Related papers: A Unifying Framework for Doubling Algorithms
The recent emergence of novel computational devices, such as quantum computers, coherent Ising machines, and digital annealers presents new opportunities for hardware-accelerated hybrid optimization algorithms. Unfortunately, demonstrations…
Recently, three numerical methods for the computation of eigenvalues of singular matrix pencils, based on a rank-completing perturbation, a rank-projection, or an augmentation were developed. We show that all three approaches can be…
In previous research, quantum resources were concretely estimated for solving Elliptic Curve Discrete Logarithm Problem(ECDLP). In [1], the quantum algorithm was optimized for the binary elliptic curves and the main optimization target was…
Many problems in linear algebra -- such as those arising from non-Hermitian physics and differential equations -- can be solved on a quantum computer by processing eigenvalues of the non-normal input matrices. However, the existing Quantum…
Time evolution of quantum systems is of interest in physics, in chemistry, and, more recently, in computer science. Quantum computers are suggested as one route to propagating quantum systems far more efficiently than ordinary numerical…
Univariate polynomial root-finding is both classical and important for modern computing. Frequently one seeks just the real roots of a polynomial with real coefficients. They can be approximated at a low computational cost if the polynomial…
Recent years have seen significant advances in quantum/quantum-inspired technologies capable of approximately searching for the ground state of Ising spin Hamiltonians. The promise of leveraging such technologies to accelerate the solution…
Generalized eigenvalue problems involving a singular pencil may be very challenging to solve, both with respect to accuracy and efficiency. While Part I presented a rank-completing addition to a singular pencil, we now develop two…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
Nowadays, fast delivery services have created the need for high-density warehouses. The puzzle-based storage system is a practical way to enhance the storage density, however, facing difficulties in the retrieval process. In this work, a…
In this paper we focus on the unconstrained binary quadratic optimization model, maximize x^t Qx, x binary, and consider the problem of identifying optimal solutions that are robust with respect to perturbations in the Q matrix.. We are…
Quantum computing technology is advancing rapidly. Yet, even accounting for these trends, a quantum leap would be needed for quantum computers to meaningfully impact deep learning over the coming decade or two. We arrive at this conclusion…
Quantum annealing is a method developed to solve combinatorial optimization problems by utilizing quantum bits. Solving such problems corresponds to minimizing a cost function defined over binary variables. However, in many practical cases,…
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
Quantum computation strongly relies on the realisation, manipulation and control of qubits. A central method for realizing qubits is by creating a double-well potential system with a significant gap between the first two eigenvalues and the…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Nonlinear equations are challenging to solve due to their inherently nonlinear nature. As analytical solutions typically do not exist, numerical methods have been developed to tackle their solutions. In this article, we give a quantum…
Logic entailment is essential to reasoning, but entailment checking has the worst-case complexity of an exponential of the variable size. With recent development, quantum computing when mature may allow an effective approach for various…
The aim of this paper is to endow the well-known family of hypercubic quantization hashing methods with theoretical guarantees. In hypercubic quantization, applying a suitable (random or learned) rotation after dimensionality reduction has…
Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…