Abstract In-depth theoretical and practical research is nowadays being performed on variational quantum algorithms (VQAs), which have the potential to surpass traditional, classical, algorithms on a variety of problems, in physics, chemistry, biology, and optimization. Because they are hybrid quantum-classical algorithms, it takes a certain set of optimal conditions for their full potential to be exploited. For VQAs, the construction of an appropriate ansatz in particular is crucial, since it lays the ground for efficiently solving the particular problem being addressed. To prevent severe negative effects that hamper quantum computation, the substantial noise, together with the structural limitations, characteristic of currently available devices must be also taken into consideration while building the ansatz. In this work the effect of the quantum hardware structure, namely the topological properties emerging from the couplings between the physical qubits and the basis gates of the device itself, on the performances of VQAs is addressed. Specifically, it is here experimentally shown that a complex connectivity in the ansatz, albeit being beneficial for exploring wider sets of solutions, introduces an overhead of gates during the transpilation on a quantum computer that increases the overall error rate, thus undermining the quality of the training. It is hence necessary, when implementing a variation quantum learning algorithm, to find the right balance between a sufficiently parametrized ansatz and a minimal cost in terms of resources during transpilation. Moreover, the experimental finding allows to construct a heuristic metric function, which aids the decision-making process on the best possible ansatz structure to be deployed on a given quantum hardware, thus fostering a more efficient application of VQAs in realistic situations. The experiments are performed on two widely used variational algorithms, the VQE (variational quantum eigensolver) and the VQC (variational quantum classifier), both tested on two different problems, the first on the Markowitz portfolio optimization using real-world financial data, and the latter on a classification task performed on the Iris dataset.
Abstract In-depth theoretical and practical research is nowadays being performed on variational quantum algorithms (VQAs), which have the potential to surpass traditional, classical, algorithms on a variety of problems, in physics, chemistry, biology, and optimization. Because they are hybrid quantum-classical algorithms, it takes a certain set of optimal conditions for their full potential to be exploited. For VQAs, the construction of an appropriate ansatz in particular is crucial, since it lays the ground for efficiently solving the particular problem being addressed. To prevent severe negative effects that hamper quantum computation, the substantial noise, together with the structural limitations, characteristic of currently available devices must be also taken into consideration while building the ansatz. In this work the effect of the quantum hardware structure, namely the topological properties emerging from the couplings between the physical qubits and the basis gates of the device itself, on the performances of VQAs is addressed. Specifically, it is here experimentally shown that a complex connectivity in the ansatz, albeit being beneficial for exploring wider sets of solutions, introduces an overhead of gates during the transpilation on a quantum computer that increases the overall error rate, thus undermining the quality of the training. It is hence necessary, when implementing a variation quantum learning algorithm, to find the right balance between a sufficiently parametrized ansatz and a minimal cost in terms of resources during transpilation. Moreover, the experimental finding allows to construct a heuristic metric function, which aids the decision-making process on the best possible ansatz structure to be deployed on a given quantum hardware, thus fostering a more efficient application of VQAs in realistic situations. The experiments are performed on two widely used variational algorithms, the VQE (variational quantum eigensolver) and the VQC (variational quantum classifier), both tested on two different problems, the first on the Markowitz portfolio optimization using real-world financial data, and the latter on a classification task performed on the Iris dataset.
In recent years, Variational Quantum Algorithms (VQAs) have emerged as a promising approach for solving optimization problems on quantum computers in the NISQ era. However, one limitation of VQAs is their reliance on fixed-structure circuits, which may not be taylored for specific problems or hardware configurations. A leading strategy to address this issue are Adaptative VQAs, which dynamically modify the circuit structure by adding and removing gates, and optimize their parameters during the training. Several Adaptative VQAs, based on heuristics such as circuit shallowness, entanglement capability and hardware compatibility, have already been proposed in the literature, but there is still lack of a systematic comparison between the different methods. In this paper, we aim to fill this gap by analyzing three Adaptative VQAs: Evolutionary Variational Quantum Eigensolver (EVQE), Variable Ansatz (VAns), already proposed in the literature, and Random Adapt-VQE (RA-VQE), a random approach we introduce as a baseline. In order to compare these algorithms to traditional VQAs, we also include the Quantum Approximate Optimization Algorithm (QAOA) in our analysis. We apply these algorithms to QUBO problems and study their performance by examining the quality of the solutions found and the computational times required. Additionally, we investigate how the choice of the hyperparameters can impact the overall performance of the algorithms, highlighting the importance of selecting an appropriate methodology for hyperparameter tuning. Our analysis sets benchmarks for Adaptative VQAs designed for near-term quantum devices and provides valuable insights to guide future research in this area.
With the advancement of quantum computing in the Noisy Intermediate-Scale Quantum (NISQ) era, hybrid quantum-classical algorithms have emerged as promising approaches for addressing certain machine learning tasks. This study investigates the Variational Quantum Classifier (VQC), a hybrid model that integrates parameterized quantum circuits with classical optimization routines, implemented via IBM’s Qiskit framework. We provide a detailed account of the VQC architecture, including feature encoding, ansatz construction, and optimization methodology. To assess its performance, we conduct a comparative analysis between VQC and classical Support Vector Classifiers (SVC) across synthetic and real-world datasets, including Iris and a binary-filtered version of MNIST. Experimental results reveal that classical models consistently achieve higher accuracy and faster training times. However, the VQC demonstrates functional viability, particularly under noise-free conditions and reduced-dimensionality settings. These findings underscore the current limitations of quantum models while highlighting the potential of VQC as a proof-of-concept for quantum-enhanced learning as quantum hardware matures.
Variational Quantum Algorithms are a major method of harnessing Noisy Intermediate-Scale Quantum devices to solve classically intractable problems in physics, chemistry, optimization, and machine learning. The current review offers a critical overview of VQAs, with special emphasis on their theoretical backgrounds, algorithmic structures, and application performance within realistic models of noise. Several key variants, such as the Variational Quantum Eigensolver, Quantum Approximate Optimization Algorithm, and Quantum Neural Networks, are compared in terms of noise robustness, ansatz archi- tecture, and hybrid quantum-classical methods of optimization. Benchmarks in fields such as quantum chemistry, finance modeling, and particles and nuclei physics reveal the poten- tial of VQAs in achieving practical quantum advantage. Fundamentally limiting factors 1such as barren plateaus, optimization overhead, and hardware constraints are considered in addition to mitigation strategies, including adaptive construction of ansatz, informed training in the presence of noise, and quantum error correction using QVECTOR. The paper is concluded with an overview of the scalability and future of VQAs in the direction of transitioning toward fault-tolerant quantum computing.
Abstract Variational quantum algorithms (VQAs) are expected to be a path to quantum advantages on noisy intermediate-scale quantum devices. However, both empirical and theoretical results exhibit that the deployed ansatz heavily affects the performance of VQAs such that an ansatz with a larger number of quantum gates enables a stronger expressivity, while the accumulated noise may render a poor trainability. To maximally improve the robustness and trainability of VQAs, here we devise a resource and runtime efficient scheme termed quantum architecture search (QAS). In particular, given a learning task, QAS automatically seeks a near-optimal ansatz (i.e., circuit architecture) to balance benefits and side-effects brought by adding more noisy quantum gates to achieve a good performance. We implement QAS on both the numerical simulator and real quantum hardware, via the IBM cloud, to accomplish data classification and quantum chemistry tasks. In the problems studied, numerical and experimental results show that QAS cannot only alleviate the influence of quantum noise and barren plateaus but also outperforms VQAs with pre-selected ansatze.
As we are entering the era of constructing practical quantum computers, suppressing the inevitable noise to accomplish reliable computational tasks will be the primary goal. Leakage noise, as the amplitude population leaking outside the qubit subspace, is a particularly damaging source of error that error-correction approaches cannot handle. However, the impact of this noise on the performance of variational quantum algorithms (VQAs), a type of near-term quantum algorithm that is naturally resistant to a variety of noises, is yet unknown. Here, we consider a typical scenario with the widely used hardware-efficient ansatz and the emergence of leakage in two-qubit gates, observing that leakage noise generally reduces the expressive power of VQAs. Furthermore, we benchmark the influence of leakage noise on VQAs in real-world learning tasks. Results show that, for both data fitting and data classification, leakage noise generally has a negative impact on the training process and final outcomes. Our findings give strong evidence that VQAs are vulnerable to leakage noise in most cases, implying that leakage noise must be effectively suppressed in order to achieve practical quantum computing applications, whether for near-term quantum algorithms or for long-term error-correcting quantum computing.
Quantum computers promise a great computational advantage over classical computers, which might help solve various computational challenges such as the simulation of complicated quantum systems, finding optimum in large optimization problems, and solving large-scale linear algebra problems. Current available quantum devices have only a limited amount of qubits and a high level of noise, limiting the size of problems that can be solved accurately with those devices. Variational quantum algorithms (VQAs) have emerged as a leading strategy to address these limitations by optimizing cost function based on measurement results of shallow depth circuits. Recently, various pulse engineering methods were suggested in order to improve VQA results, including optimizing pulse parameters instead of gate angles as part of the VQA optimization process. In this paper, we suggest a novel pulse-based ansatz, which is parameterized mainly by pulses’ duration of pre-defined pulse structures. This ansatz structure provides relatively low amounts of optimization parameters while maintaining high expressibility, allowing fast convergence. In addition, the ansatz has structured adaptivity to the entanglement level required by the problem, allowing low noise and accurate results. We tested this ansatz against quantum chemistry problems. Specifically, finding the ground-state energy associated with the electron configuration problem, using the variational quantum eigensolver (VQE) algorithm for several different molecules. We manage to achieve chemical accuracy both in simulation for several molecules and on one of IBM’s NISQ devices for the H2 molecule in the STO-3G basis, without the need for extensive error mitigation. Our results are compared to a common gate-based ansatz and show better accuracy and significant latency reduction—up to 7× shorter ansatz schedules.