Model Of Quantum Computation Research Articles

Electronic and structural perturbations of microporous ZIF-67 nanoparticles and Cr(VI) molecule during adsorptive water decontamination unveiled by experimental and quantum computational investigations

Metal organic frameworks (MOFs) have attracted great attention due to their unique characteristics and accordingly found their way to a multitude of applications including water remediation. Co-based zeolite imidazole framework (ZIF-67) has recently shown interesting adsorptive decontamination capabilities towards metallic and organic water pollutants. Yet, ZIF-67 adsorption mechanism and stability have not been studied enough. In this study, ZIF-67 nanocrystals (∼40 nm) were synthesized and applied as an adsorbent for Cr2O72− from water. The Cr2O72−−ZIF-67 adsorption mechanism and both of Cr2O72− and ZIF-67 consequent structural changes were investigated by analyzing the elemental composition and oxidation states, the adsorption isotherms, kinetics and thermodynamics, and the optimized quantum computational models. The experimental results fitted well with pseudo-second order and Langmuir models, and gave ΔH° and ΔG° of −86.4 ± 17.6 and 12.8 ± 2.4 kJ/mol, respectively, suggesting exothermic spontaneous monolayer chemical adsorption, with maximum capacity of 370 mg/g. Kinetics also show concurrence surface adsorption with intra-particle diffusion within the micropores. XPS results reveal that both Cr6+ and the less-toxic Cr3+ co-existed in Cr2O72−−ZIF-67, whilst the Co3+/Co2+ ratio increased, referring to an oxidation–reduction reaction between Cr and Co. Computational analysis concede that the Cr2O72−−ZIF-67 high affinity is based on H-bonding between the Cr2O72− oxygens and the imidazole hydrogens, van der Waals attraction between the Cr2O72− lone pairs and the imidazole π cloud, the Cr2O72−−ZIF-67 electron transfer, and CrN coordination interaction. However, these computations show that the Cr2O72−−ZIF-67 interaction causes internal destabilization within each of Cr2O72− and ZIF-67, as Cr2O72− tends to dissociate and ZIF-67 integrity weakens.

Characterizing q-Bessel Functions of the First Kind with Their New Summation and Integral Representations

As a powerful tool for models of quantum computing, q-calculus has drawn the attention of many researchers in the discipline of special functions. In this paper, we present new properties and characterize q-Bessel functions of the first kind using some identities of q-calculus. The results presented in this article help us to obtain new expression results related to q-special functions. New summation and integral representations for q-Bessel functions of the first kind are also established. A few examples are also provided to demonstrate the effectiveness of the proposed strategy.

Quaternionic quantum Turing machines

Quaternionic quantum theory is an extension of the standard complex quantum theory. Inspired by this, we study the quaternionic quantum computation using quaternions. We first develop a theory of quaternionic quantum Turing machines as a model of quaternionic quantum computation. Quaternionic quantum Turing machines can also be seen as a generalization of the complex quantum Turing machine. Then, we introduce the weighted sum of quaternionic quantum Turing machines and establish some of their basic properties.

Multi-qubit quantum computing using discrete-time quantum walks on closed graphs

Universal quantum computation can be realised using both continuous-time and discrete-time quantum walks. We present a version based on single particle discrete-time quantum walk to realize multi-qubit computation tasks. The scalability of the scheme is demonstrated by using a set of walk operations on a closed lattice form to implement the universal set of quantum gates on multi-qubit system. We also present a set of experimentally realizable walk operations that can implement Grover’s algorithm, quantum Fourier transformation and quantum phase estimation algorithms. An elementary implementation of error detection and correction is also presented. Analysis of space and time complexity of the scheme highlights the advantages of quantum walk based model for quantum computation on systems where implementation of quantum walk evolution operations is an inherent feature of the system.

A Remote Quantum Error-Correcting Code Preparation Protocol on Cluster States

The blind quantum computation (BQC) protocol allows for privacy-preserving remote quantum computations. In this paper, we introduce a remote quantum error correction code preparation protocol for BQC using a cluster state and analyze its blindness in the measurement-based quantum computation model. Our protocol requires fewer quantum resources than previous methods, as it only needs weak coherent pulses, eliminating the need for quantum memory and limited quantum computing. The results of our theoretical analysis and simulations show that our protocol requires fewer quantum resources compared to non-coding methods with the same qubit error rate.

Multiple silicon dangling-bond charge qubits for quantum computing: a Hilbert-space analysis of the Hamiltonian

Silicon-based dangling-bond charge qubit is one of the auspicious models for universal fault-tolerant solid-state quantum computing. In universal quantum computing, it is crucial to evaluate and characterize the computational Hilbert space and reduce the complexity and size of the computational space. Here, we recognize this problem to understand the complexity and characteristics of the Hilbert space in our dangling-bond qubit model. The size of the desired Hilbert space can prominently be reduced by considering assumptions regarding the qubit loss. Moreover, the dimension of the desired subsets in the space shrinks by a factor of two due to the spin preservation property. Finally, the required classical memory for storage of the qubit information, Hamiltonian and Hilbert space is analysed when the number of qubits grows.

Quantum machine learning assisted lung cancer telemedicine

The rapidly increasing human population, the high cost of medical equipment, and the spread of multifactor diseases have transformed the entire healthcare industry into an electronic consulting, telediagnosis, delivery, and treatment model to avoid the physical personalization of patients. Despite this, we face many challenges, including low sensitivity of medical instruments, signal losses, and security of medical records. This study aims to develop a lung cancer telemedicine platform that utilizes classical and quantum computing models to classify lung cancer subtypes and stages and develop effective telemedicine techniques. By using optoplasmonic biosensors, the biosignals (that show lung cancer) were extracted and correlated with cloud datasets (containing patient information) to determine the dose of laser interstitial thermal therapy (LITT). Then, applying quantum teleportation, the biosignals and doses of LITT were teleported between two healthcare stations. From the numerical result, we observed the maximum sensitivity (10 421 nm/RIU) of the proposed biosensor, a minimum degree of the loss function and maximum correlation of data from the quantum machine learning model, and high teleportation fidelity (96% transmission fidelity for biosignals and 98% teleportation fidelity for doses LITT). This shows the proposed telemedicine schemes anticipated solutions for the long-distance faithful lung cancer telemedicine.

Theoretical Insights into the Ultrafast Deactivation Mechanism and Photostability of a Natural Sunscreen System: Mycosporine Glycine.

In this work, different levels of quantum computational models such as MP2, ADC(2), CASSCF/CASPT2, and DFT/TD-DFT have been employed to investigate the photophysics and photostability of a mycosporine system, mycosporine glycine (MyG). First of all, a molecular mechanics approach based on the Monte Carlo conformational search has been employed to investigate the possible geometry structures of MyG. Then, comprehensive studies on the electronic excited states and deactivation mechanism have been conducted on the most stable conformer. The first optically bright electronic transition responsible for the UV absorption of MyG has been assigned as the S2 (1ππ*) owing to the large oscillator strength (0.450). The first excited electronic state (S1) has been assigned as an optically dark (1nπ*) state. From the nonadiabatic dynamics simulation model, we propose that the initial population in the S2 (1ππ*) state transfers to the S1 state in under 100 fs, through an S2/S1 conical intersection (CI). The barrierless S1 potential energy curves then drive the excited system to the S1/S0 CI. This latter CI provides a significant route for ultrafast deactivation of the system to the ground state via internal conversion.

Temporal information processing induced by quantum noise

Quantum computing has been moving from a theoretical phase to practical one, presenting daunting challenges in implementing physical qubits, which are subjected to noises from the surrounding environment. These quantum noises are ubiquitous in quantum devices and generate adverse effects in the quantum computational model, leading to extensive research on their correction and mitigation techniques. But do these quantum noises always provide disadvantages? We show that some abstract quantum noise models can induce useful information processing capabilities for temporal input data in a framework called quantum reservoir computing. We demonstrate this ability in several typical benchmarks and investigate the information processing capacity to clarify the framework's processing mechanism and memory profile. We verified our perspective by implementing the framework in a number of IBM quantum processors and obtained similar characteristic memory profiles with model analyses. As a surprising result, information processing capacity increased with quantum devices' higher noise levels and error rates. Our study opens up a path for diverting useful information from quantum computer noises into a more sophisticated information processor.

Addressable Quantum Gates

We extend the circuit model of quantum computation so that the wiring between gates is soft-coded within registers inside the gates. The addresses in these registers can be manipulated and put into superpositions. This aims at capturing indefinite causal orders and making their geometrical layout explicit: we express the quantum switch and the polarizing beam-splitter within the model. In this context, our main contribution is a full characterization of the anonymity constraints. Indeed, the names used as addresses should not matter beyond the wiring they describe; i.e., quantum evolutions should commute with “renamings.” We show that these quantum evolutions can still act non-trivially upon the names. We specify the structure of “nameblind” matrices.

Uncertainties and coherence in DQC1

Correlations have been identified as a necessary ingredient for the speedup of certain mixed-state quantum computation. In this work, we analyze the model of deterministic quantum computation with one bit (DQC1) and study its information-theoretic aspects involving state-channel interaction. This state-channel interaction provides a new perspective for investigating DQC1. More specifically, by calculating some important information-theoretic quantities related to the state-channel interaction, such as uncertainties, coherence of quantum states as measured with respect to channels, etc., we reveal some basic features of quantum resources for the quantum speedup in this model. Moreover, since the state-channel framework is general enough to encompass all computational models, the studies performed here can be similarly applied to analyze other computational models from the perspective of quantum resources.

Quaternionic quantum automata

Quaternionic quantum theory is a generalization of the standard complex quantum theory. Inspired by this, we study the quaternionic quantum computation using quaternions. We first develop a theory of quaternionic quantum automata as a model of quaternionic quantum computation. Quaternionic quantum automata also can be seen as an extension of complex quantum automata. Then we introduce some operations of quaternionic quantum automata and establish some of their basic properties.

Two-level quantum walkers on directed graphs. I. Universal quantum computing

In the present paper, the first in a series of two, we propose a model of universal quantum computation using a fermionic or bosonic multiparticle continuous-time quantum walk with two internal states (e.g., the spin-up and -down states of an electron). A dual-rail encoding is adopted to convert information: A single qubit is represented by the presence of a single quantum walker in either of the two parallel paths. We develop a roundabout gate that moves a walker from one path to the next, either clockwise or counterclockwise, depending on its internal state. It can be realized by a single-particle scattering on a directed weighted graph with the edge weights 1 and $\ifmmode\pm\else\textpm\fi{}i$. The roundabout gate also allows the spatial information of the quantum walker to be temporarily encoded in its internal states. The universal gates are constructed by appropriately combining several roundabout gates, some unitary gates that act on the internal states, and two-particle scatterings on straight paths. No ancilla qubits are required in our model. The computation is done by just passing quantum walkers through properly designed paths. Namely, there is no need for any time-dependent control. A physical implementation of quantum random access memory compatible with the present model will be considered in the second paper [R. Asaka et al., following paper, Phys. Rev. A 107, 022416 (2023)].

Topological quantum computation using analog gravitational holonomy and time dilation

Non-universal topological quantum computation models, such as the Majorana fermion-based Ising anyon model, have to be supplemented with an additional non-topological noisy gate in order to achieve universality. Here we endeavour to remedy this using an Einstein­—Cartan analog gravity picture of scalar fields. Specifically, we show that the analog gravity picture enables unitary transformations to be realized in two distinct ways: (i) via space-time holonomy and (ii) as gravitational time dilation. The non-abelian geometric phases are enabled by gravitational interactions, which are mediated by the spin-connection. We analytically compute its matrix elements as a function of the scalar field density distribution. This density can be regarded as the gravitating distribution of matter in an analog universe. We show via explicit calculations that there exists an infinite set of asymptotically flat analog gravitational fields, each of which implements a unique unitary transformation, that render the interactions topological. We emphasise the generality of this result by asserting that such gravitational gates could potentially be implemented in a broad range of real systems modeled by scalar field with an acoustic metric.

Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation.

Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by the property of being fully-coherent: the algorithm succeeds with arbitrarily high success probability 1 - δ while only requiring a single copy of the initial state. We subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time t, ln(1/δ), and ln(1/ϵ) for error tolerance ϵ: Θ‖H‖|t|+ln(1/ϵ)+ln(1/δ). Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H2 molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves as a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields.

A quantum walks assisted algorithm for peptide and protein folding prediction

Proteins are considered as the working force of cells. Their functionality is determined by their spatial form. In 1973 Anfinsen proposed that the spatial form is determined by the sequence of amino acids in the protein backbone. Yet, the number of possible sequences as well as the possible configurations is very large, making the task of predicting the protein's spatial form very difficult. Many approaches have been proposed, both classical and hybrid quantum – classical ones. We propose a novel hybrid algorithm. In our approach we utilized quantum walks, a proven model for universal quantum computation. We considered a simplified version of the protein backbone to be the evolution space of the quantum walk. The dihedral angles φ and ψ are introduced as phase factors to the quantum walk evolution. We also utilized a cost function to describe the system, where the R – chain, describing the specific amino acid, corresponds to a discrete value, affecting the cost functions value. Our aim is to minimize the cost function value, by updating the dihedral angles for specific regions of the Ramachandran plot, using a Metropolis algorithm.

Contextuality and Wigner Negativity Are Equivalent for Continuous-Variable Quantum Measurements.

Quantum computers promise considerable speedups with respect to their classical counterparts. However, the identification of the innately quantum features that enable these speedups is challenging. In the continuous-variable setting-a promising paradigm for the realization of universal, scalable, and fault-tolerant quantum computing-contextuality and Wigner negativity have been perceived as two such distinct resources. Here we show that they are in fact equivalent for the standard models of continuous-variable quantum computing. While our results provide a unifying picture of continuous-variable resources for quantum speedup, they also pave the way toward practical demonstrations of continuous-variable contextuality and shed light on the significance of negative probabilities in phase-space descriptions of quantum mechanics.

Monoidal reverse differential categories

AbstractCartesian reverse differential categories (CRDCs) are a recently defined structure which categorically model the reverse differentiation operations used in supervised learning. Here, we define a related structure called a monoidal reverse differential category, prove important results about its relationship to CRDCs, and provide examples of both structures, including examples coming from models of quantum computation.

Dimer states of Rydberg atoms on the Kagome lattice as resources for universal measurement-based quantum computation

We show that the quantum dimer state on the Kagome lattice, which was recently realized with high fidelity in a Rydberg quantum simulator [G. Semeghini et al., Science 374, 6572 (2021)], offers a sufficient resource for universal measurement-based quantum computations. In particular, we provide an efficient encoding of logical qubits in this state and give explicit measurement sequences that implement a universal set of gates on these qubits. Since the building blocks of the proposed measurements have already been experimentally implemented, our work highlights one possible path toward promoting Rydberg simulators to universal quantum computers relying on the measurement-based model of quantum computation with currently existing technology.

DNA Sequence and Structure under the Prism of Group Theory and Algebraic Surfaces.

Taking a DNA sequence, a word with letters/bases A, T, G and C, as the relation between the generators of an infinite group π, one can discriminate between two important families: (i) the cardinality structure for conjugacy classes of subgroups of π is that of a free group on one to four bases, and the DNA word, viewed as a substitution sequence, is aperiodic; (ii) the cardinality structure for conjugacy classes of subgroups of π is not that of a free group, the sequence is generally not aperiodic and topological properties of π have to be determined differently. The two cases rely on DNA conformations such as A-DNA, B-DNA, Z-DNA, G-quadruplexes, etc. We found a few salient results: Z-DNA, when involved in transcription, replication and regulation in a healthy situation, implies (i). The sequence of telomeric repeats comprising three distinct bases most of the time satisfies (i). For two-base sequences in the free case (i) or non-free case (ii), the topology of π may be found in terms of the SL(2,C) character variety of π and the attached algebraic surfaces. The linking of two unknotted curves-the Hopf link-may occur in the topology of π in cases of biological importance, in telomeres, G-quadruplexes, hairpins and junctions, a feature that we already found in the context of models of topological quantum computing. For three- and four-base sequences, other knotting configurations are noticed and a building block of the topology is the four-punctured sphere. Our methods have the potential to discriminate between potential diseases associated to the sequences.