Large-scale portfolio optimization using Pauli Correlation Encoding

Variational quantum algorithms (VQAs) are promising hybrid quantum-classical methods designed to leverage the computational advantages of quantum computing while mitigating the limitations of current noisy intermediate-scale quantum (NISQ) hardware. Although VQAs have been demonstrated as proofs of concept, their practical utility in solving real-world problems—and whether quantum-inspired classical algorithms can match their performance—remains an open question. We present a novel application of the variational quantum linear solver (VQLS) and its classical neural quantum states-based counterpart, the variational neural linear solver (VNLS), as key components within a minimum map Newton solver for a complementarity-based rigid-body contact model. We demonstrate using the VNLS that our solver accurately simulates the dynamics of rigid spherical bodies during collision events. These results suggest that quantum and quantum-inspired linear algebra algorithms can serve as viable alternatives to standard linear algebra solvers for modelling certain physical systems.This article is part of the theme issue ‘Numerical analysis, spectral graph theory, orthogonal polynomials and quantum algorithms’.

Portfolio optimization aims at constructing a realistic portfolio with significant out-of-sample performance, which is typically measured by the out-of-sample Sharpe ratio. However, due to in-sample optimism, it is inappropriate to use the in-sample estimated covariance to evaluate the out-of-sample Sharpe, especially in the high dimensional settings. In this article, we propose a novel method to estimate the out-of-sample Sharpe ratio using only in-sample data, based on random matrix theory. Furthermore, portfolio managers can use the estimated out-of-sample Sharpe as a criterion to decide the best tuning for constructing their portfolios. Specifically, we consider the classical framework of Markowits mean-variance portfolio optimization under high dimensional regime of p / n → c ∈ ( 0 , ∞ ) , where p is the portfolio dimension and n is the number of samples or time points. We propose to correct the sample covariance by a regularization matrix and provide a consistent estimator of its Sharpe ratio. The new estimator works well under either of the following conditions: (a) bounded covariance spectrum, (b) arbitrary number of diverging spikes when c < 1 , and (c) fixed number of diverging spikes with weak requirement on their diverging speed when c ≥ 1 . We can also extend the results to construct global minimum variance portfolio and correct out-of-sample efficient frontier. We demonstrate the effectiveness of our approach through comprehensive simulations and real data experiments. Our results highlight the potential of this methodology as a useful tool for portfolio optimization in high dimensional settings. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Abstract: This chapter explores the transformative potential of quantum algorithms in solving complex optimization problems across industries such as logistics, finance, and material science. Quantum algorithms, including Quantum Annealing, Quantum Approximate Optimization Algorithm (QAOA), and Variational Quantum Eigensolver (VQE), offer unprecedented computational capabilities for addressing challenges that are impractical for classical algorithms. In logistics, quantum algorithms optimize supply chains, vehicle routing, and warehouse operations, significantly reducing costs and improving efficiency. In finance, quantum optimization enables better portfolio management, risk assessment, and high-frequency trading strategies, providing faster, more accurate solutions. In material science, quantum algorithms accelerate the discovery and design of new materials, such as superconductors and catalysts, by simulating molecular interactions more efficiently. The chapter discusses real-world implementations, current technical challenges, and the future potential of quantum algorithms to revolutionize industries through faster and more scalable optimization solutions. Keywords: Quantum algorithms, Quantum Annealing, QAOA, VQE, optimization, logistics, finance, material science, portfolio optimization, risk management, supply chain, molecular simulation, quantum computing, quantum optimization, quantum chemistry, high-frequency trading.

This article explores the role of physical residential real estate within the optimal multi-asset portfolio. Specifically, we consider direct housing within the Grand Paris metropolis between 1996 and 2017 as an asset class together with financial assets. Our findings bring several contributions to the residential market literature. First, directly held housing investment brings diversification benefits to the mixed-asset portfolio. Second, using hierarchical clustering technique, we divide the Greater Paris area into five homogenous groups of communes and compute the optimal weight of each commune as well as each group of communes in the tangency portfolio. Third, we check the weights’ stability through time and confirm that residential real estate always catches the highest weight in the optimal portfolio. Finally, we run additional tests to compare listed real estate performances in a mixed asset portfolio with those obtained by considering physical residential real estate. We conclude that listed real estate is not a substitute for direct housing.

Quantum computing serves as a revolutionary paradigm in computing, harnessing quantum mechanics principles such as quantum entanglement and superposition for optimization simulation, machine learning, and other problems that are a challenge to classical computer systems. The article will examine different usage opportunities in retail and supply chain operations, healthcare and life sciences domains, insurance operations, and financial service industries. Better computation can be achieved with quantum algorithms in discrete and continuous optimization, logistics network optimization, warehouse management, and product delivery optimized by quantum algorithms. Application domains in healthcare include simulation of molecules for medical breakthroughs, genomic analysis, and medical studies optimized by quantum eigenvalue algorithms and quantum eigensolver algorithms. The insurance industry portfolio targets catastrophic modeling, identification, and risk assessment optimized by quantum amplitude estimation algorithms and quantum machine learning algorithms. Financial service industries include derivative pricing, portfolio optimization, credit risk evaluation, and real-time risk calculation optimized in quantum algorithms. The path towards achieving quantum benefit in quantum technology involves using noisy intermediate quantum technology with hybrid quantum and classical designs and error management schemes, where integration opportunities for different industries arise from their common computation problem schemas in need of further scaling in hardware technology.

Portfolio Analysis is one of the alternative alternative tools in making investment decisions in stocks. In investing, if it only depends on one type of stock, it is likely that many investors will bear the risk. This stage involves identifying which securities will be chosen to form a portfolio and what proportion of funds will be invested in each of these securities. The selection of these securities (in other words, investors diversify) is intended to minimize the risk borne. The selection of these securities will be influenced by risk preferences, cash needs patterns, and tax status. Investment decisions are decisions taken by investors to allocate the funds they have in the form of certain assets (financial assets) in the hope that they will get economic benefits in the future. If the decision taken is to buy a certain number of shares, then that is expected to get dividends and capital gains if the shares are resold. The main consideration for fund owners (investors) in optimizing investment decisions is to maximize the level of return on investment (risk) for certain investments (Saragih et al., 2006). The making of an investment decision framework largely determines the success of an investor in optimizing the level of investment returns and reducing as little as possible the risks faced (Markowitz, 1952). In connection with the above, the main problem in this study is how to design an optimal portfolio simulation which is a combination of LQ 45 liquid stocks listed on the Indonesia Stock Exchange (IDX). The research data was conducted on LQ 45 shares during the period March - June 2012. The variables of this study were stock prices, returns, standard deviations of returns. The statistical method used is the F-test for homogeneity of variants. The results showed that only 16 stocks had optimal portfolios. Optimal portfolio, characterized by high return and low risk.

Quantum computing has become a pivotal innovation in computational science, offering novel avenues for tackling the increasingly complex and high-dimensional optimization challenges inherent in engineering design. This paradigm shift is particularly pertinent in the domain of structural optimization, where the intricate interplay of design variables and constraints necessitates advanced computational strategies. In this vein, the gate-based variational quantum algorithm utilizes quantum superposition and entanglement to improve search efficiency in large solution spaces. This paper delves into the gate-based variational quantum algorithm for the discrete variable truss structure size optimization problem. By reformulating this optimization challenge into a quadratic, unconstrained binary optimization framework, we bridge the gap between the discrete nature of engineering optimization tasks and the quantum computational paradigm. A detailed algorithm is outlined, encompassing the translation of the truss optimization problem into the quantum problem, the initialization and iterative evolution of a quantum circuit tailored to this problem, and the integration of classical optimization techniques for parameter tuning. The proposed approach demonstrates the feasibility and potential of quantum computing to transform engineering design and optimization, with numerical experiments validating the effectiveness of the method and paving the way for future explorations in quantum-assisted engineering optimizations.

We introduce a method for solving combinatorial optimization problems on digital quantum computers, where we incorporate auxiliary counterdiabatic (CD) terms into the adiabatic Hamiltonian, while integrating bias terms derived from an iterative digitized counterdiabatic quantum algorithm. We call this protocol bias-field digitized counterdiabatic quantum optimization (BF-DCQO). Designed to effectively tackle large-scale combinatorial optimization problems, BF-DCQO demonstrates resilience against the limitations posed by the restricted coherence times of current quantum processors and shows clear enhancement even in the presence of noise. Additionally, our purely quantum approach eliminates the dependency on classical optimization required in hybrid classical-quantum schemes, thereby circumventing the trainability issues often associated with variational quantum algorithms. Through the analysis of an all-to-all connected general Ising spin-glass problem, we exhibit a polynomial scaling enhancement in ground-state success probability compared to traditional DCQO and finite-time adiabatic quantum optimization methods. Furthermore, it achieves scaling improvements in ground-state success probabilities, increasing by up to two orders of magnitude, and offers an average 1.3× better approximation ratio than the quantum approximate optimization algorithm for the problem sizes studied. We validate these findings through experimental implementations on both trapped-ion quantum computers and superconducting processors, tackling a maximum weighted independent set problem with 36 qubits and a spin glass on a heavy-hexagonal lattice with 100 qubits, respectively. These results mark a significant advancement in gate-based quantum computing, employing a fully quantum algorithmic approach.

Quantum computing is conceived as a promising and powerful next-generation platform for information processing and it has been shown that it could bring significant accelerations to certain tasks, compared to its classical counterparts. With recent advances in noisy intermediate-scale quantum (NISQ) devices, we can process classical data from real-world problems using hybrid quantum systems. In this work, we investigate the critical problem of designing a gate-based hybrid quantum neuron under NISQ constraints to enable the construction of scalable hybrid quantum deep neural networks (HQDNNs). We explore and characterize diverse quantum circuits for hybrid quantum neurons and discuss related critical components of HQDNNs. We also utilize a new schema to infer multiple predictions from a single hybrid neuron. We further compose a highly customizable platform for simulating HQDNNs via Qiskit and test them on diverse classification problems including the iris and the wheat seed datasets. The results show that even HQDNNs with the simplest neurons could lead to superior performance on these tasks. Finally, we show that the HQDNNs are robust to certain levels of noise, making them preferred on NISQ devices. Our work provides a comprehensive investigation of building scalable near-term gate-based HQDNNs and paves the way for future studies of quantum deep learning via both simulations on classical computers and experiments on accessible NISQ devices.

Interconnections and contagion among cryptocurrencies, DeFi, NFT and traditional financial assets: Some new evidence from tail risk driven network

Transaction lot as a rule in real stock market had implemented in several portfolio optimization models. In almost all these models, the stock price became part of the constraint(s), but the role is not well understood. In this study, we compare the effectiveness of portfolio optimization models with transaction lot in different asset price level. We conduct a simulation study using 15 portfolios, each consists of four assets with various price range. We find that the usage of different stock price did not affect the performance of minimum- variance portfolio optimization with transaction lots. On the other hand, the performance of minimum-CVaR portfolio optimization with transaction lots is largely affected by stock price.

A further look at household portfolio choice and health status

The investment value of optimized portfolios depends on proper input estimation as well as effective portfolio optimization. For many analysts and investors, input estimation methods may seem a largely settled and uncontroversial issue. Managers usually base asset allocation risk-return estimates on sample means, standard deviations, and correlations computed from historic returns, with adjustments for current information. Institutional equity portfolio optimization generally employs commercial risk measurement services for estimating the components of portfolio risk and advanced statistical methods for computing return. Contemporary professional statisticians use a variety of modern statistical techniques that are designed to improve the forecast value of estimates of risk and return from historic data.1 Many of these new procedures are based on results that indicate current investment practice may be suboptimal. These results are particularly important because investment intuition is unreliable. Portfolio optimization requires multivariate statistical estimation; that is, the simultaneous estimation of means, standard deviations, and correlations for many securities. Since financial assets are generally related to each other, there is likely to be information in the group of returns that can improve parameter estimates for each asset.

Portfolio optimization is an important research field in modern finance. The most important characteristic within this optimization problem is the risk and the returns. Modern portfolio theory provides a well-developed paradigm to form a portfolio with the highest expected return for a given level of risk tolerance. Multi objective portfolio optimization problem is the portfolio selection process that result highest expected return and smallest identified risk among the various financial assets. In this paper, we propose to identify expected return (mean profit) and risk using historical data of stock prices. The downside values of the variance of each stock are considered to be the identified risk in first case. The value at risk of each stock that we obtained using parametric and historical simulation methodology are considered to be the identified risk in second case. One of method being widely used lately for optimization need is Genetic Algorithm or GA. This method adapted the mechanism of biology mechanism involving natural selection. With many advantages it has, numerical process of a portfolio optimization in both case are attempted to be coupled with Genetic Algorithm. The values of expected return and risk of each stock will be used as inputs into a fitness function in Genetic Algorithm. Performance evaluation is done by examining the parameters of GA, such as population size, stall generation and number of elitism.

Circuit-based quantum computing (CBQC), also known as the gate model, is currently regarded as the leading paradigm for performing quantum computation and has garnered widespread interest due to its relatively better-established implementation and close intuitive resemblance to classical computation. However, an alternative model that solely utilizes single-qubit measurements on entangled states to perform computation, namely the measurement-based quantum computing (MBQC), has started to attract further research interest as it is deemed more naturally suited for certain quantum hardware architectures, though its actual implementation remains largely underexplored. Recently, there have been preliminary efforts to characterize the specific regimes in which MBQC may potentially be more advantageous compared to CBQC. Nevertheless, a more systematic assessment is necessary to assess the suitability of each model across a broader range of more practical cases. In this work, we present a detailed comparative analysis of CBQC and MBQC, beginning with reviewing the theoretical foundations of each model before highlighting its distinguishing features that set the two paradigms apart. Furthermore, building on previous work, we propose a generalized regime analysis that more accurately captures the conditions under which a given quantum algorithm is more favorably executed in MBQC or CBQC. Subsequently, we identify critical parameters that likely determine whether a quantum algorithm is better suited to CBQC or MBQC, categorizing detailed key factors and performance metrics into layers of quantum computation. Next, we propose a decision flow that, given specific hardware constraints and algorithm requirements, guides the selection to the most appropriate model, discussing suitability in two representative worked examples of quantum algorithm applications: Quantum Fourier Transform (QFT) and Variational Quantum Algorithm (VQE). Last, we discuss the potential to combine both models as a hybrid approach to leverage the best of both worlds and explore its benefits for practical quantum computing applications.