symplectic inner product (SIP) for the construction of quantum stabilizer codes. In the second construction, we modify the first construction to generate parity-check matrices based on the Calderbank–Shor–Stean structure for the construction of quantum stabilizer codes. The binary and nonbinary quantum stabilizer codes whose parameters achieve equality of the quantum singleton bound are investigated with the code lengths ranging from 4 to 12.

A memetic approach for training set selection in imbalanced data sets

Imbalanced data classification is a challenging problem in the field of machine learning. The problem occurs when data samples have an uneven distribution amongst the classes and classical classifiers are not suitable for classifying such datasets. To overcome this problem, in this paper, the best training samples are selected from data samples with the goal of improving the performance of classifier when dealing with imbalanced data. To do so, some heuristic methods are presented which use local information to give a proper view about whether removing or retaining each sample of training set. Subsequently, the methods are considered as local search algorithms and combined with a global search algorithm in a framework to form memetic algorithms. The global search used in this paper is binary quantum inspired gravitational search algorithm (BQIGSA) which is a new metaheuristic search for optimization of binary encoded problems. BQIGSA is employed since we seek for a highly stochastic and random search algorithm to solve our problem. We propose to use six different local search algorithms, three of which are application oriented that we designed based on the problem and the rest are general, and the best local search is then determined. Experiments are performed on 45 standard datasets, and G-mean and AUC criteria are considered as evaluation tools. Then, the data sets are employed to compare the best memetic approaches with some popular state of the art algorithms as well as a recently proposed memetic algorithm and the results show their superiority. At the last step, the performance of the proposed algorithm for four different classifiers is evaluated and the best classifier is determined to be utilized for this method.

Mutual Energy Transfer in a Binary Colloidal Quantum Well Complex.

Förster resonance energy transfer (FRET) is a fundamental process that is key to optical biosensing, photosynthetic light harvesting, and down-converted light emission. However, in total, conventional FRET in a donor-acceptor pair is essentially unidirectional, which impedes practical application of FRET-based technologies. Here, we propose a mutual FRET scheme that is uniquely bidirectional in a binary colloidal quantum well (CQW) complex enabled by utilizing the d orbital electrons in a dopant-host CQW system. Steady-state emission intensity, time-resolved, and photoluminescence excitation spectroscopies have demonstrated that two distinct CQWs play the role of donor and acceptor simultaneously in this complex consisting of 3 monolayer (ML) copper-doped CQWs and 4 ML undoped CQWs. Band-edge excitons in 3 ML CQWs effectively transfer the excitation to excitons in 4 ML CQWs, whose energy is also harvested backward by the dopants in 3 ML CQWs. This binary CQW complex, which offers a unique mutual energy-transfer mechanism, may unlock revolutionary FRET-based technologies.

Analysis of Properties of Quantum Hashing

We analyze a method of binary quantum hashing that allows one to represent binary sets as quantum states. We show that this method is very stable with respect to the recovery of preimages. Moreover, we propose heuristic approaches to small-bias sets on which the construction of quantum hash-functions is based and show that they are stable with respect to collisions.

Large-alphabet encoding for higher-rate quantum key distribution

The manipulation of high-dimensional degrees of freedom provides new opportunities for more efficient quantum information processing. It has recently been shown that high-dimensional encoded states can provide significant advantages over binary quantum states in applications of quantum computation and quantum communication. In particular, high-dimensional quantum key distribution enables higher secret-key generation rates under practical limitations of detectors or light sources, as well as greater error tolerance. Here, we demonstrate high-dimensional quantum key distribution capabilities both in the laboratory and over a deployed fiber, using photons encoded in a high-dimensional alphabet to increase the secure information yield per detected photon. By adjusting the alphabet size, it is possible to mitigate the effects of receiver bottlenecks and optimize the secret-key rates for different channel losses. This work presents a strategy for achieving higher secret-key rates in receiver-limited scenarios and marks an important step toward high-dimensional quantum communication in deployed fiber networks.

Quaternary Quantum/Reversible Half-Adder, Full-Adder, Parallel Adder and Parallel Adder/Subtractor Circuits

Multiple valued quantum logic is a promising research area in quantum computing technology having several advantages over binary quantum logic. Adder circuits as well as subtractor circuits are the major components of various computational units in computers and other complex computational systems. In this paper, we propose a quaternary quantum reversible half-adder circuit using quaternary 1-qudit gates, 2-qudit Feynman and Muthukrishnan-Stroud gates. Then we propose a quaternary quantum reversible full adder and a quaternary quantum parallel adder circuit. In addition, we propose a quaternary quantum reversible parallel adder/subtractor circuit. The proposed designs are compared with existing designs and improvements in terms of hardware complexity, quantum cost, number of constant inputs and garbage outputs are reported.