arXiv subjects

Junpeng Zhan

Publications and source records attributed to Junpeng Zhan.

12 recordsLinked to original sources

arXiv2024

Quantum Multiplier Based on Exponent Adder

Quantum multiplication is a fundamental operation in quantum computing. It is important to have a quantum multiplier with low complexity. In this paper, we propose the Quantum Multiplier Based on Exponent Adder (QMbead), a new approach that requires just $\log_2(n)$ qubits to multiply two $n$-bit integer numbers, in addition to $O(n)$ ancillary qubits used for quantum state preparation. The QMbead uses a so-called exponent encoding to respectively represent two multiplicands as two superposition states which are prepared by a quantum state preparation method, 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. Different quantum adders can be used in the QMbead. The circuit depth and time complexity of the QMbead, using a logarithmic-depth quantum carry lookahead adder (QCLA) as adder, are $O(\log n)$ and $O(n \log n)$, respectively. The gate complexity of the QMbead is $O(n)$. The circuit depth and gate complexity of the QMbead is better than existing quantum multipliers such as the quantum Karatsuba multiplier and the QFT based multiplier. The time complexity of the QMbead is identical to that of the fastest classical multiplication algorithm, Harvey-Hoeven algorithm. Interestingly, the QMbead maintains an advantage over the Harvey-Hoeven algorithm, given that the latter is only suitable for excessively large numbers, whereas the QMbead is valid for both small and large numbers. The multiplicand can be either an integer or a decimal number. The QMbead has been implemented on quantum simulators to compute products with a bit length of up to 273 bits using only 17 qubits, excluding the ancillary qubits used for quantum state preparation. This establishes QMbead as an efficient solution for multiplying large integer or decimal numbers with many bits.

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arXiv2024

Quantum Neural Networks for Solving Power System Transient Simulation Problem

Quantum computing, leveraging principles of quantum mechanics, represents a transformative approach in computational methodologies, offering significant enhancements over traditional classical systems. This study tackles the complex and computationally demanding task of simulating power system transients through solving differential algebraic equations (DAEs). We introduce two novel Quantum Neural Networks (QNNs): the Sinusoidal-Friendly QNN and the Polynomial-Friendly QNN, proposing them as effective alternatives to conventional simulation techniques. Our application of these QNNs successfully simulates two small power systems, demonstrating their potential to achieve good accuracy. We further explore various configurations, including time intervals, training points, and the selection of classical optimizers, to optimize the solving of DAEs using QNNs. This research not only marks a pioneering effort in applying quantum computing to power system simulations but also expands the potential of quantum technologies in addressing intricate engineering challenges.

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arXiv2024

Quantum Global Minimum Finder based on Variational Quantum Search

The search for global minima is a critical challenge across multiple fields including engineering, finance, and artificial intelligence, particularly with non-convex functions that feature multiple local optima, complicating optimization efforts. We introduce the Quantum Global Minimum Finder (QGMF), an innovative quantum computing approach that efficiently identifies global minima. QGMF combines binary search techniques to shift the objective function to a suitable position and then employs Variational Quantum Search to precisely locate the global minimum within this targeted subspace. Designed with a low-depth circuit architecture, QGMF is optimized for Noisy Intermediate-Scale Quantum (NISQ) devices, utilizing the logarithmic benefits of binary search to enhance scalability and efficiency. This work demonstrates the impact of QGMF in advancing the capabilities of quantum computing to overcome complex non-convex optimization challenges effectively.

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arXiv2023

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.

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arXiv2023

Comparison of Quantum Simulators for Variational Quantum Search: A Benchmark Study

Simulating quantum circuits using classical computers can accelerate the development and validation of quantum algorithms. Our newly developed algorithm, variational quantum search (VQS), has shown an exponential advantage over Grover's algorithm in the range from 5 to 26 qubits, in terms of circuit depth, for searching unstructured databases. We need to further validate the VQS for more than 26 qubits. Numerous simulators have been developed. However, it is not clear which simulator is most suitable for executing VQS with many qubits. To solve this issue, we implement a typical quantum circuit used in VQS on eight mainstream simulators. Results show that the time and memory required by most simulators increase exponentially with the number of qubits and that Pennylane with GPU and Qulacs are the most suitable simulators for executing VQS efficiently. Our results aid researchers in selecting suitable quantum simulators without the need for exhaustive implementation, and we have made our codes available for community contributions.

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arXiv2023

Variational Quantum Search with Shallow Depth for Unstructured Database Search

With the advent of powerful quantum computers, the quest for more efficient quantum algorithms becomes crucial in attaining quantum supremacy over classical counterparts in the noisy intermediate-scale quantum era. While Grover's search algorithm and its generalization, quantum amplitude amplification, offer quadratic speedup in solving various important scientific problems, their exponential time complexity limits scalability as the quantum circuit depths grow exponentially with the number of qubits. To overcome this challenge, we propose Variational Quantum Search (VQS), a novel algorithm based on variational quantum algorithms and parameterized quantum circuits. We show that a depth-10 Ansatz can amplify the total probability of $k$ ($k \geq 1$) good elements, out of $2^n$ elements represented by $n$+1 qubits, from $k/2^n$ to nearly 1, as verified for $n$ up to 26, and that the maximum depth of quantum circuits in the VQS increases linearly with the number of qubits. Our experimental results have validated the efficacy of VQS and its exponential advantage over Grover's algorithm in circuit depth for up to 26 qubits. We demonstrate that a depth-56 circuit in VQS can replace a depth-270,989 circuit in Grover's algorithm. Envisioning its potential, VQS holds promise to accelerate solutions to critical problems.

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arXiv2023

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.

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arXiv2023

Near-perfect Reachability of Variational Quantum Search with Depth-1 Ansatz

Grover's search algorithm is renowned for its dramatic speedup in solving many important scientific problems. The recently proposed Variational Quantum Search (VQS) algorithm has shown an exponential advantage over Grover's algorithm for up to 26 qubits. However, its advantage for larger numbers of qubits has not yet been proven. Here we show that the exponentially deep circuit required by Grover's algorithm can be replaced by a multi-controlled NOT gate together with either a single layer of Ry gates or two layers of circuits consisting of Hadamard and NOT gates, which is valid for any number of qubits greater than five. We prove that the VQS, with a single layer of Ry gates as its Ansatz, has near-perfect reachability in finding the good element of an arbitrarily large unstructured data set, and its reachability exponentially improves with the number of qubits, where the reachability is defined to quantify the ability of a given Ansatz to generate an optimal quantum state. Numerical studies further validate the excellent reachability of the VQS. Proving the near-perfect reachability of the VQS, with a depth-1 Ansatz, for any number of qubits completes an essential step in proving its exponential advantage over Grover's algorithm for any number of qubits, and the latter proving is significant as it means that the VQS can efficiently solve NP-complete problems.

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arXiv2023

Quantum Feasibility Labeling for NP-complete Vertex Coloring Problem

Many important science and engineering problems can be converted into NP-complete problems which are of significant importance in computer science and mathematics. Currently, neither existing classical nor quantum algorithms can solve these problems in polynomial time. To address this difficulty, this paper proposes a quantum feasibility labeling (QFL) algorithm to label all possible solutions to the vertex coloring problem, which is a well-known NP-complete problem. The QFL algorithm converts the vertex coloring problem into the problem of searching an unstructured database where good and bad elements are labeled. The recently proposed variational quantum search (VQS) algorithm was demonstrated to achieve an exponential speedup, in circuit depth, up to 26 qubits in finding good element(s) from an unstructured database. Using the labels and the associated possible solutions as input, the VQS can find all feasible solutions to the vertex coloring problem. The number of qubits and the circuit depth required by the QFL each is a polynomial function of the number of vertices, the number of edges, and the number of colors of a vertex coloring problem. We have implemented the QFL on an IBM Qiskit simulator to solve a 4-colorable 4-vertex 3-edge coloring problem.

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arXiv2022

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.

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arXiv2022

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.

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arXiv2019

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.

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