Following the recent great advance of quantum computing technology, there are growing interests in its applications to industries, including finance. In this article, we focus on derivative pricing based on solving the Black–Scholes partial differential equation by the finite-difference method (FDM), which is a suitable approach for some types of derivatives but suffers from the […]
This article extends the Radon transform, a classical image-processing tool for fast tomography and denoising, to the quantum computing platform. A new kind of periodic discrete Radon transform (PDRT), called the quantum periodic discrete Radon transform (QPRT), is proposed. The quantum implementation of QPRT based on the amplitude encoding method is exponentially faster than the […]
Graph coloring is a computationally difficult problem, and currently the best known classical algorithm for k -coloring of graphs on n vertices has runtimes Ω(2n) for k≥5 . The list coloring problem asks the following more general question: given a list of available colors for each vertex in a graph, does it admit a proper coloring? We propose a hybrid classical-quantum algorithm based […]
The qubit-mapping problem aims to assign and route qubits of a quantum circuit onto an noisy intermediate-scale quantum (NISQ) device in an optimized fashion, with respect to some cost function. Finding an optimal solution to this problem is known to scale exponentially in computational complexity; as such, it is imperative to investigate scalable qubit-mapping solutions […]
In this article, we demonstrate that, by employing the OpenPulse design kit for IBM superconducting quantum devices, the controlled-V gate ( cv gate) can be implemented in about half the gate time to the controlled-X gate ( cx or cnot gate) and consequently 65.5% reduced gate time compared to the cx -based implementation of cv […]
Variational quantum algorithms (VQAs) are prime contenders to gain computational advantages over classical algorithms using near-term quantum machines. As such, many endeavors have been made to accelerate the optimization of modern VQAs in past years. To further improve the capability of VQAs, here, we propose a quantum distributed optimization scheme (dubbed as QUDIO), whose back […]
The well-known 3-bit Hermitian gate (a Toffoli gate) has been implemented using Clifford+T circuits. Compared with the Peres gate, its implementation circuit requires more controlled- not (cnot) gates. However, the Peres gate is not Hermitian. This article reports four 3-bit Hermitian gates named LI gates, whose realized circuits have the same T-count, T-depth, and cnot […]
Variational quantum algorithms (VQAs) are prime contenders to gain computational advantages over classical algorithms using near-term quantum machines. As such, many endeavors have been made to accelerate the optimization of modern VQAs in past years. To further improve the capability of VQAs, here, we propose a quantum distributed optimization scheme (dubbed as QUDIO), whose back […]
Hybrid quantum-classical algorithms, such as variational quantum algorithms (VQAs), are suitable for implementation on noisy intermediate-scale quantum computers. In this article, we expand an implicit step of VQAs: the classical precomputation subroutine, which can nontrivially use classical algorithms to simplify, transform, or specify problem instance-specific variational quantum circuits. In VQA, there is a tradeoff between […]
In this article, we extend variational quantum optimization algorithms for quadratic unconstrained binary optimization problems to the class of mixed binary optimization problems. This allows us to combine binary decision variables with continuous decision variables, which, for instance, enables the modeling of inequality constraints via slack variables. We propose two heuristics and introduce the transaction […]