[Paper Review] Models of Quantum Computers and Decoherence Problem

И. В. Волович|ArXiv.org|Feb 15, 1999

Quantum Computing Algorithms and Architecture14 references6 citations

TL;DR

This paper proposes a control-based approach to mitigate decoherence in quantum computers by analyzing the spin-boson Hamiltonian in the stochastic limit approximation. It suggests tuning system parameters to suppress environmental coupling, offering a theoretical framework for stabilizing quantum states in models like the quantum Turing machine and quantum circuits.

ABSTRACT

Mathematical models of quantum computers such as a multidimensional quantum Turing machine and quantum circuits are described and its relations with lattice spin models are discussed. One of the main open problems one has to solve if one wants to build a quantum computer is the decoherence due to the coupling with the environment. We propose a possible solution of this problem by using a control of parameters of the system. This proposal is based on the analysis of the spin-boson Hamiltonian performed in the stochastic limit approximation.

Motivation & Objective

• To address the fundamental challenge of decoherence in physical implementations of quantum computers.
• To explore the connection between quantum computing models and lattice spin systems.
• To propose a viable mechanism for suppressing decoherence through active control of system parameters.
• To analyze the spin-boson Hamiltonian in the stochastic limit to derive conditions for decoherence suppression.
• To provide a theoretical foundation for stable quantum computation despite environmental coupling.

Proposed method

• Analyzes the spin-boson Hamiltonian as a model for system-environment interaction in quantum computing.
• Applies the stochastic limit approximation to study the long-time dynamics of open quantum systems.
• Identifies control parameters in the Hamiltonian that influence the rate of decoherence.
• Proposes tuning these parameters to minimize the coupling strength between the quantum system and its environment.
• Uses mathematical modeling to show that under specific parameter regimes, decoherence can be effectively suppressed.
• Relates the findings to quantum circuit and quantum Turing machine models through their underlying spin-lattice representations.

Experimental results

Research questions

• RQ1 How does the coupling between a quantum system and its environment lead to decoherence in quantum computing models?
• RQ2 What role does the spin-boson Hamiltonian play in modeling decoherence in quantum systems?
• RQ3 Can decoherence be suppressed by adjusting control parameters in the system Hamiltonian?
• RQ4 What are the implications of the stochastic limit approximation for long-time dynamics in open quantum systems?
• RQ5 How can quantum computing models like the quantum Turing machine and quantum circuits be stabilized against environmental noise?

Key findings

• The stochastic limit approximation reveals that decoherence can be significantly reduced when system parameters are appropriately tuned.
• The analysis shows that the decay rate of quantum coherence depends on the spectral properties of the environment and the coupling strength.
• Control of the system's energy level spacing and coupling to bath modes can suppress decoherence effects.
• The proposed method provides a theoretical pathway to stabilize quantum states in quantum circuits and quantum Turing machines.
• The spin-boson model serves as a valid framework for understanding and mitigating decoherence in realistic quantum computing architectures.
• Parameter control offers a feasible strategy to extend coherence times in quantum systems, even in the presence of environmental noise.