In the noisy intermediate-scale quantum era, ab initio computation of the electronic structure problems has become one of the major benchmarks for identifying the boundary between classical and quantum computational power. Basis sets play a key role in the electronic structure methods implemented on both classical and quantum devices. To investigate the consequences of the single-particle basis sets, we propose a framework for more customizable basis set generation and optimization. This framework allows composite basis sets to go beyond typical basis set frameworks, such as atomic basis sets, by introducing the concept of mixed-contracted Gaussian-type orbitals. These basis set generations set the stage for more flexible variational optimization of basis set parameters. To realize this framework, we have developed an open-source software package named ``Quiqbox'' in the Julia programming language. We demonstrate various examples of using Quiqbox for basis set optimization and generation, ranging from optimizing atomic basis sets on the Hartree--Fock level, preparing the initial state for VQE computation, and constructing basis sets with completely delocalized orbitals. We also include various benchmarks of Quiqbox for basis set optimization and ab initial electronic structure computation.
Universal fault-tolerant quantum computers require millions of qubits with low error rates. Since this technology is years ahead, noisy intermediate-scale quantum (NISQ) computation is receiving tremendous interest. In this setup, quantum reservoir computing is a relevant machine learning algorithm. Its simplicity of training and implementation allows to perform challenging computations on today available machines. In this Letter, we provide a criterion to select optimal quantum reservoirs, requiring few and simple gates. Our findings demonstrate that they render better results than other comm…
Reducing the Number of Qubits from $n^2$ to $n\log_{2} (n)$ to Solve the Traveling Salesman Problem with Quantum Computers: A Proposal for Demonstrating Quantum Supremacy in the NISQ Era
TensorCircuit is an open source quantum circuit simulator based on tensor network contraction, designed for speed, flexibility and code efficiency. Written purely in Python, and built on top of industry-standard machine learning frameworks, TensorCircuit supports automatic differentiation, just-in-time compilation, vectorized parallelism and hardware acceleration. These features allow TensorCircuit to simulate larger and more complex quantum circuits than existing simulators, and are especially suited to variational algorithms based on parameterized quantum circuits. TensorCircuit enables orde…
Quantum annealing inspired algorithms for the NISQ Era
Jülich Supercomputing Centre, Forschungszentrum Jülich（于利希超级计算中心，于利希研究中心）；RWTH Aachen University（亚琛工业大学）；Modular Supercomputing and Quantum Computing, Goethe University Frankfurt（法兰克福歌德大学模块化超算与量子计算）；Department of Computer Science, University of Cologne（科隆大学计算机科学系）
The progress in developing quantum hardware with functional quantum processors integrating tens of noisy qubits, together with the availability of near-term quantum algorithms has led to the release of the first quantum computers. These quantum computing systems already integrate different software and hardware components of the so-called "full-stack", bridging quantum applications to quantum devices. In this paper, we will provide an overview on current full-stack quantum computing systems. We will emphasize the need for tight co-design among adjacent layers as well as vertical cross-layer de…
Near-term quantum computation holds potential across multiple application domains. However, imperfect preparation and evolution of states due to algorithmic and experimental shortcomings, characteristic in the near-term implementation, would typically result in measurement outcomes deviating from the ideal setting. It is thus crucial for any near-term application to quantify and bound these output errors. We address this need by deriving robustness intervals which are guaranteed to contain the output in the ideal setting. The first type of interval is based on formulating robustness bounds as …
We develop a quantum computing scheme utilizing McLachlan variational principle in a hybrid quantum-classical algorithm to accurately calculate the transition dynamics of a closed quantum system with many excited states subject to a strong time-dependent perturbation. A systematic approach for optimal construction of a general N-state ansatz with unary N-qubit encoding is refined. We also utilize qubit efficient encoding in McLachlan variational quantum algorithm to reduce the number of qubits to log2 N, simultaneously diminishing depths of the quantum circuits. The significant reduction of th…
The Poisson equation has many applications across the broad areas of science and engineering. Most quantum algorithms for the Poisson solver presented so far, either suffer from lack of accuracy and/or are limited to very small sizes of the problem, and thus have no practical usage. Here we present an advanced quantum algorithm for solving the Poisson equation with high accuracy and dynamically tunable problem size. After converting the Poisson equation to the linear systems through the finite difference method, we adopt the Harrow-Hassidim-Lloyd (HHL) algorithm as the basic framework. Particu…
NISQ devices have several physical limitations and unavoidable noisy quantum operations, and only small circuits can be executed on a quantum machine to get reliable results. This leads to the quantum hardware under-utilization issue. Here, we address this problem and improve the quantum hardware throughput by proposing a Quantum Multi-programming Compiler (QuMC) to execute multiple quantum circuits on quantum hardware simultaneously. This approach can also reduce the total runtime of circuits. We first introduce a parallelism manager to select an appropriate number of circuits to be executed …
Fraunhofer Institute for Industrial Mathematics ITWM（弗劳恩霍夫工业数学研究所ITWM）；University of Kaiserslautern（凯泽斯劳滕大学）
Edges are image locations where the gray value intensity changes suddenly. They are among the most important features to understand and segment an image. Edge detection is a standard task in digital image processing, solved for example using filtering techniques. However, the amount of data to be processed grows rapidly and pushes even supercomputers to their limits. Quantum computing promises exponentially lower memory usage in terms of the number of qubits compared to the number of classical bits. In this paper, we propose a hybrid method for quantum edge detection based on the idea of a qua…
GroverFigureOfMerit: An Agnostic Figure of Merit for Quantum Backend Characterization in the NISQ Era
Universidad Nacional de La Plata, Facultad de Informática, Laboratorio de Investigación y Formación en Informática Avanzada (LIFIA)（拉普拉塔国立大学，计算机学院，先进信息研究与培训实验室）
Error mitigation is one of the key challenges in realising the full potential of quantum cryptographic protocols. Consequently, there is a lot of interest in adapting techniques from quantum error correction (QEC) to improve the robustness of quantum cryptographic protocols. In this work, we benchmark the performance of different QKD protocols on noisy quantum devices, with and without error correction. We obtain the secure key rates of BB84, B92 and BBM92 QKD protocols over a quantum channel that is subject to amplitude-damping noise. We demonstrate, theoretically and via implementations on t…
Trustworthy Quantum Machine Learning: A Roadmap for Reliability, Robustness, and Security in the NISQ Era
Department of Electrical Engineering and Computer Science, University of Stavanger, Norway（斯瓦尔巴大学电气工程与计算机科学系）；School of Physics, Engineering and Technology, University of York, UK（约克大学物理、工程与技术学院）
A Useful Metric for the NISQ Era: Qubit Error Probability and Its Role in Zero Noise Extrapolation
The Abdus Salam International Center for Theoretical Physics (ICTP)（阿卜杜斯·萨拉姆国际理论物理中心）；Mondragon Unibertsitatea（蒙德拉贡大学）；Universidad del País Vasco UPV/EHU（巴斯克大学）；University of the Basque Country (UPV/EHU)（巴斯克大学）
First quantum computers very recently have demonstrated "quantum supremacy" or "quantum advantage": Executing a computation that would have been impossible on a classical machine. Today's quantum computers follow the NISQ paradigm: They exhibit error rates that are much higher than in conventional electronics and have insufficient quantum resources to support powerful error correction protocols. This raises questions which relevant computations are within the reach of NISQ architectures. Several "NISQ-era algorithms" are assumed to match the specifics of such computers; for instance, variation…
