Riemannian Quantum Circuit

Abstract

Number theory is an abstract mathematical field that has found a fertile environment for development in theoretical physics. In particular, several physical systems were related to the zeros of the Riemann-zeta function. In this work we present the theory of a quantum circuit related to a finite number of zeros of the Riemann-zeta function. The existence of such circuit will permit in the future the solution of some number theory problems through the realization of quantum algorithms based on those zeros.

7 pages

References in corpus (5)

• Quantum Circuits for General Multiqubit Gates
• Physics of the Riemann Hypothesis
• Quantum mechanical potentials related to the prime numbers and Riemann zeros
• Classical and Quantum Algorithms for Exponential Congruences
• Riemann Hypothesis as an Uncertainty Relation

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• Will a physicist prove the Riemann Hypothesis?
• The Riemann zeros as energy levels of a Dirac fermion in a potential built from the prime numbers in Rindler spacetime
• The Riemann zeros as spectrum and the Riemann hypothesis
• A Non-Linear Difference Equation for Calculation of the Zeros of the Riemann Zeta-Function on the Critical Line
• Riemann Hypothesis as an Uncertainty Relation
• The zeros of the Riemann-zeta function and the transition from pseudo-random to harmonic behavior
• Quantum Sequence States
• A quantum number theory
• Quantum Physics, Algorithmic Information Theory and the Riemanns Hypothesis