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With the advent of quantum computers, many quantum computing algorithms are being developed. Solving linear systems is one of the most fundamental problems in almost all science and engineering. The Harrow-Hassidim-Lloyd algorithm, a…
Despite the successful enhancement to the Harrow-Hassidim-Lloyd algorithm by Childs et al., who introduced the Fourier approach leveraging linear combinations of unitary operators, our research has identified non-trivial redundancies within…
Binary Neural Networks are a promising technique for implementing efficient deep models with reduced storage and computational requirements. The training of these is however, still a compute-intensive problem that grows drastically with the…
Rapid progress in developing near- and long-term quantum algorithms for quantum chemistry has provided us with an impetus to move beyond traditional approaches and explore new ways to apply quantum computing to electronic structure…
With the advent and development of quantum computers, various quantum algorithms that can solve linear equations and eigenvalues faster than classical computers have been developed. The Harrow-Hassidim-Lloyd algorithm is an algorithm that…
This work presents a new approach for simulating the HHL linear systems of equations solver algorithm with tensor networks. First, a novel HHL in the qudits formalism, the generalization of qubits, is developed, and then its operations are…
The application of quantum algorithms to classical problems is generally accompanied by significant bottlenecks when transferring data between quantum and classical states, often negating any intrinsic quantum advantage. Here we address…
The rapid integration of renewable energy resources presents formidable challenges in managing power grids. While advanced computing and machine learning techniques offer some solutions for accelerating grid modeling and simulation, there…
We propose a natural application of Quantum Linear Systems Problem (QLSP) solvers such as the HHL algorithm to efficiently prepare highly excited interior eigenstates of physical Hamiltonians in a variational and targeted manner. This is…
Quantum algorithms have the ability to reduce runtime for executing tasks beyond the capabilities of classical algorithms. Therefore, identifying the resources responsible for quantum advantages is an interesting endeavour. We prove that…
Quantum algorithms offer significant speedups over their classical counterparts for a variety of problems. The strongest arguments for this advantage are borne by algorithms for quantum search, quantum phase estimation, and Hamiltonian…
In this paper, we model and solve a fundamental power system problem, i.e., DC power flow, using a practical quantum computer. The Harrow-Hassidim-Lloyd (HHL) quantum algorithm is used to solve the DC power flow problem. The HHL algorithm…
We propose an iterative improvement method for the Harrow-Hassidim-Lloyd (HHL) algorithm to solve a linear system of equations. This is a quantum-classical hybrid algorithm. The accuracy is essential to solve the linear system of equations.…
The total least squares~(TLS) method is widely used in data-fitting. Compared with the least squares fitting method, the TLS fitting takes into account not only observation errors, but also errors from the measurement matrix of the…
Harrow-Hassidim-Lloyd algorithm (HHL) allows for the exponentially faster solution of a system of linear equations. However, this algorithm requires the postselection of an ancilla qubit to obtain the solution. This postselection makes the…
The Harrow-Hassidim-Lloyd quantum algorithm was proposed to solve linear systems of equations $A\vec{x} = \vec{b}$ and it is the core of various applications. However, there is not an explicit quantum circuit for the subroutine which maps…
We present a classical enhancement to improve the accuracy of the Hybrid variant (Hybrid HHL) of the quantum algorithm for solving linear systems of equations proposed by Harrow, Hassidim, and Lloyd (HHL). We achieve this by using higher…
We extend the Harrow-Hassidim-Lloyd (HHL) algorithm, which is well-studied in the qubit framework, to its qutrit counterpart (which we call qutrit HHL, as opposed to qubit HHL, which is HHL using qubits), and develop a program for its…
This work presents a quantum algorithm for solving linear systems of equations of the form $\mathbf{A}{\frac{\mathbf{\partial f}}{\mathbf{\partial x}}} = \mathbf{B}\mathbf{f}$, based on the Quantum Singular Value Transformation (QSVT). The…
Recently, an efficient quantum algorithm for linear systems of equations introduced by Harrow, Hassidim, and Lloyd, has received great concern from the academic community. However, the error and complexity analysis for this algorithm seems…