Towards practical Quantum Credit Risk Analysis

A dominating set of a graph G = (V, E) 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 O(2^{n/2}) 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.

Low rank approximation in simulations of quantum algorithms

Loan default prediction is an important aspect of risk management in financial institutions. Accurate prediction models enable banks and lending organizations to mitigate risks, allocate resources effectively, and optimize decision-making processes. This study investigates the application of decision tree algorithms in predicting loan default risk in the financial sector. Decision trees are renowned for their interpretability, adaptability to non-linear data, and ability to handle missing values, making them a valuable tool in credit risk analysis. Using a dataset consisting of borrower profiles, credit scores, income levels, and payment history, the model identifies key predictors that influence default outcomes. The study uses the C4.5 decision tree model, which will demonstrate that decision trees achieve high prediction accuracy and offer a transparent decision-making framework, enhancing their applicability in real-world scenarios. Furthermore, the paper highlights the implications of these findings for financial institutions, emphasizing the scalability and cost-effectiveness of the model. By integrating decision tree-based models into existing risk assessment systems, lenders can proactively manage loan portfolios and reduce default rates. Future research directions are proposed to explore hybrid approaches that combine decision trees with advanced combined methods to enhance predictive capabilities. The potential of decision tree algorithms in transforming credit risk assessment and supporting more accurate data-driven financial decision-making processes

This study examines the integration of financial mathematics and artificial intelligence (AI), focusing on credit risk analysis within the financial industry. Traditionally, financial mathematics has played a central role in modeling and assessing credit risk. However, recent technological advancements have enabled a more synergistic relationship between financial mathematics and AI, particularly through the use of machine learning. This integration enhances risk assessment by leveraging classification algorithms to uncover complex patterns in historical data patterns that are often difficult to detect using conventional methods. Through a case study in the financial sector, this research explores the application of classification algorithms to better understand customer behavior, evaluate credit history, and predict the likelihood of future loan repayment. In the realm of machine learning, classification techniques are essential for processing large volumes of data and generating accurate risk predictions. By combining the analytical rigor of financial mathematics with the predictive power of machine learning, this study aims to develop a robust and adaptive model for credit risk analysis one capable of responding to dynamic market and economic conditions, and improving the overall decision-making process in credit assessment.

Bilinear interpolation is widely used in classical signal and image processing. Quantum algorithms have been designed for efficiently realizing bilinear interpolation. However, these quantum algorithms have limitations in circuit width and garbage outputs, which block the quantum algorithms applied to noisy intermediate-scale quantum devices. In addition, the existing quantum bilinear interpolation algorithms cannot keep the consistency between the geometric centers of the original and target images. To save the above questions, we propose quantum bilinear interpolation algorithms based on geometric centers using fault-tolerant implementations of quantum arithmetic operators. Proposed algorithms include the scaling-up and scaling-down for signals (grayscale images) and signals with three channels (color images). Simulation results demonstrate that the proposed bilinear interpolation algorithms obtain the same results as their classical counterparts with an exponential speedup. Performance analysis reveals that the proposed bilinear interpolation algorithms keep the consistency of geometric centers and significantly reduce circuit width and garbage outputs compared to the existing works.

We present a simple and general simulation technique that transforms any black-box quantum algorithm (a la Grover's database search algorithm) to a quantum communication protocol for a related problem, in a way that fully exploits the quantum parallelism. This allows us to obtain new positive and negative results. The positive results are novel quantum communication protocols that are built from nontrivial quantum algorithms via this simulation. These protocols, combined with (old and new) classical lower bounds, are shown to provide the first asymptotic separation results between the quantum and classical (probabilistic) two-party communication complexity models. In particular, we obtain a quadratic separation for the bounded-error model, and an exponential separation for the zero-error model. The negative results transform known quantum communication lower bounds to computational lower bounds in the black-box model. In particular, we show that the quadratic speed-up achieved by Grover for the OR function is impossible for the PARITY function or the MAJORITY function in the bounded-error model, nor is it possible for the OR function itself in the exact case. This dichotomy naturally suggests a study of bounded-depth predicates (i.e. those in the polynomial hierarchy) between OR and MAJORITY. We present black-box algorithms that achieve near quadratic speed up for all such predicates.

With small-scale quantum processors transitioning from experimental physics labs to industrial products, these processors in a few years are expected to scale up and be more robust for efficiently computing important algorithms in various fields. In this paper, we propose a quantum algorithm to address the challenging field of data processing for genome sequence reconstruction. This research describes an architecture-aware implementation of a quantum algorithm for sub-sequence alignment. A new algorithm named QiBAM (quantum indexed bidirectional associative memory) is proposed, which uses approximate pattern-matching based on Hamming distances. QiBAM extends the Grover’s search algorithm in two ways, allowing: (1) approximate matches needed for read errors in genomics, and (2) a distributed search for multiple solutions over the quantum encoding of DNA sequences. This approach gives a quadratic speedup over the classical algorithm. A full implementation of the algorithm is provided and verified using the OpenQL compiler and QX Simulator framework. Our implementation represents a first exploration towards a full-stack quantum accelerated genome sequencing pipeline design.

Quantum computing introduces an efficient way for unfolding complex problems on computing systems. It uses concept of superposition and entanglement, & hence supports intrinsic parallelism for obtaining the speedup in context of time over classical computing. Quantum algorithms can be efficiently implemented over quantum computing system. Most popular quantum algorithms like Grover's and Shor's provide a great foundation to specifically design the algorithms. These algorithms work on improving the lower runtime bounds of classical algorithms. Grover's algorithm exhibits a quadratic polynomial speedup while searching an element among ‘N’ elements unstructured database. The algorithmic strategy can be applied over various computer science related applications and some important are being considered in this article i.e. pattern matching, data mining and machine learning. This article explores quantum fundamentals; history based evolution followed by Grover's search algorithm in detail with cascading advantages, limitations & applications and also finally concludes with the significance of quantum computing & quantum algorithmic domains.

Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce. Recent progress in quantum algorithms for linear-algebra positioned quantum machine learning (QML) as a potential source of such useful exponential improvements. Yet, in an unexpected development, a recent series of "dequantization" results has equally rapidly removed the promise of exponential speedups for several QML algorithms. This raises the critical question whether exponential speedups of other linear-algebraic QML algorithms persist. In this paper, we study the quantum-algorithmic methods behind the algorithm for topological data analysis of Lloyd, Garnerone and Zanardi through this lens. We provide evidence that the problem solved by this algorithm is classically intractable by showing that its natural generalization is as hard as simulating the one clean qubit model – which is widely believed to require superpolynomial time on a classical computer – and is thus very likely immune to dequantizations. Based on this result, we provide a number of new quantum algorithms for problems such as rank estimation and complex network analysis, along with complexity-theoretic evidence for their classical intractability. Furthermore, we analyze the suitability of the proposed quantum algorithms for near-term implementations. Our results provide a number of useful applications for full-blown, and restricted quantum computers with a guaranteed exponential speedup over classical methods, recovering some of the potential for linear-algebraic QML to become one of quantum computing's killer applications.

Tandem mass spectrometry (MS/MS) is a widely used technology for identifying metabolites. De novo metabolite identification is an identification strategy that does not refer to any spectral or metabolite database. However, this strategy is time-consuming and cannot meet the need for high-throughput metabolite identification. Böcker et al. converted the de novo identification problem into the maximum colorful subtree (MCS) problem. Unfortunately, the MCS problem is NPhard, which indicates there are no existing efficient exact algorithms. To address this issue, we propose to apply quantum computing to accelerate metabolite identification. Quantum computing performs computations on quantum computers. The recent progress in this area has brought the hope of making some computationally intractable areas trackable, although there are still no general approaches to converting regular computer algorithms into quantum algorithms. Specifically, there is no efficient quantum algorithm for the MCS problem. The MCS problem can be considered as the combination of many maximum spanning tree problems that can be converted into minimum spanning tree problems. This work applies a quantum algorithm designed for the minimum spanning problem to speed up de novo metabolite identification. The possible strategy for further improving the performance is also briefly discussed.

As quantum computing technology continues to develop, the need for research into novel quantum algorithms is growing. However, such algorithms cannot yet be reliably tested on actual quantum hardware, which is still limited in several ways, including qubit coherence times, connectivity, and available qubits. To facilitate the development of novel algorithms despite this, simulators on classical computing systems are used to verify the correctness of an algorithm, and study its behaviour under different error models. In general, this involves operating on a memory space that grows exponentially with the number of qubits. In this work, we introduce quantum circuit transformations that allow for the construction of parameterised circuits for quantum algorithms. The parameterised circuits are in an ideal form to be processed by quantum compilation tools, such that the circuit can be partially evaluated prior to simulation, and a smaller specialised circuit can be constructed by eliminating fixed input qubits. We show significant reduction in the number of qubits for various quantum arithmetic circuits. Divide-by-n-bits quantum integer dividers are used as an example demonstration. It is shown that the complexity reduces from 4n+2 to 3n+2 qubits in the specialised versions. For quantum algorithms involving divide-by-8 arithmetic operations, a reduction by 28=256 in required memory is achieved for classical simulation, reducing the memory required from 137 GB to 0.53 GB.

Quantum computing is regarded as the future of computing that hopefully provides exponentially large processing power compared to the conventional digital computing. However, current quantum computers do not have the capability to correct errors caused by environmental noise, so that it is difficult to run useful algorithms that require deep quantum circuits. Therefore, emulation of quantum circuits in digital computers is essential. However, emulation of large quantum circuits requires enormous amount of computations, and leads to a very large processing time. To reduce the processing time, we propose an FPGA emulator with high-bandwidth-memory to emulate quantum Fourier transform (QFT), which is a major part of many quantum algorithms. The proposed FPGA emulator is scalable in terms of both processing speed and the number of qubits, and extendable to multiple FPGAs. We performed QFT emulations up to 30 qubits using two FPGAs. According to the measured results, we have achieved 23.6 ~ 24.5 times speed-up compared to a fully optimized 24-core CPU emulator.

With the advancement of quantum computing, verifying the correctness of the quantum circuits becomes critical while developing new quantum algorithms. Constrained by the obstacles of building practical quantum computers, quantum circuit simulation has become a feasible approach to develop and verify quantum algorithms. Although there are many quantum simulators available, they either achieve low performance on CPUs, or limited simulation scale (e.g., number of qubits) on GPUs due to limited memory capacity. Therefore, we propose dgQuEST, a novel acceleration method that utilizes hybrid CPU-GPU memory hierarchies for large-scale quantum circuit simulation across multiple nodes. dgQuEST adopts efficient memory management and communication schemes to leverage the distributed CPU and GPU memories for accelerating large-scale quantum simulation. Our evaluation demonstrates that dgQuEST achieves an average speedup of 403\(\times \) compared to QuEST on quantum circuit simulation with 32 qubits, and scales to quantum circuit simulation with 35 qubits on two GPU nodes, far beyond the state-of-the-art implementation HyQuas can support.KeywordsQuantum simulationDistributed GPU accelerationMemory and communication optimization

We present quantum circuits to implement an exhaustive key search for the Advanced Encryption Standard (AES) and analyze the quantum resources required to carry out such an attack. We consider the overall circuit size, the number of qubits, and the circuit depth as measures for the cost of the presented quantum algorithms. Throughout, we focus on Clifford $$+T$$ gates as the underlying fault-tolerant logical quantum gate set. In particular, for all three variants of AES (key size 128, 192, and 256 bit) that are standardized in FIPS-PUB 197, we establish precise bounds for the number of qubits and the number of elementary logical quantum gates that are needed to implement Grover’s quantum algorithm to extract the key from a small number of AES plaintext-ciphertext pairs.

Motivated by limitations on the depth of near-term quantum devices, we study the depth-computation trade-off in the query model, where depth corresponds to the number of adaptive query rounds and the computation per layer corresponds to the number of parallel queries per round. We achieve the strongest known separation between quantum algorithms with r versus r−1 rounds of adaptivity. We do so by using the k-fold Forrelation problem introduced by Aaronson and Ambainis (SICOMP’18). For k=2r, this problem can be solved using an r round quantum algorithm with only one query per round, yet we show that any r−1 round quantum algorithm needs an exponential (in the number of qubits) number of parallel queries per round. Our results are proven following the Fourier analytic machinery developed in recent works on quantum-classical separations. The key new component in our result are bounds on the Fourier weights of quantum query algorithms with bounded number of rounds of adaptivity. These may be of independent interest as they distinguish the polynomials that arise from such algorithms from arbitrary bounded polynomials of the same degree.