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The next few years will be exciting as prototype universal quantum processors emerge, enabling the implementation of a wider variety of algorithms. Of particular interest are quantum heuristics, which require experimentation on quantum hardware for their evaluation and which have the potential to significantly expand the breadth of applications for which quantum computers have an established advantage. A leading candidate is Farhi et al.’s quantum approximate optimization algorithm, which alternates between applying a cost function based Hamiltonian and a mixing Hamiltonian. Here, we extend this framework to allow alternation between more general families of operators. The essence of this extension, the quantum alternating operator ansatz, is the consideration of general parameterized families of unitaries rather than only those corresponding to the time evolution under a fixed local Hamiltonian for a time specified by the parameter. This ansatz supports the representation of a larger, and potentially more useful, set of states than the original formulation, with potential long-term impact on a broad array of application areas. For cases that call for mixing only within a desired subspace, refocusing on unitaries rather than Hamiltonians enables more efficiently implementable mixers than was possible in the original framework. Such mixers are particularly useful for optimization problems with hard constraints that must always be satisfied, defining a feasible subspace, and soft constraints whose violation we wish to minimize. More efficient implementation enables earlier experimental exploration of an alternating operator approach, in the spirit of the quantum approximate optimization algorithm, to a wide variety of approximate optimization, exact optimization, and sampling problems. In addition to introducing the quantum alternating operator ansatz, we lay out design criteria for mixing operators, detail mappings for eight problems, and provide a compendium with brief descriptions of mappings for a diverse array of problems.

Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of Riemannian geometry to perform optimization on the manifolds of unitary and isometric matrices as well as the cone of positive-definite matrices. Combining this approach with the up-to-date computational methods of automatic differentiation, we demonstrate the efficacy of the Riemannian optimization in the study of the low-energy spectrum and eigenstates of multipartite Hamiltonians, variational search of a tensor network in the form of the multiscale entanglement-renormalization ansatz, preparation of arbitrary states (including highly entangled ones) in the circuit implementation of quantum computation, decomposition of quantum gates, and tomography of quantum states. Universality of the developed approach together with the provided open source software enable one to apply the Riemannian optimization to complex quantum architectures well beyond the listed problems, for instance, to the optimal control of noisy quantum systems.

Variational quantum algorithms are among the most promising algorithms to achieve quantum advantages in the noisy intermediate-scale quantum (NISQ) era. One important challenge in implementing such algorithms is to construct an effective parameterized quantum circuit (also called an ansatz). In this work, we propose a single entanglement connection architecture (SECA) for a bipartite hardware efficient ansatz (HEA) by balancing its expressibility, entangling capability, and trainability. Numerical simulations with a one-dimensional Heisenberg model and quadratic unconstrained binary optimization (QUBO) issues were conducted. Our results indicate the superiority of SECA over the common full entanglement connection architecture in terms of computational performance. Furthermore, combining SECA with gate-cutting technology to construct distributed quantum computation (DQC) can efficiently expand the size of NISQ devices under low overhead. We also demonstrated the effectiveness and scalability of the DQC scheme. Our study is a useful indication for understanding the characteristics associated with an effective training circuit.

Material discovery is a phenomenon practiced since the evolution of the world. The discovery of materials has led to significant development in varied fields such as Science, Engineering and Technology. Computationally simulating molecules has been an area of interest in the industry as well as academia. However, simulating large molecules can be computationally expensive in terms of computing power and complexity. Quantum computing is a recent development that can improve the efficiency in predicting properties of atoms and molecules which will be useful for material design. The Variational Quantum Eigensolver (VQE) is one such quantum algorithm used to calculate the ground state energy of molecules or ions. In this study, we have done a comparative analysis of the parameters that constitute the VQE algorithm. This includes components such as basis, qubit mapping, ansatz, and optimizers used. We have also developed a database consisting of 79 single atoms and their variations of oxidation states and 33 molecules with the data of their Hamiltonian and ground state energy and dipole moment.

The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons with relatively low-depth circuits, which are otherwise difficult to solve on classical computers. The variational eigenstate is constructed from a number of factorized unitary coupled-cluster terms applied onto an initial (single-reference) state. Current algorithms for applying one of these operators to a quantum state require a number of operations that scale exponentially with the rank of the operator. We exploit a hidden SU(2) symmetry to allow us to employ the linear combination of unitaries approach, Our Prepare subroutine uses n+2 ancilla qubits for a rank-n operator. Our Select(U^) scheme uses O(n)Cnot gates. This results in a full algorithm that scales like the cube of the rank of the operator n3, a significant reduction in complexity for rank five or higher operators. This approach, when combined with other algorithms for lower-rank operators (when compared to the standard implementation), will make the factorized form of the unitary coupled-cluster approach much more efficient to implement on all types of quantum computers.

The taxonomic composition and abundance of phytoplankton have a direct impact on marine ecosystem dynamics and global environment change. Phytoplankton classification is crucial for phytoplankton analysis, but it is challenging due to their large quantity and small size. Machine learning is the primary method for automatically performing phytoplankton image classification. As large-scale research on marine phytoplankton generates overwhelming amounts of data, more powerful computational resources are required for the success of machine learning methods. Recently, quantum machine learning has emerged as a potential solution for large-scale data processing by harnessing the exponentially computational power of quantum computers. Here, for the first time, we demonstrate the feasibility of using quantum deep neural networks for phytoplankton classification. Hybrid quantum-classical convolutional and residual neural networks are developed based on the classical architectures. These models strike a balance between the limited function of current quantum devices and the large size of phytoplankton images, making it possible to perform phytoplankton classification on near-term quantum computers. Our quantum models demonstrate superior performance compared to their classical counterparts, exhibiting faster convergence, higher classification accuracy and lower accuracy fluctuation. The present quantum models are versatile and can be applied to various tasks of image classification in the field of marine science.

The variational quantum eigensolver (VQE) is a method that uses a hybrid quantum-classical computational approach to find eigenvalues of a Hamiltonian. VQE has been proposed as an alternative to fully quantum algorithms such as quantum phase estimation (QPE) because fully quantum algorithms require quantum hardware that will not be accessible in the near future. VQE has been successfully applied to solve the electronic Schrödinger equation for a variety of small molecules. However, the scalability of this method is limited by two factors: the complexity of the quantum circuits and the complexity of the classical optimization problem. Both of these factors are affected by the choice of the variational ansatz used to represent the trial wave function. Hence, the construction of an efficient ansatz is an active area of research. Put another way, modern quantum computers are not capable of executing deep quantum circuits produced by using currently available ansatzes for problems that map onto more than several qubits. In this review, we present recent developments in the field of designing efficient ansatzes that fall into two categories—chemistry–inspired and hardware–efficient—that produce quantum circuits that are easier to run on modern hardware. We discuss the shortfalls of ansatzes originally formulated for VQE simulations, how they are addressed in more sophisticated methods, and the potential ways for further improvements.

The rising environmental cost of deep learning has placed Green AI, which promotes focus on reducing the carbon footprint of AI, at the forefront of sustainable computing. In this study, we investigate Quantum Machine Learning (QML) as a novel and energy-efficient alternative by benchmarking two quantum models, the Quantum Neural Network (QNN) and Quantum Long Short-Term Memory (QLSTM), on the N-BaIoT anomaly detection dataset. Our first phase of experiments compares the QNN and QLSTM models using ten distinct quantum circuit designs (ansätze A1–A10). We systematically compare trade-offs between classification performance, model complexity, training time, and energy consumption. The results indicate that simpler QNN ansätze can achieve accuracy comparable to more complex ones while consuming significantly less energy and converging faster. In particular, QNN with ansatz A4 provided the optimal balance between performance and energy efficiency, consistently outperforming QLSTM across most metrics. A detailed energy breakdown confirmed GPU usage as the dominant source of power consumption, underscoring the importance of circuit-efficient quantum design. To contextualize QML’s viability, we conducted a second phase of experiments comparing quantum models with three benchmark classical machine learning models: Artificial Neural Network (ANN), Long Short-Term Memory (LSTM), and CatBoost. We find that the classical models demonstrated faster training times and lower energy consumption, highlighting and contrasting the maturity of algorithmic development that classical ML algorithms have already seen. Finally, we examined the energy implications of developing quantum models on actual quantum hardware. This third phase of experiments compared training on IBM Qiskit’s emulation environment (running on GPU servers) versus execution on real IBM Quantum hardware. Highlighting the significant differences in execution time and energy footprint, extrapolated results indicate that quantum hardware still incurs higher energy costs. This suggests that further hardware-aware ansätz optimization and improvements in quantum infrastructure are essential to realizing carbon-efficient QML at scale.