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Portfolio construction has been a long-standing topic of research in finance. The computational complexity and the time taken both increase rapidly with the number of investments in the portfolio. It becomes difficult, even impossible for…
A suitable measure for the similarity of shapes represented by parameterized curves or surfaces is the Fr\'echet distance. Whereas efficient algorithms are known for computing the Fr\'echet distance of polygonal curves, the same problem for…
A hierarchical, reversible mapping between levels of tree structured computation, applicable for structuring the Quantum Computation algorithm for NP-complete problem is presented. It is proven that confining the state of a quantum computer…
(Abridged.) Quantum computers promise to solve some problems exponentially faster than traditional computers, but we still do not fully understand why this is the case. While the most studied model of quantum computation uses qubits, which…
Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming…
Quantum computing offers significant potential for solving NP-hard combinatorial (optimization) problems that are beyond the reach of classical computers. One way to tap into this potential is by reformulating combinatorial problems as a…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
We establish a connection between continuous-variable quantum computing and high-dimensional integration by showing that the outcome probabilities of continuous-variable instantaneous quantum polynomial (CV-IQP) circuits are given by…
We suggest that quantum computers can solve quantum many-body problems that are impracticable to solve on a classical computer.
For the first time in history, we are seeing a branching point in computing paradigms with the emergence of quantum processing units (QPUs). Extracting the full potential of computation and realizing quantum algorithms with a…
We introduce hybrid classical-quantum algorithms for problems involving a large classical data set X and a space of models Y such that a quantum computer has superposition access to Y but not X. These algorithms use data reduction…
It is known that quantum computers yield a speed-up for certain discrete problems. Here we want to know whether quantum computers are useful for continuous problems. We study the computation of the integral of functions from the classical…
The difficulty of simulating quantum systems, well-known to quantum chemists, prompted the idea of quantum computation. One can avoid the steep scaling associated with the exact simulation of increasingly large quantum systems on…
Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…
This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named…
Can NP-complete problems be solved efficiently in the physical universe? I survey proposals including soap bubbles, protein folding, quantum computing, quantum advice, quantum adiabatic algorithms, quantum-mechanical nonlinearities, hidden…
Quantum computers are expected to revolutionize our ability to process information. The advancement from classical to quantum computing is a product of our advancement from classical to quantum physics -- the more our understanding of the…
In modelling complex processes, the potential past data that influence future expectations are immense. Models that track all this data are not only computationally wasteful but also shed little light on what past data most influence the…
The two essential ideas in this paper are, on the one hand, that a considerable amount of the power of quantum computation may be obtained by adding to a classical computer a few specialized quantum modules and, on the other hand, that such…
We elucidate the profound connection between physics and computation by proposing and examining the model of the non-Hermitian quantum computer (NQC). In addition to conventional quantum gates such as the Hadamard, phase, and CNOT gates,…