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Image processing is a fascinating field for exploring quantum algorithms. However, achieving quantum speedups turns out to be a significant challenge. In this work, we focus on image filtering to identify a class of images that can achieve…
Fast multidimensional convolution can be performed naively in quadratic time and can often be performed more efficiently via the Fourier transform; however, when the dimensionality is large, these algorithms become more challenging. A…
The quantum permutation algorithm provides computational speed-up over classical algorithms in determining the parity of a given cyclic permutation. For its $n$-qubit implementations, the number of required quantum gates scales…
We introduce a framework for simulating hybrid oscillator-qubit quantum processors on qubit-only systems through position encoding. By encoding continuous-variable position and momentum wave functions into qubit amplitudes, our method…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
We consider cloning transformations of equatorial qubits and qutrits, with the transformation covariant for rotation of the phases. The optimal cloning maps are derived without simplifying assumptions from first principles, for any number…
A new method for quantum computation in the presence of detected spontaneous emission is proposed. The method combines strong and fast (dynamical decoupling) pulses and a quantum error correcting code that encodes $n$ logical qubits into…
We present recursive multiport schemes for implementing quantum Fourier transforms and the inversion step in Grover's algorithm on an integrated linear optics device. In particular, each scheme shows how to execute a quantum operation on…
The pseudo-polar Fourier transform is a specialized non-equally spaced Fourier transform, which evaluates the Fourier transform on a near-polar grid, known as the pseudo-polar grid. The advantage of the pseudo-polar grid over other…
Two different algorithms are presented for generating a quantum circuit realization of a matrix representing a permutation on $2^n$ letters. All circuits involve $n$ qubits and only use multi--controlled Toffoli gates. The first algorithm…
Quantum computers will allow calculations beyond existing classical computers. However, current technology is still too noisy and imperfect to construct a universal digital quantum computer with quantum error correction. Inspired by the…
Fourier and fractional-Fourier transformations are widely used in theoretical physics. In this paper we make quantum perspectives and generalization for the fractional Fourier transformation (FrFT). By virtue of quantum mechanical…
The entanglement of a quantum system can be valuated using Mermin polynomials. This gives us a means to study entanglement evolution during the execution of quantum algorithms. We first consider Grover's quantum search algorithm, noticing…
High-throughput approximations of quantum mechanics calculations and combinatorial experiments have been traditionally used to reduce the search space of possible molecules, drugs and materials. However, the interplay of structural and…
A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability…
Quantum comparators and modular arithmetic are fundamental in many quantum algorithms. Current research mainly focuses on operations between two quantum states. However, various applications, such as integer factorization, optimization,…
A gate sequence of single-qubit transformations may be condensed into a single microwave pulse that maps a qubit from an initialized state directly into the desired state of the composite transformation. Here, machine learning is used to…
We found that the actual computational time-cost of the QFT is O(n 2^n) for large n in a quantum computer using nuclear spins. The computational cost of a quantum algorithm has usually been estimated as the sum of the universal gates…
A quantum computer will use the properties of quantum physics to solve certain computational problems much faster than otherwise possible. One promising potential implementation is to use superconducting quantum bits in the circuit quantum…
After the appearance of the no-cloning theorem, approximate quantum cloning machines (QCMs) have become one of the most well-studied subject in quantum information theory. Among several measures to quantify the performance of a QCM,…