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Cylindrical Algebraic Decomposition (CAD) by projection and lifting requires many iterated univariate resultants. It has been observed that these often factor, but to date this has not been used to optimise implementations of CAD. We…
The kernel trick is a widely applicable technique in machine learning domains that maps datasets that are difficult to classify into a computationally friendly feature space. As the dimension of the dataset scales, these kernel calculations…
Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point…
New families of time-dependent potentials related with the stationary singular oscillator are introduced. This is achieved after noticing that a non stationary quantum invariant can be constructed for the singular oscillator. Such invariant…
We study the equivalence of mixed states under local unitary transformations. First we express quantum states in Bloch representation. Then based on the coefficient matrices, some invariants are constructed. This method and results can be…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
We derive the time dilation formula for charged quantum clocks in electromagnetic fields. As a concrete example of non-inertial motion, we consider a cyclotron motion in a uniform magnetic field. Applying the time dilation formula to…
The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational…
Quantum systems governed by time-dependent Hamiltonians pose significant challenges for the accurate computation of unitary time-evolution operators, which are essential for predicting quantum state dynamics. In this work, we introduce a…
In this short letter, I present a powerful application in dimensionality reduction of the lesser-used Jacobi-Davidson algorithm for the generalized eigenvalue decomposition. When combined with matrix-free implementations of relevant…
We present a quantum algorithm which simulates the quantum kicked rotator model exponentially faster than classical algorithms. This shows that important physical problems of quantum chaos, localization and Anderson transition can be…
The iterative qubit coupled cluster (iQCC) method is a systematic variational approach to solve the electronic structure problem on universal quantum computers. It is able to use arbitrarily shallow quantum circuits at expense of iterative…
Efficiency of time-evolution of quantum observables, and thermal states of quenched hamiltonians, is studied using time-dependent density matrix renormalization group method in a family of generic quantum spin chains which undergo a…
Solving quantum many-body systems is one of the most significant regimes where quantum computing applies. Currently, as a hardware-friendly computational paradigms, variational algorithms are often used for finding the ground energy of…
We consider the interpolation problem with the inverse multiquadric radial basis function. The problem usually produces a large dense linear system that has to be solved by iterative methods. The efficiency of such methods is strictly…
A critical step in developing circuits for quantum simulation is to synthesize a desired unitary operator using the circuit building blocks. Studying unitaries and their generators from the Lie algebraic perspective has given rise to…
Electron transport in realistic physical and chemical systems often involves the non-trivial exchange of energy with a large environment, requiring the definition and treatment of open quantum systems. Because the time evolution of an open…
We develop a system consisting of a quantum kicked rotor with an additional degree of freedom. This models a single two-level atom with internal ground and excited states, and it is characterized by its quantum resonances with ballistic…
In this work, we present a method to exponentiate non-sparse indefinite low-rank matrices on a quantum computer. Given an operation for accessing the elements of the matrix, our method allows singular values and associated singular vectors…
Quantum repeaters hold the promise to prevent the photon losses in communication channels. Most recently, the serious efforts have been applied to achieve scalable distribution of entanglement over long distances. However, the probabilistic…