Related papers: Quantum Phase Estimation Algorithm for Finding Pol…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
Quantum computing promises to speed up some of the most challenging problems in science and engineering. Quantum algorithms have been proposed showing theoretical advantages in applications ranging from chemistry to logistics optimization.…
Quantum devices use qubits to represent information, which allows them to exploit important properties from quantum physics, specifically superposition and entanglement. As a result, quantum computers have the potential to outperform the…
Quantum computing holds significant promise for scientific computing due to its potential for polynomial to even exponential speedups over classical methods, which are often hindered by the curse of dimensionality. While neural networks…
Machines are possible to have some artificial intelligence like human beings owing to particular algorithms or software. Such machines could learn knowledge from what people taught them and do works according to the knowledge. In practical…
Quantum signal processing (QSP) represents a real scalar polynomial of degree $d$ using a product of unitary matrices of size $2\times 2$, parameterized by $(d+1)$ real numbers called the phase factors. This innovative representation of…
Suppose we have n algorithms, quantum or classical, each computing some bit-value with bounded error probability. We describe a quantum algorithm that uses O(sqrt{n}) repetitions of the base algorithms and with high probability finds the…
The advantage that many quantum algorithms have over their classical counterparts may be lost when the results are extracted as classical data (output problem). One example are eigenpair solvers, which encode the eigenpairs in a quantum…
This work is a continuation of "Fast and backward stable computation of roots of polynomials" by J.L. Aurentz, T. Mach, R. Vandebril, and D.S. Watkins, SIAM Journal on Matrix Analysis and Applications, 36(3): 942--973, 2015. In that paper…
A quantum algorithm is developed to calculate decay rates and cross sections using quantum resources that scale polynomially in the system size assuming similar scaling for state preparation and time evolution. This is done by computing…
Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…
Quantum computation has received great attention in recent years for its possible application to difficult problem in classical calculation. Despite the experimental problems of implementing quantum devices, theoretical physicists have…
With reference to a search in a database of size N, Grover states: "What is the reason that one would expect that a quantum mechanical scheme could accomplish the search in O(square root of N) steps? It would be insightful to have a simple…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed correct after a time that is upper-bounded by a polynomial in the worst case. In an oracle setting, it is shown that such machines…
Quantum Phase Estimation is a crucial component of several front-running quantum algorithms. Improving the efficiency and accuracy of QPE is currently a very active field of research. In this work, we present a hybrid quantum-classical…
Matrix scaling and matrix balancing are two basic linear-algebraic problems with a wide variety of applications, such as approximating the permanent, and pre-conditioning linear systems to make them more numerically stable. We study the…
In the field of quantum linear system algorithms, quantum computing has realized exponential computational advantages over classical computing. However, the focus has been on square coefficient matrices, with few quantum algorithms…
It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…
Quantum signal processing (QSP) is a powerful quantum algorithm to exactly implement matrix polynomials on quantum computers. Asymptotic analysis of quantum algorithms based on QSP has shown that asymptotically optimal results can in…
Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring…