Quantum Speedup and Mathematical Solutions of Implementing Bio-Molecular Solutions for the Independent Set Problem on IBM Quantum Computers

New Tiaoxin Recipe Alleviates Energy Metabolism Disorders in an APPswe/PS1DE9 Mouse Model of Alzheimer's Disease

BACKGROUND

Alzheimer's disease (AD) is a typical neurodegenerative disease with a complex etiology. Until now, there has been no effective treatment available for AD; however, improving energy dysmetabolism, the key pathological event in the early stage of AD, can effectively delay the progression of AD.

OBJECTIVE

This paper aims to investigate the therapeutic effect and potential mechanism of the new Tiaoxin recipe on early AD.

METHODS

APP/PS1 mice were divided into a model group, a new Tiaoxin recipe group, and a donepezil group, and C57/BL mice were used for the control group. Mouse cognitive and learning abilities were tested using the Morris water maze test and a new object-recognition experiment. The 42 amino acid form of amyloid β peptide (Aβ1-42) content was detected by enzyme-linked immunosorbent assay, the senile plaque area was detected by thioflavin S staining, and the senescence- associated β-galactosidase (SA-β-gal)-positive area was detected by chemical staining. Also, the adenosine triphosphate (ATP), nicotinamide adenine dinucleotide (NAD+), and nicotinamide adenine dinucleotide hydride (NADH) contents were detected using a biochemical method, and the cluster of differentiation 38 (CD38) and silent mating-type information regulation 2 homolog 3 (SIRT3) protein expression levels were detected by immunofluorescence and Western blot analysis.

RESULTS

Compared with those of the control group, the learning and memory abilities of the model group were impaired; the senile plaque deposition, Aβ1-42 content, and SA-βgal-positive staining area were increased; the ATP concentration, NAD+ concentration, and NAD+/NADH ratio were decreased; the CD38 protein expression level was increased; and the SIRT3 protein expression level was decreased. Following intervention with the new Tiaoxin recipe, the learning and memory abilities were improved; the senile plaque deposition, Aβ1-42 content, and SA-βgal-positive area were reduced; the ATP concentration, NAD+ concentration, and NAD+/NADH ratio were increased; CD38 protein expression was decreased, and SIRT3 protein expression was increased.

CONCLUSION

This study shows that the new Tiaoxin Recipe can improve cognitive ability and reduce the Aβ1-42 content and senile plaque deposition in APP/PS1 mice, which may occur through the downregulation of CD38 protein expression, upregulation of SIRT3 protein expression, restoration of the NAD+ level, promotion of ATP synthesis, mitigation of energy metabolism disorders.

RBS: A Rotational Coding Based on Blocking Strategy for DNA Storage

The data volume of global information has grown exponentially in recent years, but the development of silicon-based memory has entered a bottleneck period. Deoxyribonucleic acid (DNA) storage is drawing attention owing to its advantages of high storage density, long storage time, and easy maintenance. However, the base utilization and information density of existing DNA storage methods are insufficient. Therefore, this study proposes a rotational coding based on blocking strategy (RBS) for encoding digital information such as text and images in DNA data storage. This strategy satisfies multiple constraints and produces low error rates in synthesis and sequencing. To illustrate the superiority of the proposed strategy, it was compared and analyzed with existing strategies in terms of entropy value change, free energy size, and Hamming distance. The experimental results show that the proposed strategy has higher information storage density and better coding quality in DNA storage, so it will improve the efficiency, practicality, and stability of DNA storage.

Biomolecular and quantum algorithms for the dominating set problem in arbitrary networks

A dominating set of a graph [Formula: see text] is a subset U of its vertices V, such that any vertex of G is either in U, or has a neighbor in U. The dominating-set problem is to find a minimum dominating set in G. Dominating sets are of critical importance for various types of networks/graphs, and find therefore potential applications in many fields. Particularly, in the area of communication, dominating sets are prominently used in the efficient organization of large-scale wireless ad hoc and sensor networks. However, the dominating set problem is also a hard optimization problem and thus currently is not efficiently solvable on classical computers. Here, we propose a biomolecular and a quantum algorithm for this problem, where the quantum algorithm provides a quadratic speedup over any classical algorithm. We show that the dominating set problem can be solved in [Formula: see text] queries by our proposed quantum algorithm, where n is the number of vertices in G. We also demonstrate that our quantum algorithm is the best known procedure to date for this problem. We confirm the correctness of our algorithm by executing it on IBM Quantum's qasm simulator and the Brooklyn superconducting quantum device. And lastly, we show that molecular solutions obtained from solving the dominating set problem are represented in terms of a unit vector in a finite-dimensional Hilbert space.

A DNA Finite-State Machine Based on the Programmable Allosteric Strategy of DNAzyme

Living organisms can produce corresponding functions by responding to external and internal stimuli, and this irritability plays a pivotal role in nature. Inspired by such natural temporal responses, the development and design of nanodevices with the ability to process time-related information could facilitate the development of molecular information processing systems. Here, we proposed a DNA finite-state machine that can dynamically respond to sequential stimuli signals. To build this state machine, a programmable allosteric strategy of DNAzyme was developed. This strategy performs the programmable control of DNAzyme conformation using a reconfigurable DNA hairpin. Based on this strategy, we first implemented a finite-state machine with two states. Through the modular design of the strategy, we further realized the finite-state machine with five states. The DNA finite-state machine endows molecular information systems with the ability of reversible logic control and order detection, which can be extended to more complex DNA computing and nanomachines to promote the development of dynamic nanotechnology.

An Enhanced Quantum K-Nearest Neighbor Classification Algorithm Based on Polar Distance

The K-nearest neighbor (KNN) algorithm is one of the most extensively used classification algorithms, while its high time complexity limits its performance in the era of big data. The quantum K-nearest neighbor (QKNN) algorithm can handle the above problem with satisfactory efficiency; however, its accuracy is sacrificed when directly applying the traditional similarity measure based on Euclidean distance. Inspired by the Polar coordinate system and the quantum property, this work proposes a new similarity measure to replace the Euclidean distance, which is defined as Polar distance. Polar distance considers both angular and module length information, introducing a weight parameter adjusted to the specific application data. To validate the efficiency of Polar distance, we conducted various experiments using several typical datasets. For the conventional KNN algorithm, the accuracy performance is comparable when using Polar distance for similarity measurement, while for the QKNN algorithm, it significantly outperforms the Euclidean distance in terms of classification accuracy. Furthermore, the Polar distance shows scalability and robustness superior to the Euclidean distance, providing an opportunity for the large-scale application of QKNN in practice.

Quantum Algorithm for Variant Maximum Satisfiability

In this paper, we proposed a novel quantum algorithm for the maximum satisfiability problem. Satisfiability (SAT) is to find the set of assignment values of input variables for the given Boolean function that evaluates this function as TRUE or prove that such satisfying values do not exist. For a POS SAT problem, we proposed a novel quantum algorithm for the maximum satisfiability (MAX-SAT), which returns the maximum number of OR terms that are satisfied for the SAT-unsatisfiable function, providing us with information on how far the given Boolean function is from the SAT satisfaction. We used Grover's algorithm with a new block called quantum counter in the oracle circuit. The proposed circuit can be adapted for various forms of satisfiability expressions and several satisfiability-like problems. Using the quantum counter and mirrors for SAT terms reduces the need for ancilla qubits and realizes a large Toffoli gate that is then not needed. Our circuit reduces the number of ancilla qubits for the terms T of the Boolean function from T of ancilla qubits to ≈⌈log₂⁡T⌉+1. We analyzed and compared the quantum cost of the traditional oracle design with our design which gives a low quantum cost.

A Parallel DNA Algorithm for Solving the Quota Traveling Salesman Problem Based on Biocomputing Model

The quota traveling salesman problem (QTSP) is a variant of the traveling salesman problem (TSP), which is a classical optimization problem. In the QTSP, the salesman visits some of the n cities to meet a given sales quota Q while having minimized travel costs. In this paper, we develop a DNA algorithm based on Adleman-Lipton model to solve the quota traveling salesman problem. Its time complexity is O(n²+Q), which is a significant improvement over previous algorithms with exponential complexity. A coding scheme of element information is pointed out, and a reasonable biological algorithm is raised by using limited conditions, whose feasibility is verified by simulation experiments. The innovation of this study is to propose a polynomial time complexity algorithm to solve the QTSP. This advantage will become more obvious as the problem scale increases compared with the algorithm of exponential computational complexity. The proposed DNA algorithm also has the significant advantages of having a large storage capacity and consuming less energy during the operation. With the maturity of DNA manipulation technology, DNA computing, as one of the parallel biological computing methods, has the potential to solve more complex NP-hard problems.

A Hash-Based Quantum-Resistant Designated Verifier Signature Scheme

Digital signatures are unsuitable for specific applications that are sensitive on a personal or commercial level because they are universally verifiable. Jakobsson et al. proposed the Designated Verifier Signature (DVS) system, which only allows the intended verifier to validate a message’s signature. It prohibits the disclosure of a conviction to a third party. This functionality is useful in applications that require both authenticity and signer privacy, such as electronic voting and tender calls. The vast majority of current DVS schemes are based on difficult number theory problems such as integer factorization or discrete log problems over various groups. The development of a large-scale quantum computer would render these schemes unsafe. As a result, it is critical to develop quantum-resistant DVS methods. In both quantum and classical computers, signatures based on one-way functions are more efficient and secure. They have several advantages over digital signatures based on trapdoor functions. As a result, hash-based signatures are now considered viable alternatives to number-theoretic signatures. Existing hash-based signatures, on the other hand, are easily verifiable by anyone. As a result, they do not protect the signer’s identity. In addition, they are one-time signatures. This paper presents a hash-based multi-time designated verifier signature scheme that ensures signer anonymity. The unforgeability of the signature scheme is also tested in the random oracle model under chosen message attack. The properties such as non-transferability and non-delegatability are investigated.

A Hash-Based Quantum-Resistant Chameleon Signature Scheme

As a standard digital signature may be verified by anybody, it is unsuitable for personal or economically sensitive applications. The chameleon signature system was presented by Krawczyk and Rabin as a solution to this problem. It is based on a hash then sign model. The chameleon hash function enables the trapdoor information holder to compute a message digest collision. The holder of a chameleon signature is the recipient of a chameleon signature. He could compute collision on the hash value using the trapdoor information. This keeps the recipient from disclosing his conviction to a third party and ensures the privacy of the signature. The majority of the extant chameleon signature methods are built on the computationally infeasible number theory problems, like integer factorization and discrete log. Unfortunately, the construction of quantum computers would be rendered insecure to those schemes. This creates a solid requirement for construct chameleon signatures for the quantum world. Hence, this paper proposes a novel quantum secure chameleon signature scheme based on hash functions. As a hash-based cryptosystem is an essential candidate of a post-quantum cryptosystem, the proposed hash-based chameleon signature scheme would be a promising alternative to the number of theoretic-based methods. Furthermore, the proposed method is key exposure-free and satisfies the security requirements such as semantic security, non-transferability, and unforgeability.

Solving the Family Traveling Salesperson Problem in the Adleman-Lipton model based on DNA computing

The Family Traveling Salesperson Problem (FTSP) is a variant of the Traveling Salesperson Problem (TSP), in which all vertices are divided into several different families, and the goal of the problem is to find a loop that concatenates a specified number of vertices with minimal loop overhead. As a Non-deterministic Polynomial Complete (NP-complete) problem, it is difficult to deal with it by the traditional computing. On the contrary, as a computer with strong parallel ability, the DNA computer has incomparable advantages over digital computers when dealing with NP problems. Based on this, a DNA algorithm is proposed to deal with FTSP based on the Adleman-Lipton model. In the algorithm, the solution of the problem can be obtained by executing several basic biological manipulations on DNA molecules with O(N2) computing complexity (N is the number of vertices in the problem without the origin). Through the simulation experiments on some benchmark instances, the results show that the parallel DNA algorithm has better performance than traditional computing. The effectiveness of the algorithm is verified by deducing the algorithm process in detail. Furthermore, the algorithm further proves that DNA computing, as one of the parallel computing methods, has the potential to solve more complex big data problems.