Binary Quantum Research Articles

Code and Data Repository for Binary Quantum Control Optimization with Uncertain Hamiltonians

The goal of this software is to implement the gradient-based and rounding algorithms proposed in the paper to solve the binary quantum control optimization problem with uncertain Hamiltonians.

Binary Quantum Control Optimization with Uncertain Hamiltonians

Binary Quantum Control Optimization with Uncertain Hamiltonians

Assessing a binary quantum channel exploiting a Silicon photomultiplier based hybrid receiver

Assessing a binary quantum channel exploiting a Silicon photomultiplier based hybrid receiver

Quantum number conservation: a tool in the design and analysis of high energy experiments

The Clifford Unification algebra Cl 7,7 is shown to provide a unified description of all the elementary fermions and hadrons in terms of seven binary quantum numbers. Four of these are defined in existing theories, namely spin-direction, fermion/anti-fermion pairing and the two commuting generators in the SU(3) description of quark colour. A Cl 3,3 sub-algebra integrates the Cl 1,3 space-time and Dirac algebras providing a new definition of time direction and identifying parity as a new quantum number. A further two quantum numbers are related to the commuting generators of an SU(3) description of fermion generations. All seven are conserved in the decays and interactions of charged particles, suggesting that quantum number conservation provides a useful tool in the design and interpretation of high energy experiments. This is especially relevant when neutral particles and parity are involved.

Qutrit representation of quantum images: new quantum ternary circuit design

Quantum computation is growing in significance and proving to be a powerful tool in meeting the high real-time computational demands of classical digital image processing. However, extensive research has been done on quantum image processing, mainly rooted in binary quantum systems. In this paper, we propose a new quantum ternary image circuit based on the analysis of the existing qutrit representation of quantum images. The proposed design utilizes ternary shift gates and ternary Muthukrishnan–Stroud gates, with the belief that this circuit can be used for ternary quantum image processing. This study makes a significant improvement compared to the existing counterpart in terms of quantum cost, the number of constant inputs, and garbage outputs, which are all essential parameters in quantum circuit design.

Binary quantum random number generator based on value indefinite observables

All quantum random number generators based on measuring value indefinite observables are at least three-dimensional because the Kochen–Specker Theorem and the Located Kochen–Specker Theorem are false in dimension two. In this article, we construct quantum random number generators based on measuring a three-dimensional value indefinite observable that generates binary quantum random outputs with the same randomness qualities as the ternary ones: the outputs are maximally unpredictable.

Empirical band-gap correction for LDA-derived atomic effective pseudopotentials

Atomic effective pseudopotentials enable atomistic calculations at the level of accuracy of density functional theory for semiconductor nanostructures with up to fifty thousand atoms. Since they are directly derived from ab-initio calculations performed in the local density approximation (LDA), they inherit the typical underestimated band gaps and effective masses. We propose an empirical correction based on the modification of the non-local part of the pseudopotential and demonstrate good performance for bulk binary materials (InP, ZnS, HgTe, GaAs) and quantum dots (InP, CdSe, GaAs) with diameters ranging from 1.0 nm to 4.45 nm. Additionally, we provide a simple analytic expression to obtain accurate quasiparticle and optical band gaps for InP, CdSe, and GaAs QDs, from standard LDA calculations.

Binary black holes and quantum off-shell recursion

The quantum off-shell recursion provides an efficient and universal computational tool for loop-level scattering amplitudes. In this work, we present a new comprehensive computational framework based on the quantum off-shell recursion for binary black hole systems. Using the quantum perturbiner method, we derive the recursions and solve them explicitly up to two-loop order. We introduce an indicator that enables straightforward distinguishing diagrams and deriving integral families in the context of off-shell recursions. By employing the soft expansion technique, we remove irrelevant terms from the loop integrands and express them in terms of master integrals. We classify the one-loop and the two-loop classical diagrams, and their loop integrands are represented by linear combinations of the master integrals. Finally, we explicitly calculate the classical scalar 2 → 2 amplitudes in the potential region up to the 3PM order and reproduce the known results.

Quantum Cluster Equilibrium Theory for Multicomponent Liquids.

In this work, we present a new theory to treat multicomponent liquids based on quantum-chemically calculated clusters. The starting point is the binary quantum cluster equilibrium theory, which is able to treat binary systems. The theory provides one equation with two unknowns. In order to obtain another linearly independent equation, the conservation of mass is used. However, increasing the number of components leads to more unknowns, and this requires linearly independent equations. We address this challenge by introducing a generalization of the conservation of arbitrary quantities accompanied by a comprehensive mathematical proof. Furthermore, a case study for the application of the new theory to ternary mixtures of chloroform, methanol, and water is presented. Calculated enthalpies of vaporization for the whole composition range are given, and the populations or weights of the different clusters are visualized.

New Binary Quantum Codes from Group Rings and Skew Group Rings

New Binary Quantum Codes from Group Rings and Skew Group Rings

Effect of double quantum dot asymmetry on electron localization

In this paper, we study the localization of an electron in a binary quantum system formed by a pair of quantum dots (QDs). The traditional theoretical consideration of such systems is limited to the symmetrical case when QDs in such double quantum dot (DQD) are assumed identical in all respects. In this paper, we model the effects of breaking QD similarities in a DQD by studying two-dimensional (2D) DQDs as a double quantum well (DQW). This is done by solving the Schrödinger equation, with parameters chosen to describe an InAs/GaAs heterostructure. We calculate the energy spectrum of the electron confinement and the spectral distribution of localized/delocalized spatial states. Both symmetric and asymmetric QW shapes are considered and their effects are compared. The effects of symmetry breaking are explained within the framework of the two-level system theory. We delineate the QW weak and strong coupling cases in DQW. In particular, we show that the coherence in ideal DQW is unstable in the case of a weak QW coupling. Within the framework of the proposed approach, a charge qubit realized on a DQD is discussed and, as an example, a qubit based on an almost ideal DQD is proposed.

Quantum Full-Duplex Communication

Integrating the full-duplex capability with quantum communication potentially equips emerging wireless networks with a quantum layer of security for the stringent communication efficiency and security requirements. This paper proposes two new full-duplex quantum communication protocols to exchange classical or quantum information between two remote parties simultaneously without transferring a physical particle over the quantum channel. The first protocol, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">quantum duplex coding</i> , enables the exchange of a classical bit using a preshared maximally entangled pair of qubits by means of counterfactual disentanglement. The second protocol, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">quantum telexchanging</i> , enables the exchange of an arbitrary unknown qubit without using preshared entanglement by means of counterfactual entanglement and disentanglement. We demonstrate that quantum duplex coding and quantum telexchanging can be achieved by exploiting counterfactual electron-photon interaction gates. It is shown that these tasks can be viewed as full-duplex transmission of bits and qubits via binary erasure channels and quantum erasure channels, respectively.

Charge exchange processes during carbon ion fragmentation at an energy of 300 MeV/nucleon: comparison with models of ion-ion interactions

Experimental data are presented on the differential cross sections to produce 11Be, 12Be, and 12B isotopes at the carbon beam fragmentation with an energy of 300 MeV/nucleon in the FRAGM experiment conducted based on the ITEP-TWAС multipurpose accelerator complex. The obtained experimental data are compared with the predictions of the models of ion-ion interactions: binary cascade and quantum molecular dynamics model.

Stabilization and Dissipative Information Transfer of a Superconducting Kerr-Cat Qubit

Today, the competition to build a quantum computer continues, and the number of qubits in hardware is increasing rapidly. However, the quantum noise that comes with this process reduces the performance of algorithmic applications, so alternative ways in quantum computer architecture and implementation of algorithms are discussed on the one hand. One of these alternative ways is the hybridization of the circuit-based quantum computing model with the dissipative-based computing model. Here, the goal is to apply the part of the algorithm that provides the quantum advantage with the quantum circuit model, and the remaining part with the dissipative model, which is less affected by noise. This scheme is of importance to quantum machine learning algorithms that involve highly repetitive processes and are thus susceptible to noise. In this study, we examine dissipative information transfer to a qubit model called Cat-Qubit. This model is especially important for the dissipative-based version of the binary quantum classification, which is the basic processing unit of quantum machine learning algorithms. On the other hand, Cat-Qubit architecture, which has the potential to easily implement activation-like functions in artificial neural networks due to its rich physics, also offers an alternative hardware opportunity for quantum artificial neural networks. Numerical calculations exhibit successful transfer of quantum information from reservoir qubits by a repeated-interactions-based dissipative scheme.

Boosted Binary Quantum Classifier via Graphical Kernel.

In terms of the logical structure of data in machine learning (ML), we apply a novel graphical encoding method in quantum computing to build the mapping between feature space of sample data and two-level nested graph state that presents a kind of multi-partite entanglement state. By implementing swap-test circuit on the graphical training states, a binary quantum classifier to large-scale test states is effectively realized in this paper. In addition, for the error classification caused by noise, we further explored the subsequent processing scheme by adjusting the weights so that a strong classifier is formed and its accuracy is greatly boosted. In this paper, the proposed boosting algorithm demonstrates superiority in certain aspects as demonstrated via experimental investigation. This work further enriches the theoretical foundation of quantum graph theory and quantum machine learning, which may be exploited to assist the classification of massive-data networks by entangling subgraphs.

Gradient Alloyed Quantum Dots for Photocatalytic Lignin Valorization via Proton Coupled Electron Transfer

In the field of photocatalytic lignin valorization, simultaneously fulfilling the requirements of broad light harvesting and strong redox ability has been a key challenge for single binary quantum dot (QD) photocatalyst systems. In order to address the problem, gradient alloyed QDs with funnel-shaped energy structures have been developed. The gradient energy level increases the photon absorption range, while the periphery energy bands at the funnel edge are sufficiently wide to preserve effective redox capacity. In this work, the gradient alloyed QD photocatalyst along with proton donors have been employed in enhancing the efficiency and selectivity of β-O-4 bond cleavage in lignin, realizing yields of target aromatic products phenol and acetophenone to increase up to 70% and 65%, respectively. The mechanism of conversion from the ketone intermediate to target products and how to choose suitable proton donors have been systematically investigated. We propose a proton-coupled electron transfer (PCET) photocatalytic strategy through producing a Cα radical from ketone with the help of acid possessing appropriate bond dissociation free energy (BDFE) and strong electronic transmission facilitating ability. The knowledge acquired in this work is useful for designing photocatalysts and proton donors that can effectively cleave bonds in lignin via the PCET mechanism.

QuDiet: A classical simulation platform for qubit‐qudit hybrid quantum systems

AbstractIn recent years, numerous research advancements have extended the limit of classical simulation of quantum algorithms. Although, most of the state‐of‐the‐art classical simulators are only limited to binary quantum systems, which restrict the classical simulation of higher‐dimensional quantum computing systems. Through recent developments in higher‐dimensional quantum computing systems, it is realised that implementing qudits improves the overall performance of a quantum algorithm by increasing memory space and reducing the asymptotic complexity of a quantum circuit. Hence, in this article, QuDiet, a state‐of‐the‐art user‐friendly python‐based higher‐dimensional quantum computing simulator is introduced. QuDiet offers multi‐valued logic operations by utilising generalised quantum gates with an abstraction so that any naive user can simulate qudit systems with ease as compared to the existing ones. Various benchmark quantum circuits is simulated in QuDiet and show the considerable speedup in simulation time as compared to the other simulators without loss in precision. Finally, QuDiet provides a full qubit‐qudit hybrid quantum simulator package with quantum circuit templates of well‐known quantum algorithms for fast prototyping and simulation. Comprehensive simulation up to 20 qutrits circuit on depth 80 on QuDiet was successfully achieved. The complete code and packages of QuDiet is available at https://github.com/LegacYFTw/QuDiet.

Lower Bounds for Quasi-Cyclic Codes and New Binary Quantum Codes

This paper considers three kinds of quasi-cyclic codes of index two with one generator or two generators and their applications in quantum code construction. In accordance with the algebraic structure of linear codes, we determine the lower bounds of the symplectic weights of these quasi-cyclic codes. Quasi-cyclic codes with the dual-containing property enable the construction of quantum codes. Defining the coefficient symmetric polynomials of the generator polynomials gives a concise condition for the dual-containing of the quasi-cyclic codes. The lower bound results can significantly reduce the scope of the search for a larger minimum distance of quasi-cyclic codes. With these algebraic results and computer supports, we obtain classical quasi-cyclic codes with better parameters and some new quantum codes under the symplectic construction. In particular, two examples of the new quantum codes [[63,42,6]]2,[[51,35,5]]2 improve the corresponding codes in Grassl’s code table.

Test-Measured Rényi Divergences

One possibility of defining a quantum R\'enyi $\alpha$-divergence of two quantum states is to optimize the classical R\'enyi $\alpha$-divergence of their post-measurement probability distributions over all possible measurements (measured R\'enyi divergence), and maybe regularize these quantities over multiple copies of the two states (regularized measured R\'enyi $\alpha$-divergence). A key observation behind the theorem for the strong converse exponent of asymptotic binary quantum state discrimination is that the regularized measured R\'enyi $\alpha$-divergence coincides with the sandwiched R\'enyi $\alpha$-divergence when $\alpha>1$. Moreover, it also follows from the same theorem that to achieve this, it is sufficient to consider $2$-outcome measurements (tests) for any number of copies (this is somewhat surprising, as achieving the measured R\'enyi $\alpha$-divergence for $n$ copies might require a number of measurement outcomes that diverges in $n$, in general). In view of this, it seems natural to expect the same when $\alpha<1$; however, we show that this is not the case. In fact, we show that even for commuting states (classical case) the regularized quantity attainable using $2$-outcome measurements is in general strictly smaller than the R\'enyi $\alpha$-divergence (which is unique in the classical case). In the general quantum case this shows that the above "regularized test-measured" R\'enyi $\alpha$-divergence is not even a quantum extension of the classical R\'enyi divergence when $\alpha<1$, in sharp contrast to the $\alpha>1$ case.

Single-qubit quantum classifier based on gradient-free optimization algorithm

A single-qubit quantum classifier (SQC) based on a gradient-free optimization (GFO) algorithm, named the GFO-based SQC, is proposed to overcome the effects of barren plateaus caused by quantum devices. Here, a rotation gate RX (ϕ) is applied on the single-qubit binary quantum classifier, and the training data and parameters are loaded into ϕ in the form of vector multiplication. The cost function is decreased by finding the value of each parameter that yields the minimum expectation value of measuring the quantum circuit. The algorithm is performed iteratively for all parameters one by one until the cost function satisfies the stop condition. The proposed GFO-based SQC is demonstrated for classification tasks in Iris and MNIST datasets and compared with the Adam-based SQC and the quantum support vector machine (QSVM). Furthermore, the performance of the GFO-based SQC is discussed when the rotation gate in the quantum device is under different types of noise. The simulation results show that the GFO-based SQC can reach a high accuracy in reduced time. Additionally, the proposed GFO algorithm can quickly complete the training process of the SQC. Importantly, the GFO-based SQC has a good performance in noisy environments.