Quantum Multiplier Based on Exponent Adder

Quantum multiplication is a fundamental operation in quantum computing. Most existing quantum multipliers require $O(n)$ qubits to multiply two $n$-bit integer numbers, limiting their applicability to multiply large integer numbers using near-term quantum computers. In this paper, we propose the Quantum Multiplier Based on Exponent Adder (QMbead), a new approach that addresses this limitation by requiring just $\log_2(n)$ qubits to multiply two $n$-bit integer numbers. QMbead uses a so-called exponent encoding to represent two multiplicands as two superposition states, respectively, and then employs a quantum adder to obtain the sum of these two superposition states, and subsequently measures the outputs of the quantum adder to calculate the product of the multiplicands. This paper presents two types of quantum adders based on the quantum Fourier transform (QFT) for use in QMbead. The circuit depth of QMbead is determined by the chosen quantum adder, being $O(\log^2 n)$ when using the two QFT-based adders. If leveraging a logarithmic-depth quantum adder, the time complexity of QMbead is $O(n \log n)$, identical to that of the fastest classical multiplication algorithm, Harvey-Hoeven algorithm. Interestingly, QMbead maintains an advantage over the Harvey-Hoeven algorithm, given that the latter is only suitable for excessively large numbers, whereas QMbead is valid for both small and large numbers. The multiplicand can be either an integer or a decimal number. QMbead has been successfully implemented on quantum simulators to compute products with a bit length of up to 273 bits using only 17 qubits. This establishes QMbead as an efficient solution for multiplying large integer or decimal numbers with many bits.Comment: 12 pages, 7 figure

Compressed Air Energy Storage-Part I: An Accurate Bi-linear Cavern Model

Compressed air energy storage (CAES) is suitable for large-scale energy storage and can help to increase the penetration of wind power in power systems. A CAES plant consists of compressors, expanders, caverns, and a motor/generator set. Currently used cavern models for CAES are either accurate but highly non-linear or linear but inaccurate. Highly non-linear cavern models cannot be directly utilized in power system optimization problems. In this regard, an accurate bi-linear cavern model for CAES is proposed in this first paper of a two-part series. The charging and discharging processes in a cavern are divided into several virtual states and then the first law of thermodynamics and ideal gas law are used to derive a cavern model, i.e., model for the variation of temperature and pressure in these processes. Thereafter, the heat transfer between the air in the cavern and the cavern wall is considered and integrated into the cavern model. By subsequently eliminating several negligible terms, the cavern model reduces to a bi-linear (linear) model for CAES with multiple (single) time steps. The accuracy of the proposed cavern model is verified via comparison with an accurate non-linear model.Comment: 8 page

Expressibility-Enhancing Strategies for Quantum Neural Networks

Quantum neural networks (QNNs), represented by parameterized quantum circuits, can be trained in the paradigm of supervised learning to map input data to predictions. Much work has focused on theoretically analyzing the expressive power of QNNs. However, in almost all literature, QNNs' expressive power is numerically validated using only simple univariate functions. We surprisingly discover that state-of-the-art QNNs with strong expressive power can have poor performance in approximating even just a simple sinusoidal function. To fill the gap, we propose four expressibility-enhancing strategies for QNNs: Sinusoidal-friendly embedding, redundant measurement, post-measurement function, and random training data. We analyze the effectiveness of these strategies via mathematical analysis and/or numerical studies including learning complex sinusoidal-based functions. Our results from comparative experiments validate that the four strategies can significantly increase the QNNs' performance in approximating complex multivariable functions and reduce the quantum circuit depth and qubits required.Comment: 16 pages, 11 figure

Compressed Air Energy Storage-Part II: Application to Power System Unit Commitment

Unit commitment (UC) is one of the most important power system operation problems. To integrate higher penetration of wind power into power systems, more compressed air energy storage (CAES) plants are being built. Existing cavern models for the CAES used in power system optimization problems are not accurate, which may lead to infeasible solutions, e.g., the air pressure in the cavern is outside its operating range. In this regard, an accurate CAES model is proposed for the UC problem based on the accurate bi-linear cavern model proposed in the first paper of this two-part series. The minimum switch time between the charging and discharging processes of CAES is considered. The whole model, i.e., the UC model with an accurate CAES model, is a large-scale mixed integer bi-linear programming problem. To reduce the complexity of the whole model, three strategies are proposed to reduce the number of bi-linear terms without sacrificing accuracy. McCormick relaxation and piecewise linearization are then used to linearize the whole model. To decrease the solution time, a method to obtain an initial solution of the linearized model is proposed. A modified RTS-79 system is used to verify the effectiveness of the whole model and the solution methodology.Comment: 8 page

Small polaron with generic open boundary conditions revisit: exact solution via the off-diagonal Bethe ansatz

The small polaron, an one-dimensional lattice model of interacting spinless fermions, with generic non-diagonal boundary terms is studied by the off-diagonal Bethe ansatz method. The presence of the Grassmann valued non-diagonal boundary fields gives rise to a typical $U(1)$-symmetry-broken fermionic model. The exact spectra of the Hamiltonian and the associated Bethe ansatz equations are derived by constructing an inhomogeneous $T-Q$ relation.Comment: 12 pages, no figure, published versio

Shallow Depth Factoring Based on Quantum Feasibility Labeling and Variational Quantum Search

Large integer factorization is a prominent research challenge, particularly in the context of quantum computing. This holds significant importance, especially in information security that relies on public key cryptosystems. The classical computation of prime factors for an integer has exponential time complexity. Quantum computing offers the potential for significantly faster computational processes compared to classical processors. In this paper, we propose a new quantum algorithm, Shallow Depth Factoring (SDF), to factor a biprime integer. SDF consists of three steps. First, it converts a factoring problem to an optimization problem without an objective function. Then, it uses a Quantum Feasibility Labeling (QFL) method to label every possible solution according to whether it is feasible or infeasible for the optimization problem. Finally, it employs the Variational Quantum Search (VQS) to find all feasible solutions. The SDF utilizes shallow-depth quantum circuits for efficient factorization, with the circuit depth scaling linearly as the integer to be factorized increases. Through minimizing the number of gates in the circuit, the algorithm enhances feasibility and reduces vulnerability to errors.Comment: 10 pages, 3 figure

An Accurate Bilinear Cavern Model for Compressed Air Energy Storage

Compressed air energy storage is suitable for large-scale electrical energy storage, which is important for integrating renewable energy sources into electric power systems. A typical compressed air energy storage plant consists of compressors, expanders, caverns, and a motor/generator set. Current cavern models used for compressed air energy storage are either accurate but highly nonlinear or linear but inaccurate. The application of highly nonlinear cavern models in power system optimization problems renders them computationally challenging to solve. In this regard, an accurate bilinear cavern model for compressed air energy storage is proposed in this paper. The charging and discharging processes in a cavern are divided into several real/virtual states. The first law of thermodynamics and ideal gas law are then utilized to derive a cavern model, i.e., a model for the variation of temperature and pressure in these processes. Thereafter, the heat transfer between the air in the cavern and the cavern wall is considered and integrated into the cavern model. By subsequently eliminating several negligible terms, the cavern model reduces to a bilinear model. The accuracy of the bilinear cavern model is verified via comparison with both an accurate nonlinear model and two sets of field-measured data. The bilinear cavern model can be easily linearized and is then suitable for integration into optimization problems considering compressed air energy storage. This is verified via comparatively solving a self-scheduling problem of compressed air energy storage using different cavern models.Comment: 18 pages, 15 figures, accepted by Applied Energy on March 201

Ordovician geology and stratigraphy of China: A synthesis

China presently comprises several tectonic blocks and regions assembled over geological time and having independent histories. During the Ordovician, these blocks included South China, North China, Tarim, Qaidam, Junggar, Qiangtang-Qamdo, Lhasa and partially Himalaya, Sibumasu and Indochina, as well as the Altay-Xingâan and Songpan-Garze fold belts, which were discrete but adjacent. Twelve stratigraphic megaregions bounded by tectonic sutures or major fault zones are recognised for the Ordovician System. Some of them are further subdivided into regions according to specific lithological and biotic facies or distinct stratigraphic successions. The palaeontological features and biostratigraphic framework of these stratigraphic megaregions and regions are summarised. The unified biostratigraphic framework presented herein includes 33 graptolite and 27 conodont biozones through the Ordovician, together with supplementary biozones, communities or associations of brachiopods, trilobites, cephalopods, chitinozoans, acritarchs and radiolarians. With the constraints of integrative chronostratigraphy, biostratigraphy, chemostratigraphy, cyclostratigraphy and magnetostratigraphy, along with some geochronological data, our understanding of the temporal and spatial distribution of the Ordovician lithostratigraphic units on these major blocks has been significantly advanced. The refined integrative stratigraphic framework of the Ordovician provides a precise constraint on the major tectonic orogenies and biotic events evident in China

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency-Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research.Peer reviewe