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We explore in the framework of Quantum Computation the notion of {\em Computability}, which holds a central position in Mathematics and Theoretical Computer Science. A quantum algorithm for Hilbert's tenth problem, which is equivalent to…
An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is…
Quantum computers (QCs) are maturing. When QCs are powerful enough, they may be able to handle problems in chemistry, physics, and finance that are not classically solvable. However, the applicability of quantum algorithms to speed up…
Recent improvements in control of quantum systems make it seem feasible to finally build a quantum computer within a decade. While it has been shown that such a quantum computer can in principle solve certain small electronic structure…
Topological quantum computers provide a fault-tolerant method for performing quantum computation. Topological quantum computers manipulate topological defects with exotic exchange statistics called anyons. The simplest anyon model for…
The generalized eigenvalue (GE) problems are of particular importance in various areas of science engineering and machine learning. We present a variational quantum algorithm for finding the desired generalized eigenvalue of the GE problem,…
It was recently shown that a hidden variable model can be constructed for universal quantum computation with magic states on qubits. Here we show that this result can be extended, and a hidden variable model can be defined for quantum…
This paper gives the first separation of quantum and classical pure (i.e., non-cryptographic) computing abilities with no restriction on the amount of available computing resources, by considering the exact solvability of a celebrated…
While quantum computers promise significant advantages, the complexity of quantum algorithms remains a major technological obstacle. We have developed and demonstrated an architecture-independent technique that simplifies adding control…
The variational quantum eigensolver is one of the most promising algorithms for near-term quantum computers. It has the potential to solve quantum chemistry problems involving strongly correlated electrons, which are otherwise difficult to…
We present a method to formulate the unit commitment problem in energy production as quadratic unconstrained binary optimization (QUBO) problem, which can be solved by classical algorithms and quantum computers. We suggest a first approach…
Certain quantum topological invariants of three manifolds can be written in the form of the Gaussian sum. It is shown that such topological invariants can be approximated efficiently by a quantum computer. The invariants discussed here are…
Making new methods for quantum problems often relies on using basic operations in linear algebra. Often these routines are hidden behind well-known libraries that have been optimized over decades. Attempting to improve on those basic…
The most general method for encoding quantum information is not to encode the information into a subspace of a Hilbert space, but to encode information into a subsystem of a Hilbert space. Recently this notion has led to a more general…
Quantum machine learning algorithms have emerged to be a promising alternative to their classical counterparts as they leverage the power of quantum computers. Such algorithms have been developed to solve problems like electronic structure…
We propose a quantum algorithm for solving the following problem: given the Hamiltonian of a physical system and one of its eigenvalues, how to obtain the corresponding eigenstate? The algorithm is based on the resonance phenomena. For a…
The author analyzes quantum computation with the hybrid qubit (HQ) that is encoded using the three-electron configuration of a double quantum dot. All gate operations are controlled with electric signals, while the qubit remains at an…
Current implementations of the Variational Quantum Eigensolver (VQE) technique for solving the electronic structure problem involve splitting the system qubit Hamiltonian into parts whose elements commute within their single qubit…
This paper introduces a completely new approach to encryption based on group theoretic quantum framework. Quantum cryptography has essentially focused only on key distribution and proceeded with classical encryption algorithm with the…
The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this…