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quantum algorithm for calculating risk contributions in a credit portfolio

EPJ quantum TECHNOLOGY 2022年第1期9卷 32-32页

作者： Miyamoto, Koichi Osaka Univ Ctr Quantum Informat & Quantum Biol 1-2 Machikaneyama Toyonaka Osaka Japan

Finance is one of the promising field for industrial application of quantum computing. In particular, quantum algorithms for calculation of risk measures such as the value at risk and the conditional value at risk of a credit portfolio have been proposed. In this paper, we focus on another problem in credit risk management, calculation of risk contributions, which quantify the concentration of the risk on subgroups in the portfolio. Based on the recent quantum algorithm for simultaneous estimation of multiple expected values, we propose the method for credit risk contribution calculation. We also evaluate the query complexity of the proposed method and see that it scales as (O) over tilde(root N-gr/epsilon) on the subgroup number N-gr and the accuracy epsilon, in contrast with the classical method with (O) over tilde (log(N-gr)/epsilon(2)) complexity. This means that, for calculation of risk contributions of finely divided subgroups, the advantage of the quantum method is reduced compared with risk measure calculation for the entire portfolio. Nevertheless, the quantum method can be advantageous in high-accuracy calculation, and in fact yield less complexity than the classical method in some practically plausible setting.

关键词： quantum algorithm Financial risk management Multiple expected value estimation

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quantum algorithm for Machine Learning and Circuit Design Based on Optimization of Ternary - Input, Binary-Output Kronecker-Reed-Muller Forms 51

Quantum Algorithm for Machine Learning and Circuit Design Ba...

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51st IEEE International Symposium on Multiple-Valued Logic (ISMVL)

作者： Bao, Maggie Powers, Cole Perkowski, Marek Portland State Univ Dept Elect & Comp Engn Portland OR 97207 USA

ISBN: (纸本)9781728192246

Paper introduces a new spectral expansion of ternary-input binary-output functions that generalizes the binary Kronecker-Reed-Muller forms. Two binary Davio Expansions are generalized to 27 Ternary-Input Davio Expansions. New KRM spectrum has 28(n) expansions for n ternary variables. By creating an oracle for this problem we generalize the quantum Grover-based algorithms presented for the binary FPRM and KRM forms in the past. Because the method finds solutions also to incompletely specified functions, it can be used to both quantum circuit design and Machine Learning classifier design.

关键词： Computers Multiplexing quantum algorithm Minimization methods Qubit Machine learning Transforms

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The duality game: a quantum algorithm for body dynamics modeling

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quantum INFORMATION PROCESSING 2024年第1期23卷 21-21页

作者： Nguyen, Phuong-Nam PHENIKAA Univ Fac Comp Sci Hanoi 12116 Vietnam

In recent years, quantum algorithms have emerged as a groundbreaking approach toward solving complex computational problems, particularly in physical modeling and artificial intelligence. This study introduces a novel quantum algorithm termed the duality game, tailored for addressing challenges in body dynamics modeling. The practicality and efficacy of the proposed algorithm are elucidated through three distinct data scenarios: (1) approximation of classical von Bertalanffy growth in the presence of random noise (simulated), (2) personalized tumor burden modeling leveraging a small dataset, and (3) modeling of COVID-19 population growth employing big data analytics. The algorithm's performance in these scenarios underscores its potential for practical applications at a large scale. Moreover, the findings foster optimism regarding the algorithm's promise in the burgeoning field of physical-based quantum artificial intelligence (quantum AI). Through the duality game, a pathway is delineated for addressing real-world problems in body dynamics, opening avenues for further research and development in quantum AI, aimed at harnessing quantum computational advantages for solving intricate physical modeling problems.

关键词： quantum algorithm quantum artificial intelligence quantum machine learning

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A Performance Comparison of Classical and quantum algorithm for Active User Detection 23

A Performance Comparison of Classical and Quantum Algorithm ...

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23rd International Workshop on Signal Processing Advances in Wireless Communication (SPAWC)

作者： Habibie, Muhammad Idham Hamie, Jihad Goursaud, Claire Univ Lyon INSA Lyon INRIA CITI EA 3720 F-69621 Villeurbanne France

ISBN: (数字)9781665494557

ISBN: (纸本)9781665494557

The strong growth in the number of connected mobile devices has imposed new challenges in efficiently exploiting the available networks resources. Code Domain Non-Orthogonal Multiple Access (NOMA) technique appears as a tremendous efficient solution. Each device uses its assigned code to simultaneously transmit its data along with the user identifier, without any resource reservation exchange, saving precious wireless resources. However, this requires a receiver capable of blindly detecting the active users, which is highly complex. Driven by the promising superposition property of quantum architecture, the goal of this paper is to adapt and apply the quantum Grover algorithm for Active User Detection (AUD) purpose in the context of NOMA, to alleviate the search complexity. This adapted Grover's algorithm is compared with the optimal classical Maximum Likelihood (ML) AUD receivers, as well as with the basic classical Conventional Correlation Receiver (CCR). A benchmark on the probability of AUD is assessed as a function of the Signal to Noise Ratio (SNR) of the received signal. We show that our adapted Grover's algorithm is very promising in high SNR regime.

关键词： NOMA AUD Maximum Likelihood quantum algorithm Grover's algorithm

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PUSHO, a pulse-level variational quantum algorithm for Rydberg atom platforms 3

PUSHO, a pulse-level variational quantum algorithm for Rydbe...

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3rd IEEE International Conference on quantum Computing and Engineering (QCE)

作者： Leclerc, Lucas Henriet, Loic Pasqal 2 Ave Augustin Fresnel F-91120 Palaiseau France

ISBN: (数字)9781665491136

ISBN: (纸本)9781665491136

The manipulation of neutral atoms by light is at the heart of countless scientific discoveries in the field of quantum physics in the last three decades. The level of control that has been achieved at the single particle level within arrays of optical traps, while preserving the fundamental properties of quantum matter (coherence, entanglement, superposition), makes these technologies prime candidates to implement disruptive computation paradigms. The current quantum processing units (QPU) are nothing close to universal computers but can already target specific combinatorial problems, on which many industrial issues can be mapped. Problems, whose classical complexity scales exponentially with their size, such as finding the Maximum Independent Set (MIS) of a Unit-Disk (UD) graph or approximating the solution of a Quadratic Unconstrained Binary Optimisation (QUBO) can be mapped to Rydberg platforms. It enables to solve them by approximating their cost function with the Hamiltonian of the atomic array. Then the atoms are optimally driven with implementable laser pulses shaped by Bayesian Optimisation (BO) to a solution state which minimises the previous cost. Initially, BO performs well with fewer iterations than others classical algorithms and additionally can maintain this level with noisier estimations, especially when the number of shots is limited for instance. Pulse Shaping Optimisation (PUSHO) provides a straightforward but powerful Variational quantum algorithm (VQA), taking advantage of our ability to precisely control the shape of the driving fields.

关键词： Heart quantum algorithm Optical pulse shaping Costs Shape quantum entanglement Rydberg atoms

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A quantum algorithm for Boolean Functions Processing

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IEEE ACCESS 2024年 12卷 164503-164519页

作者： Aljuaydi, Fahad Abdelazim, Samar Darwish, Mohamed M. Zidan, Mohammed Prince Sattam bin Abdulaziz Univ Coll Sci & Humanities Dept Math Al Kharj 11942 Saudi Arabia Assiut Univ Fac Comp & Informat Dept Comp Sci Asyut 71515 Egypt Univ Tabuk Univ Coll Al Wajh Dept Comp Sci Tabuk 71491 Saudi Arabia Hurghada Univ Fac Comp & Artificial Intelligence Dept Artificial Intelligence Hurghada Egypt

Detecting junta variables is a critical issue in Boolean function analysis, circuit design optimization, and machine learning feature selection. In this paper, we investigate a novel quantum computation algorithm based on the Mz operator. The algorithm takes in an unknown oracle concealing a Boolean function with n variables and an unknown input state, which can be quantum or classical. The input state can be complete or incomplete quantum basis states, and it can be a weighted or uniform superposition of basis states. The proposed approach determines whether a given variable is a junta with a time cost of O (2 /& varepsilon;(2) ) and a memory cost of 2n+ 6. The algorithm is analyzed and experimentally implemented using the Qiskit simulator and IBM's real quantum computer. Experimental results show that the proposed approach achieved a quantum supremacy ratio 6300% higher than that of the classical method when verifying junta variables for Boolean functions with 12 variables. The results suggest that the proposed quantum method can verify junta variables in scenarios beyond the capabilities of current classical or quantum methods.

关键词： quantum computing Boolean functions Qubit Computational modeling quantum entanglement Machine learning Costs Testing Computer science Time complexity quantum algorithm junta problem Mz entanglement

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quantum algorithm for credit valuation adjustments

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NEW JOURNAL OF PHYSICS 2022年第2期24卷 023036页

作者： Alcazar, Javier Cadarso, Andrea Katabarwa, Amara Mauri, Marta Peropadre, Borja Wang, Guoming Cao, Yudong Zapata Comp Canada Inc 325 Front St W Toronto ON M5V 2Y1 Canada BBVA Corp & Investment Banking Calle Sauceda 28 Madrid 28050 Spain Zapata Comp Inc 100 Fed St Boston MA 02110 USA

quantum mechanics is well known to accelerate statistical sampling processes over classical techniques. In quantitative finance, statistical samplings arise broadly in many use cases. Here we focus on a particular one of such use cases, credit valuation adjustment (CVA), and identify opportunities and challenges towards quantum advantage for practical instances. To build a NISQ-friendly quantum circuit able to solve such problem, we draw on various heuristics that indicate the potential for significant improvement over well-known techniques such as reversible logical circuit synthesis. In minimizing the resource requirements for amplitude amplification while maximizing the speedup gained from the quantum coherence of a noisy device, we adopt a recently developed Bayesian variant of quantum amplitude estimation using engineered likelihood functions. We perform numerical analyses to characterize the prospect of quantum speedup in concrete CVA instances over classical Monte Carlo simulations.

关键词： quantum algorithm quantum finance Monte Carlo simulation quantum information

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Study of Error Propagation and Generation in Harrow-Hassidim-Lloyd (HHL) quantum algorithm

Study of Error Propagation and Generation in Harrow-Hassidim...

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IEEE Latin American Electron Devices Conference (LAEDC)

作者： Zaman, Anika Wong, Hiu Yung San Jose State Univ Elect Engn San Jose CA 95192 USA

ISBN: (数字)9781665497671

ISBN: (纸本)9781665497671

In this paper, we study the error propagation and generation in the Harrow-Hassidim-Lloyd (HHL) quantum algorithm runs on IBM-Q hardware with the help of a MATLAB simulator. HHL is a quantum algorithm that can provide exponential speedup over the fastest classical algorithm ( conjugate gradient method) in solving systems of linear equations (SLE). However, without error correction, it cannot give correct results even in a 2-variable system due to its complexity. In this study, an HHL quantum circuit for a 2-variable SLE is implemented in IBM-Q and the error is extracted after each stage of the circuit and compared to a MATLAB simulator. We identified three major sources of errors, namely single-qubit flipping, gate infidelity, and error propagation. We also found that at the ancillary bit rotation stage, the error becomes large but the encoded solution still has high fidelity. However, the solution is mostly lost after the inverse quantum phase estimation which is necessary to extract the solution efficiently. Therefore, it is suggested that error correction resources, if limited, should be added to the second half of the circuit.

关键词： Error HHL quantum algorithm quantum Computing Qubit Flipping

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An Improved quantum algorithm for Ridge Regression

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2021年第3期33卷 858-866页

作者： Yu, Chao-Hua Gao, Fei Wen, Qiao-Yan Beijing Univ Posts & Telecommun State Key Lab Networking & Switching Technol Beijing 100876 Peoples R China State Key Lab Cryptol POB 5159 Beijing 100878 Peoples R China Jiangxi Univ Finance & Econ Sch Informat Technol Nanchang 330032 Jiangxi Peoples R China Univ Western Australia Sch Phys Nedlands WA 6009 Australia Peng Cheng Lab Ctr Quantum Comp Shenzhen 518055 Peoples R China

Ridge regression (RR) is an important machine learning technique which introduces a regularization hyperparameter a to ordinary multiple linear regression for analyzing data suffering from multicollinearity. In this paper, we present a quantum algorithm for RR, where the technique of parallel Hamiltonian simulation to simulate a number of Hermitian matrices in parallel is proposed and used to develop a quantum version of K-fold cross-validation approach, which can efficiently estimate the predictive performance of RR. Our algorithm consists of two phases: (1) using quantum K-fold cross-validation to efficiently determine a good a with which RR can achieve good predictive performance, and then (2) generating a quantum state encoding the optimal fitting parameters of RR with such a, which can be further utilized to predict new data. Since indefinite dense Hamiltonian simulation has been adopted as a key subroutine, our algorithm can efficiently handle non-sparse data matrices. It is shown that our algorithm can achieve exponential speedup over the classical counterpart for (low-rank) data matrices with low condition numbers. But when the condition numbers of data matrices are large to be amenable to full or approximately full ranks of data matrices, only polynomial speedup can be achieved.

关键词： quantum algorithm ridge regression regularization hyperparameter parallel Hamiltonian simulation quantum K-fold cross validation

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An Exact quantum algorithm for the 2-Junta Problem

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INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS 2021年第1期60卷 80-91页

作者： Chen, Chien-Yuan Natl Univ Kaohsiung Dept Comp Sci & Informat Engn 700 Kaohsiung Univ Rd Kaohsiung Taiwan

This paper proposes a novel quantum learning algorithm based on Bernstein and Vazirani's quantum circuit to find the dependent variables of the 2-junta problem. Typically, for a given Boolean function f : {0, 1}(n) -> {0, 1} that depends on only 2 out of n variables, the dependent variables are obtained by evaluating the function 4n times in the worst-case. However, the proposed quantum algorithm only requires O(log(2)n) function operations in the worst-case. Moreover, the algorithm requires an average of 5.3 function operations at the most when n >= 8.

关键词： quantum algorithm quantum learning algorithm The Bernstein-Vazirani algorithm

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