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A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…
We study the complexity of problems solvable in deterministic polynomial time with access to an NP or Quantum Merlin-Arthur (QMA)-oracle, such as $P^{NP}$ and $P^{QMA}$, respectively. The former allows one to classify problems more finely…
The predictions that quantum theory makes about the outcomes of measurements are generally probabilistic. This has raised the question whether quantum theory can be considered complete, or whether there could exist alternative theories that…
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
I shall discuss some "conditions of possibility" of a quantum theory of gravity, stressing the need for solutions to some of fundamental problems confronting any attempt to apply some method of quantization to the field equations of general…
While historically many quantum mechanical simulations of molecular dynamics have relied on the Born-Oppenheimer approximation to separate electronic and nuclear behavior, recently a lot of interest has arisen towards quantum effects in…
This is the final article in a series of four articles. Richard Karp has proven that a deterministic polynomial time solution to K-SAT will result in a deterministic polynomial time solution to all NP-Complete problems. However, it is…
It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum…
Quantum algorithms offer a compelling new avenue for addressing difficult NP-complete optimization problems, such as the Generalized Assignment Problem (GAP). Given the operational constraints of contemporary Noisy Intermediate-Scale…
We present a deterministic polynomial-time algorithm that solves the 3-satisfiability problem.
We consider the problem of mapping digital data encoded on a quantum register to analog amplitudes in parallel. It is shown to be unlikely that a fully unitary polynomial-time quantum algorithm exists for this problem; NP becomes a subset…
We use one photon to simulate an n-qubit quantum system for the first time. We propose a new scheme to realize universal quantum computation in polynomial time O(n^5). A generating set of gates can be realized with high accuracy in the lab.…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented…
We present a universal algorithm for the optimal quantum state estimation of an arbitrary finite dimensional system. The algorithm specifies a physically realizable positive operator valued measurement (POVM) on a finite number of…
In a recent result, Frauchiger and Renner argue that if quantum theory accurately describes complex systems like observers who perform measurements, then "we are forced to give up the view that there is one single reality." Following a…
Polynomial quantified entailments with existentially and universally quantified variables arise in many problems of verification and program analysis. We present PolyQEnt which is a tool for solving polynomial quantified entailments in…
A non-relativistic quantum mechanical theory is proposed that describes the universe as a continuum of worlds whose mutual interference gives rise to quantum phenomena. A logical framework is introduced to properly deal with propositions…
In this short communication, it is shown a simple problem using quantum circuits for which the algorithmic information theory guarantee that the minimal length of the algorithm able to solve it grows exponentially with the number of qubits.