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We study the problem of compilation of quantum algorithms into optimized physical-level circuits executable in a quantum information processing (QIP) experiment based on trapped atomic ions. We report a complete strategy: starting with an algorithm in the form of a quantum computer program, we compile it into a high-level logical circuit that goes through multiple stages of decomposition into progressively lower-level circuits until we reach the physical execution-level specification. We skip the fault-tolerance layer, as it is not within the scope of this work. The different stages are structured so as to best assist with the overall optimization while taking into account numerous optimization criteria, including minimizing the number of expensive two-qubit gates, minimizing the number of less expensive single-qubit gates, optimizing the runtime, minimizing the overall circuit error, and optimizing classical control sequences. Our approach allows a trade-off between circuit runtime and quantum error, as well as to accommodate future changes in the optimization criteria that may likely arise as a result of the anticipated improvements in the physical-level control of the experiment.

The non-Markovianity of physical systems is considered to be a valuable resource that has potential applications to quantum information processing. The control of traveling quantum fields encoded with information (flying qubit) is crucial for quantum networks. In this work, we propose to catch and release the propagating photon/phonon with a non-Markovian giant atom, which is coupled to the environment via multiple coupling points. Based on the Heisenberg equation of motion for the giant atom and field operators, we calculate the time-dependent scattering coefficients from the linear response theory and define the criteria for the non-Markovian giant atom. We analyze and numerically verify that the field bound states due to non-Markovianity can be harnessed to catch and release the propagating bosonic field on demand by tuning the parameters of giant atom.

In this paper we study the ways to use a global entangling operator to efficiently implement circuitry common to a selection of important quantum algorithms. In particular, we focus on the circuits composed with global Ising entangling gates and arbitrary addressable single-qubit gates. We show that under various circumstances the use of global operations can substantially improve the entangling gate count.

We present a new hardware-efficient paradigm for universal quantum computation which is based on encoding, protecting and manipulating quantum information in a quantum harmonic oscillator. This proposal exploits multi-photon driven dissipative processes to encode quantum information in logical bases composed of Schrödinger cat states. More precisely, we consider two schemes. In a first scheme, a two-photon driven dissipative process is used to stabilize a logical qubit basis of two-component Schrödinger cat states. While such a scheme ensures a protection of the logical qubit against the photon dephasing errors, the prominent error channel of single-photon loss induces bit-flip type errors that cannot be corrected. Therefore, we consider a second scheme based on a four-photon driven dissipative process which leads to the choice of four-component Schrödinger cat states as the logical qubit. Such a logical qubit can be protected against single-photon loss by continuous photon number parity measurements. Next, applying some specific Hamiltonians, we provide a set of universal quantum gates on the encoded qubits of each of the two schemes. In particular, we illustrate how these operations can be rendered fault-tolerant with respect to various decoherence channels of participating quantum systems. Finally, we also propose experimental schemes based on quantum superconducting circuits and inspired by methods used in Josephson parametric amplification, which should allow one to achieve these driven dissipative processes along with the Hamiltonians ensuring the universal operations in an efficient manner.

Quantum computing is expected to fundamentally change computer systems in the future. Recently, a new research topic of quantum computing is the hybrid quantum–classical approach for machine learning, in which a parameterized quantum circuit, also called quantum neural network (QNN), is optimized by a classical computer. This hybrid approach can have the benefits of both quantum computing and classical machine learning methods. In this early stage, it is of crucial importance to understand the new characteristics of quantum neural networks for different machine learning tasks. In this paper, we will study quantum neural networks for the task of classifying images, which are high-dimensional spatial data. In contrast to previous evaluations of low-dimensional or scalar data, we will investigate the impacts of practical encoding types, circuit depth, bias term, and readout on classification performance on the popular MNIST image dataset. Various interesting findings on learning behaviors of different QNNs are obtained through experimental results. To the best of our knowledge, this is the first work that considers various QNN aspects for image data.

Fault-tolerant quantum computation enables reliable quantum computation but incurs a significant overhead from both time and resource perspectives. To reduce computation time, Austin G. Fowler proposed time-optimal quantum computation by constructing a quantum circuit for a fault-tolerant T gate without probabilistic S gate correction. In this work, we introduce a resource-compact quantum circuit that significantly reduces resource requirements by more than 60% for a fault-tolerant T gate without probabilistic S gate correction. Consequently, we present a quantum circuit that minimizes resource utilization for time-optimal quantum computation, demonstrating efficient time-optimal quantum computation. Additionally, we describe an efficient form involving initialization, CNOT s, and measurements, laying the foundation for the development of an efficient compiler for fault-tolerant quantum computation.

Optimizing quantum circuits is critical for enhancing computational speed and mitigating errors caused by quantum noise. Effective optimization must be achieved without compromising the correctness of the computations. This survey explores recent advancements in quantum circuit optimization, encompassing both hardware-independent and hardware-dependent techniques. It reviews state-of-the-art approaches, including analytical algorithms, heuristic strategies, machine learning-based methods, and hybrid quantum-classical frameworks. The paper highlights the strengths and limitations of each method, along with the challenges they pose. Furthermore, it identifies potential research opportunities in this evolving field, offering insights into the future directions of quantum circuit optimization.

This research paper delves into the realm of quantum machine learning (QML) by conducting a comprehensive study on time-series data. The primary objective is to compare the results and time complexity of classical machine learning algorithms on traditional hardware to their quantum counterparts on quantum computers. As the amount and complexity of time-series data in numerous fields continues to expand, the investigation of advanced computational models becomes critical for efficient analysis and prediction. We employ a time-series dataset that include temperature records from different nations throughout the world spanning the previous half of the century. The study compares the performance of classical machine learning algorithms to quantum algorithms, which use the concepts of superposition and entanglement to handle subtle temporal patterns in time-series data. This study attempts to reveal the different benefits and drawbacks of quantum machine learning in the time-series domain through rigorous empirical analysis. The findings of this study not only help to comprehend the applicability of quantum algorithms in real-world contexts, but they also open the way for future advances in utilizing quantum computing for increased time-series analysis and prediction. This study’s findings could have ramifications in industries ranging from finance to healthcare, where precise forecasting using time-series data is critical for informed decision-making.

Artificial intelligence (AI) technology leads to new insights into the manipulation of quantum systems in the Noisy Intermediate-Scale Quantum (NISQ) era. Classical agent-based artificial intelligence algorithms provide a framework for the design or control of quantum systems. Traditional reinforcement learning methods are designed for the Markov Decision Process (MDP) and, hence, have difficulty in dealing with partially observable or quantum observable decision processes. Due to the difficulty of building or inferring a model of a specified quantum system, a model-free-based control approach is more practical and feasible than its counterpart of a model-based approach. In this work, we apply a model-free deep recurrent Q-network (DRQN) reinforcement learning method for qubit-based quantum circuit architecture design problems. This paper is the first attempt to solve the quantum circuit design problem from the recurrent reinforcement learning algorithm, while using discrete policy. Simulation results suggest that our long short-term memory (LSTM)-based DRQN method is able to learn quantum circuits for entangled Bell–Greenberger–Horne–Zeilinger (Bell–GHZ) states. However, since we also observe unstable learning curves in experiments, suggesting that the DRQN could be a promising method for AI-based quantum circuit design application, more investigation on the stability issue would be required.

Multiple linear regression assumes an imperative role in supervised machine learning. In 2009, Harrow et al. [Phys. Rev. Lett. 103, 150502 (2009)] showed that their Harrow Hassidim Lloyd (HHL) algorithm can be used to sample the solution of a linear system ${\\bi Ax = b}$Ax=b exponentially faster than any existing classical algorithm. The entire field of quantum machine learning gained considerable traction after the discovery of this celebrated algorithm. However, effective practical applications and experimental implementations of HHL are still sparse in the literature. Here, the authors demonstrate a potential practical utility of HHL, in the context of regression analysis, using the remarkable fact that there exists a natural reduction of any multiple linear regression problem to an equivalent linear systems problem. They put forward a 7-qubit quantum circuit design, motivated from an earlier work by Cao et al. [Mol. Phys. 110, 1675 (2012)], to solve a three-variable regression problem, using only elementary quantum gates. They also implement the group leaders optimisation algorithm (GLOA) [Mol. Phys. 109 (5), 761 (2011)] and elaborate on the advantages of using such stochastic algorithms in creating low-cost circuit approximations for the Hamiltonian simulation. Further, they discuss their Qiskit simulation and explore certain generalisations to the circuit design.