We consider digitized-counterdiabatic quantum computing as an advanced paradigm to approach quantum advantage for industrial applications in the NISQ era. We apply this concept to investigate a discrete mean-variance portfolio optimization problem, showing its usefulness in a key finance application. Our analysis shows a drastic improvement in the success probabilities of the resulting digital quantum algorithm when approximate counterdiabatic techniques are introduced. Along these lines, we discuss the enhanced performance of our methods over variational quantum algorithms like QAOA and DC-QAOA.
We consider digitized-counterdiabatic quantum computing as an advanced paradigm to approach quantum advantage for industrial applications in the NISQ era. We apply this concept to investigate a discrete mean-variance portfolio optimization problem, showing its usefulness in a key finance application. Our analysis shows a drastic improvement in the success probabilities of the resulting digital quantum algorithm when approximate counterdiabatic techniques are introduced. Along these lines, we discuss the enhanced performance of our methods over variational quantum algorithms like QAOA and DC-QAOA.
We propose a faster digital quantum algorithm for portfolio optimization using the digitized counterdiabatic quantum optimization paradigm in the impulse regime, that is, where the counterdiabatic terms are dominant. Our approach notably reduces the circuit depth requirement of the algorithm and enhances the solution accuracy, making it suitable for current quantum processors. We apply this protocol to a real-case scenario of portfolio optimization with 20 assets, using purely quantum and hybrid classical-quantum paradigms. We demonstrate the advantages of our protocol using up to 20 qubits on an IonQ trapped-ion quantum computer. By benchmarking our method against the standard quantum approximate optimization algorithm and finite-time digitized adiabatic algorithms, we obtain a significant reduction in the circuit depth by factors of 2.5 to 40, while minimizing the dependence on the classical optimization subroutine. Besides portfolio optimization, the proposed method is applicable to a large class of combinatorial optimization problems.
Portfolio optimization is a fundamental problem in quantitative finance that seeks to maximize risk-adjusted returns while managing investment risk. With the advent of quantum computing, there is growing interest in applying quantum algorithms to solve complex optimization problems. This paper presents a comprehensive comparative study of quantum and classical approaches to portfolio optimization, specifically comparing the Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigensolver (VQE), and classical mean-variance optimization. We evaluate these methods on both real market data and synthetic datasets with varying correlation structures. Our experimental results show that while classical methods currently outperform quantum approaches on near-term quantum devices in terms of solution quality and computational efficiency, quantum algorithms demonstrate conceptual viability and promise for future applications as quantum hardware improves. The classical method achieves optimal Sharpe ratios of 1.2-1.8, while QAOA and VQE achieve 80-95% and 75-90% of classical performance respectively. This work provides insights into the current state and future potential of quantum computing for financial optimization.
The digital version of adiabatic quantum computing enhanced by counterdiabatic driving, known as digitized counterdiabatic quantum computing, has emerged as a paradigm that opens the door to fast and low-depth algorithms. In this work, we explore the extension of this paradigm to high-dimensional systems. Specifically, we consider qutrits in the context of quadratic problems, obtaining the qutrit Hamiltonian codifications and the counterdiabatic drivings. Our findings show that qutrits can improve the solution quality up to 90 times compared to the qubit counterpart. We tested our proposal on 1000 random instances of the multiway number partitioning, max 3-cut, and portfolio optimization problems, demonstrating that, in general, without prior knowledge, it is better to use qutrits and, apparently, high-dimensional systems in general instead of qubits. Finally, considering the state-of-the-art quantum platforms, we show the experimental feasibility of our high-dimensional counterdiabatic quantum algorithms at least in a fully digital form. This work paves the way for the efficient codification of optimization problems in high-dimensional spaces and their efficient implementation using counterdiabatic quantum computing.
Portfolio optimization under realistic constraints represents a computationally intensive problem for classical financial models, particularly in volatile and high-dimensional markets such as India.Conventional mean-variance approaches become NP-hard when integer, cardinality, and regulatory constraints are incorporated.This paper investigates the applicability of quantum computing techniques for constrained portfolio optimization in the Indian financial context.The study analyzes quantum annealing and gate-based variational algorithms, including the Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE), with emphasis on Quadratic Unconstrained Binary Optimization (QUBO) formulations.In addition, quantum amplitude estimation methods are examined for accelerating financial risk metrics such as Value-at-Risk and Conditional Value-at-Risk.Empirical results derived from thematic and regression analyses indicate that perceived computational advantage and organizational readiness significantly influence adoption intent, while quantum-related security risks act as a moderating factor.The findings suggest that hybrid classical-quantum architectures provide a practical pathway during the Noisy Intermediate-Scale Quantum era.The paper concludes that early-stage quantum adoption, combined with post-quantum cryptographic preparedness, can enhance portfolio efficiency and risk governance for Indian institutional investors
Quantum computing is no longer in its early stages. There already exists quantum computers with more qubits than a classical computer is capable of efficiently simulating. This current stage is considered intermediate and is therefore called the NISQ era (noisy intermediate-scale quantum). The main feature of this current stage is that there are still not enough qubits to perform quantum error correction, hence the noisy name. In this context of quantum computing without quantum error correction and with an intermediate number of qubits, variational algorithms gained prominence and, among them, there is one called QAOA (quantum approximate optimization algorithm). As the name suggests, this is a quantum algorithm that approximates the solution of optimization problems. The objective of this work was to apply this algorithm to solve an optimization problem in the finance area known as portfolio optimization. This application took place both in an ideal way (without noise) and in a way consistent with the current capacity of quantum computers (with noise). Both were simulated using IBM’s Python tool for simulation and access of quantum computers via cloud called Qiskit. The results suggest that the QAOA performance with noise was, as expected, worse than the ideal case, but still satisfactory within the limitations of the method.
Portfolio optimization under conditions of risk and market uncertainty remains a foundational challenge in financial economics and investment management. Classical optimization frameworks, including mean–variance models and stochastic programming approaches, often struggle with high-dimensional asset universes, nonlinear correlations, and dynamic market regimes. This paper examines quantum computing approaches to portfolio optimization under risk and market uncertainty, focusing on hybrid quantum–classical algorithms designed to enhance combinatorial optimization and probabilistic modeling. By integrating quantum annealing, variational quantum circuits, and quantum-enhanced sampling techniques with classical financial analytics, the study evaluates their potential to improve computational efficiency and scenario sensitivity. The analysis considers both theoretical advantages and practical limitations within the Noisy Intermediate-Scale Quantum (NISQ) era. The findings suggest that quantum-assisted optimization may complement traditional portfolio models by expanding feasible solution spaces and improving robustness under uncertainty, thereby contributing to more adaptive and resilient investment strategies.