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Simulating quantum systems is believed to be one of the first applications for which quantum computers may demonstrate a useful advantage. For many problems in physics, we are interested in studying the evolution of the electron–phonon Hamiltonian, for which efficient digital quantum computing schemes exist. Yet to date, no accurate simulation of this system has been produced on real quantum hardware. In this work, we consider the absolute resource cost for gate-based quantum simulation of small electron–phonon systems as dictated by the number of Trotter steps and bosonic energy levels necessary for the convergence of dynamics. We then apply these findings to perform experiments on IBM quantum hardware for both weak and strong electron–phonon coupling. Despite significant device noise, through the use of approximate circuit recompilation we obtain electron–phonon dynamics on current quantum computers comparable to exact diagonalisation. Our results represent a significant step in utilising near term quantum computers for simulation of quantum dynamics and highlight the novelty of approximate circuit recompilation as a tool for reducing noise.

Optimization problems are prevalent in various fields, and the gradient-based gradient descent algorithm is a widely adopted optimization method. However, in classical computing, computing the numerical gradient for a function with d variables necessitates at least d + 1 function evaluations, resulting in a computational complexity of O ( d ) . As the number of variables increases, the classical gradient estimation methods require substantial resources, ultimately surpassing the capabilities of classical computers. Fortunately, leveraging the principles of superposition and entanglement in quantum mechanics, quantum computers can achieve genuine parallel computing, leading to exponential acceleration over classical algorithms in some cases. In this paper, we propose a novel quantum-based gradient calculation method that requires only a single oracle calculation to obtain the numerical gradient result for a multivariate function. The complexity of this algorithm is just O ( 1 ) . Building upon this approach, we successfully implemented the quantum gradient descent algorithm and applied it to the variational quantum eigensolver (VQE), creating a pure quantum variational optimization algorithm. Compared with classical gradient-based optimization algorithm, this quantum optimization algorithm has remarkable complexity advantages, providing an efficient solution to optimization problems.The proposed quantum-based method shows promise in enhancing the performance of optimization algorithms, highlighting the potential of quantum computing in this field.

In this study, the PennyLane quantum device simulator was used to investigate quantum and hybrid, quantum/classical physics-informed neural networks (PINNs) for solutions to both transient and steady-state, 1D and 2D partial differential equations. The comparative expressibility of the purely quantum, hybrid and classical neural networks is discussed, and hybrid configurations are explored. The results show that (1) for some applications, quantum PINNs can obtain comparable accuracy with less neural network parameters than classical PINNs, and (2) adding quantum nodes in classical PINNs can increase model accuracy with less total network parameters for noiseless models.

For the building emergency evacuation path planning problem, existing algorithms suffer from low convergence efficiency and the problem of getting trapped in local optima. The Bloch Spherical Quantum Genetic Algorithm (BQGA) based on the least-squares principle for single-robot path planning and Bloch Spherical Quantum Bee Colony Algorithm (QABC) for multi-robots path planning are studied. Firstly, the characteristics of three-dimensional path planning are analyzed, and a linear decreasing inertia weighting approach is used to balance the global search ability of chromosomes and accelerate the search performance of the algorithm. Then, the application algorithm can generate a clear motion trajectory in the raster map. Thirdly, the least squares approach is used to fit the results, thus obtaining a progressive path. Finally, multi-robots path planning approaches based on QABC are discussed, respectively. The experimental results show that BQGA and QABC do not need to have a priori knowledge of the map, and they have strong reliability and practicality and can effectively avoid local optimum. In terms of convergence speed, BQGA improved by 3.39% and 2.41%, respectively, while QABC improved by 13.31% and 17.87%, respectively. They are more effective in sparse paths.

An arbitrary amount of entanglement shared among nodes of a quantum network might be nondistillable if the nodes lack the information on the entangled Bell pairs they share. Making such a system distillable, which is called the superactivation of bound entanglement (BE), was shown to be possible through systematic quantum teleportation between the nodes, requiring the implementation of controlled-gates scaling with the number of nodes. In this work, we show in two scenarios that the superactivation of BE is possible if nodes implement the proposed local quantum Zeno strategies based on only single qubit rotations and simple threshold measurements. In the first scenario we consider, we obtain a two-qubit distillable entanglement system as in the original superactivation proposal. In the second scenario, we show that superactivation can be achieved among the entire network of eight qubits in five nodes. In addition to obtaining all-particle distillable entanglement, the overall entanglement of the system in terms of the sum of bipartite cuts is increased. We also design a general algorithm with variable greediness for optimizing the QZD evolution tasks. Implementing our algorithm for the second scenario, we show that a significant improvement can be obtained by driving the initial BE system into a maximally entangled state. We believe our work contributes to quantum technologies from both practical and fundamental perspectives bridging nonlocality, bound entanglement and the quantum Zeno dynamics among a quantum network.

In the last decade quantum machine learning has provided fascinating and fundamental improvements to supervised, unsupervised and reinforcement learning (RL). In RL, a so-called agent is challenged to solve a task given by some environment. The agent learns to solve the task by exploring the environment and exploiting the rewards it gets from the environment. For some classical task environments, an analogue quantum environment can be constructed which allows to find rewards quadratically faster by applying quantum algorithms. In this paper, we analytically analyze the behavior of a hybrid agent which combines this quadratic speedup in exploration with the policy update of a classical agent. This leads to a faster learning of the hybrid agent compared to the classical agent. We demonstrate that if the classical agent needs on average ⟨ J ⟩ rewards and ⟨ T ⟩ cl epochs to learn how to solve the task, the hybrid agent will take ⟨ T ⟩ q ⩽ α s α o ⟨ T ⟩ c l ⟨ J ⟩ epochs on average. Here, α s and α o denote constants depending on details of the quantum search and are independent of the problem size. Additionally, we prove that if the environment allows for maximally α o k max sequential coherent interactions, e.g. due to noise effects, an improvement given by ⟨ T ⟩ q ≈ α o ⟨ T ⟩ cl /(4 k max ) is still possible.

Finite-element methods are industry standards for finding numerical solutions to partial differential equations. However, the application scale remains pivotal to the practical use of these methods, even for modern-day supercomputers. Large, multi-scale applications, for example, can be limited by their requirement of prohibitively large linear system solutions. It is therefore worthwhile to investigate whether near-term quantum algorithms have the potential for offering any kind of advantage over classical linear solvers. In this study, we investigate the recently proposed variational quantum linear solver (VQLS) for discrete solutions to partial differential equations. This method was found to scale polylogarithmically with the linear system size, and the method can be implemented using shallow quantum circuits on noisy intermediate-scale quantum (NISQ) computers. Herein, we utilize the hybrid VQLS to solve both the steady Poisson equation and the time-dependent heat and wave equations.

We present the enhanced feature quantum autoencoder, or EF-QAE, a variational quantum algorithm capable of compressing quantum states of different models with higher fidelity. The key idea of the algorithm is to define a parameterized quantum circuit that depends upon adjustable parameters and a feature vector that characterizes such a model. We assess the validity of the method in simulations by compressing ground states of the Ising model and classical handwritten digits. The results show that EF-QAE improves the performance compared to the standard quantum autoencoder using the same amount of quantum resources, but at the expense of additional classical optimization. Therefore, EF-QAE makes the task of compressing quantum information better suited to be implemented in near-term quantum devices.

The search for useful applications of noisy intermediate-scale quantum (NISQ) devices in quantum simulation has been hindered by their intrinsic noise and the high costs associated with achieving high accuracy. A promising approach to finding utility despite these challenges involves using quantum devices to generate training data for classical machine learning (ML) models. In this study, we explore the use of noisy data generated by quantum algorithms in training an ML model to learn a density functional for the Fermi–Hubbard model. We benchmark various ML models against exact solutions, demonstrating that a neural-network ML model can successfully generalize from small datasets subject to noise typical of NISQ algorithms. The learning procedure can effectively filter out unbiased sampling noise, resulting in a trained model that outperforms any individual training data point. Conversely, when trained on data with expressibility and optimization error typical of the variational quantum eigensolver, the model replicates the biases present in the training data. The trained models can be applied to solving new problem instances in a Kohn–Sham-like density optimization scheme, benefiting from automatic differentiability and achieving reasonably accurate solutions on most problem instances. Our findings suggest a promising pathway for leveraging NISQ devices in practical quantum simulations, highlighting both the potential benefits and the challenges that need to be addressed for successful integration of quantum computing and ML techniques.

Many quantum algorithms have daunting resource requirements when compared to what is available today. To address this discrepancy, a quantum-classical hybrid optimization scheme known as 'the quantum variational eigensolver' was developed (Peruzzo et al 2014 Nat. Commun. 5 4213) with the philosophy that even minimal quantum resources could be made useful when used in conjunction with classical routines. In this work we extend the general theory of this algorithm and suggest algorithmic improvements for practical implementations. Specifically, we develop a variational adiabatic ansatz and explore unitary coupled cluster where we establish a connection from second order unitary coupled cluster to universal gate sets through a relaxation of exponential operator splitting. We introduce the concept of quantum variational error suppression that allows some errors to be suppressed naturally in this algorithm on a pre-threshold quantum device. Additionally, we analyze truncation and correlated sampling in Hamiltonian averaging as ways to reduce the cost of this procedure. Finally, we show how the use of modern derivative free optimization techniques can offer dramatic computational savings of up to three orders of magnitude over previously used optimization techniques.