Related papers: On the power quantum computation over real Hilbert…
An algorithm for quantum computing Hamiltonian cycles of simple, cubic, bipartite graphs is discussed. It is shown that it is possible to evolve a quantum computer into an entanglement of states which map onto the set of all possible paths…
In quantum mechanics, a state is an element of a Hilbert space whose dimension exponentially grows with the increase of the number of particles (or qubits, in quantum computing). The vague question "is this huge Hilbert space really there?"…
The space of quantum Hamiltonians has a natural partition in classes of operators that can be adiabatically deformed into each other. We consider parametric families of Hamiltonians acting on a bi-partite quantum state-space. When the…
The complexity class NP is quintessential and ubiquitous in theoretical computer science. Two different approaches have been made to define "Quantum NP," the quantum analogue of NP: NQP by Adleman, DeMarrais, and Huang, and QMA by Knill,…
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness…
Realistic quantum mechanics based on complex probability theory is shown to have a frequency interpretation, to coexist with Bell's theorem, to be linear, to include wavefunctions which are expansions in eigenfunctions of Hermitian…
We construct a large class of multipartite qudit states which are positive under the family of partial transpositions. The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic…
Many physicists limit oneself to an instrumentalist description of quantum phenomena and ignore the problems of foundation and interpretation of quantum mechanics. This instrumentalist approach results to "specialization barbarism" and mass…
Although near-term quantum computing devices are still limited by the quantity and quality of qubits in the so-called NISQ era, quantum computational advantage has been experimentally demonstrated. Moreover, hybrid architectures of quantum…
Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…
Quantized integrable systems can be made to perform universal quantum computation by the application of a global time-varying control. The action-angle variables of the integrable system function as qubits or qudits, which can be coupled…
Quantum Image Processing (QIP)is an exciting new field showing a lot of promise as a powerful addition to the arsenal of Image Processing techniques. Representing image pixel by pixel using classical information requires an enormous amount…
We investigate the boundary between classical and quantum computational power. This work consists of two parts. First we develop new classical simulation algorithms that are centered on sampling methods. Using these techniques we generate…
The controlled-NOT gate of qubit quantum circuits is shown to be described in terms of a Hopf algebra. Accordingly, any qubit quantum circuit can be expressed as the Hopf algebraic computations and unitary transformations on one qubit.
Quantum computing can provide speedups in solving many problems as the evolution of a quantum system is described by a unitary operator in an exponentially large Hilbert space. Such unitary operators change the phase of their eigenstates…
General relativity and quantum mechanics are incompatible at the Planck scale. This contention can be examined if a quantum computer is set to operate at a rate that exceeds the classical limit of one operation per Planck volume-time, or…
We have studied quantum systems on finite-dimensional Hilbert spaces and found that all these systems are connected through local transformations. Actually, we have shown that these transformations give rise to a gauge group that connects…
A central problem in quantum computing is to identify computational tasks which can be solved substantially faster on a quantum computer than on any classical computer. By studying the hardest such tasks, known as BQP-complete problems, we…
The theory of positive maps plays a central role in operator algebras and functional analysis, and has countless applications in quantum information science. The theory was originally developed for operators acting on complex Hilbert…
The development of complex circuits for practical applications in the current quantum computing ecosystem is based on basic primitives such as Bell states, which provide superposition, entanglement, and coherence. The range of…