Quantum: Dynamics of an open quantum system: decoherence processes and encoded control

University Of California-Riverside, Riverside CA

Investigators

Abstract

Need for the proposed research: Feasibility of a useful quantum computer (QC) crucially depends upon the performance of quantum error correcting codes (QECC). Current theory of QECC relies upon overly simplistic models of error operators in controlled systems. Errors associated with such simplification can ruin the group-theoretical structure of QECC and substantially degrade their practical performance. The problem is further amplified for embedded, concatenated code constructions, due to the error propagation between different layers of concatenated encoding. The goal of the proposed research is to build a unified description of the decoherence processes applicable for a range of existing passive and active QECC, and use the results to develop highly-optimized heterogeneous concatenated codes for several QC implementations. Research effort proposed: The proposed research will be conducted by an interdisciplinary team, the PI with a strong background in many-body quantum physics, and the co-PI with an extensive experience in coding theory. The proposed research concerns two fundamental problems: quantum kinetics of a driven open system and continuous measurement for such a system. Decoherence processes in several solid-state QC implementations will be analyzed for encoded quantum systems, with projective syndrome measurements done either intermittently during, or at the end of the computation cycle. The effects of second and higher orders in error operators will be addressed in the approximation of the master equation, with the continuously-varying control fields treated exactly. This study will address temporal and spatial correlations between errors and will specifically target schemes based upon shaped-pulse encoded dynamical recoupling, decoherence-free subspaces, quantum Zeno effect, and stabilizer-based QECC. Subsequently, quantum coding will be applied to schemes with ground-state protected qubits and the continuous measurement. The results will be formulated as scaling laws characteristic of different classes of errors and control schemes, and will enable new quantum techniques that use methods of classical coding theory. The PIs plan to construct efficient concatenated coherent control schemes combining the benefits of different approaches. New mathematical methods will be developed that yield the encoding tools and corresponding control sequences for codes protecting large numbers of qubits, without the need of solving for their collective quantum dynamics. The focus will be on codes whose error rates scale down with the interval between measurements faster than linear. The proposed program integrates both graduate and undergraduate participation at UC, Riverside. In particular, the innovative Mathematica-based class seeks to actively boost the undergraduate participation in research and may establish an alternative way to teach quantum mechanics to students majoring in Physics, Chemistry, and Electrical Engineering.