Methods of geometric control theory for quantum computations

Erik Sjöqvist, Vahid Azimi Mousolou, Carlo M. Canali

Zakaria Giunashvili

The applications of geometric control theory methods on Lie groups and homogeneous spaces to the theory of quantum computations are investigated. These methods are shown to be very useful for the problem of constructing an universal set of gates for quantum computations: the well-known result that the set of all one-bit gates together with almost any one two-bit gate is universal is considered from the control theory viewpoint.

Jun Zhang

Gia Giorgadze

Preface Basic of Quantum Computation Quantum Computers Based on Exactly Solvable Models & Geometric Phases Quantum Processor Based on the Three-Level Quantum System Methods of Geometric Control Theory for Quantum Computations Analytic Methods in Quantum Computation References Index.

lichao

This paper presents a novel quantum state control method basedon Multi-Path Closure Time (MPCT) theory. Through purely ge-ometric dynamical processes without external Hamiltonian driving,we achieve: (1) Significant quantum state amplification with aver-age 3.29× (maximum 3.70×) local state probability enhancement viaweak marking; (2) Observation of quantized peak spacing followingn2 patterns, specifically n2 = 4 corresponding to n = 2; (3) Naturalformation of multi-peak superposition states with average 3.2 signifi-cant peaks in geometric mode. The core mechanism involves MPCTclosure phase driving for temporal emergence, geometric vibration sta-bilization for coherence maintenance, and weak dissipation balancingimplementing the Principle of Existence Cost (PEC). This work es-tablishes a new paradigm for low-energy geometric quantum control,potentially revolutionizing quantum computation approaches.

Eduardo Jose Bayro-Corrochano