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We study the complexity of a class of problems involving satisfying constraints which remain the same under translations in one or more spatial directions. In this paper, we show hardness of a classical tiling problem on an N x N…
We consider the problem of a semiclassical description of quantum chaotic transport, when a tunnel barrier is present in one of the leads. Using a semiclassical approach formulated in terms of a matrix model, we obtain transport moments as…
Quantum circuits are typically represented by a (ordered) sequence of gates over a set of virtual qubits. During compilation, the virtual qubits of the gates are assigned to the physical qubits of the underlying quantum hardware, a step…
Resonant tunneling through identical potential barriers is a textbook problem in quantum mechanics. Its solution yields total transparency (100% tunneling) at discrete energies. This dramatic phenomenon results from coherent interference…
Aspects of quantum mechanics on a ring are studied. Either one or two impenetrable barriers are inserted at nodal and non-nodal points to turn the ring into either one or two infinite square wells. In the process, the wave function of a…
We study the influence of a tunnel barrier on the quantum transport through a circular cavity. Our analysis in terms of classical trajectories shows that the semiclassical approaches developed for ballistic transport can be adapted to deal…
Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the…
If quantum states exhibit small nonlinearities during time evolution, then quantum computers can be used to solve NP-complete problems in polynomial time. We provide algorithms that solve NP-complete and #P oracle problems by exploiting…
A semiclassical method of complex trajectories for the calculation of the tunneling exponent in systems with many degrees of freedom is further developed. It is supplemented with an easily implementable technique, which enables one to…
Quantum annealing is a promising paradigm for building practical quantum computers. Compared to other approaches, quantum annealing technology has been scaled up to a larger number of qubits. On the other hand, deep learning has been…
In this paper, we develop a way to encode several NP-Complete problems in Abstract Argumentation to Quadratic Unconstrained Binary Optimization (QUBO) problems. In this form, a solution for a QUBO problem involves minimizing a quadratic…
Each year, the gap between theoretical proposals and experimental endeavours to create quantum computers gets smaller, driven by the promise of fundamentally faster algorithms and quantum simulations. This occurs by the combination of…
Exact solutions describing trapped modes in a plane quantum waveguide with a small rigid obstacle are constructed in the form of convergent series in powers of the small parameter characterizing the smallness of the obstacle. The terms of…
How many mutually non-attacking queens can be placed on a d-dimensional chessboard of size n? The n-queens problem in higher dimensions is a generalization of the well-known n-queens problem. We present an integer programming formulation of…
A model for quantum tunnelling of a cluster comprising A identical particles, coupled by oscillator-type potential, through short-range repulsive potential barriers is introduced for the first time in the new symmetrized-coordinate…
We present an algorithm to compute the number of solutions of the (constrained) number partitioning problem. A concrete implementation of the algorithm on an Ising-type quantum computer is given.
An efficient quantum algorithm is proposed to solve in polynomial time the parity problem, one of the hardest problems both in conventional quantum computation and in classical computation, on NMR quantum computers. It is based on the…
In this work we develop an alternative approach for solution of Quantum Trajectories using the Path Integral method. The state-of-the-art technique in the field is to solve a set of non-linear, coupled partial differential equations (PDEs)…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
The quantum marginal problem asks, given a set of reduced quantum states of a multipartite system, whether there exists a joint quantum state consistent with these reduced states. The quantum marginal problem is known to be hard to solve in…