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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…
The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the solution of a linear system provides an exponential speed-up over its classical counterpart. The problem of solving a system of linear equations has a wide scope of…
Solving linear systems of equations plays a fundamental role in numerous computational problems from different fields of science. The widespread use of numerical methods to solve these systems motivates investigating the feasibility of…
Quantum algorithms for solving linear systems of equations have generated excitement because of the potential speed-ups involved and the importance of solving linear equations in many applications. However, applying these algorithms can be…
After learning basic quantum computing concepts, it is desirable to reinforce the learning using an important and relatively complex algorithm through which the students can observe and appreciate how the qubits evolve and interact with…
We propose a hybrid quantum algorithm based on the Harrow-Hassidim-Lloyd (HHL) algorithm for solving a system of linear equations. In our hybrid scheme, a classical information feed-forward is required from the quantum phase estimation…
The Harrow-Hassidim-Lloyd algorithm is intended for solving the system of linear equations on quantum devices. The exponential advantage of the algorithm comes with four caveats. We present a numerical study of the performance of the…
Quantum computing, a prominent non-Von Neumann paradigm beyond Moore's law, can offer superpolynomial speedups for certain problems. Yet its advantages in efficiency for tasks like machine learning remain under investigation, and quantum…
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…
In this paper, we explore using the Harrow-Hassidim-Lloyd (HHL) algorithm to address scientific and engineering problems through quantum computing, utilizing the NWQSim simulation package on a high-performance computing platform. Focusing…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
The limited capabilities of current quantum hardware significantly constrain the scale of experimental demonstrations of most quantum algorithmic primitives. This makes it challenging to perform benchmarking of the current hardware using…
In an extension of the Unconventional Noiseless Intermediate Quantum Emulator, this work introduces a classical emulation of the quantum Harrow-Hassidim-Lloyd algorithm for sampling from the solution space of linear systems. The emulated…
Quantum computing enables the efficient resolution of complex problems, often outperforming classical methods across various applications. In 2009, Harrow, Hassidim and Lloyd proposed an algorithm for solving linear systems of equations,…
In the era of quantum computing, the emergence of quantum computers and subsequent advancements have led to the development of various quantum algorithms capable of solving linear equations and eigenvalues, surpassing the pace of classical…
Recent works have shown that quantum computers can polynomially speed up certain SAT-solving algorithms even when the number of available qubits is significantly smaller than the number of variables. Here we generalise this approach. We…
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…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
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…
The Harrow-Hassidim-Lloyd (HHL) algorithm is a quantum algorithm for solving systems of linear equations that, in principle, offers an exponential improvement in scaling with the system size compared to classical approaches. In this work,…