[Paper Review] Physical Implementation of Quantum Random Walks

Kia Manouchehri, Jingbo Wang|arXiv (Cornell University)|Sep 12, 2006

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This paper proposes a physical implementation of discrete-time quantum random walks using laser-excited electrons in a quantum dot, where energy levels serve as nodes and multi-photon STIRAP enables coherent quantum walk steps. Simulations confirm strong agreement with theoretical models and demonstrate modest robustness against noise and parameter variations.

ABSTRACT

Quantum random walks are shown to have non-intuitive dynamics, which make them an attractive area of study for devising quantum algorithms for well-known classical problems as well as those arising in the field of quantum computing. In this work we propose a novel scheme for the physical implementation of a discrete time quantum random walk using the laser excitations of a single electron in a quantum dot. The energy levels inside the dot represent the discrete nodes and multi-photon STIRAP processes are employed to induce the steps in the walk. The quantum dot design is tailored in such a way as to enable selective coupling of the energy levels. Our simulation results show a close agreement with the theoretical models of a quantum random walk as well as modest robustness towards noise disturbance and system parameter uncertainty.

Motivation & Objective

• To develop a scalable and physically realizable platform for implementing discrete-time quantum random walks.
• To address the challenge of realizing quantum walk dynamics in a solid-state system with controlled coherence.
• To demonstrate that quantum dot systems can support the necessary selective coupling of energy levels for quantum walk evolution.
• To evaluate the resilience of the proposed scheme against noise and parameter uncertainty in realistic conditions.

Proposed method

• Utilizes a single electron in a quantum dot, where quantized energy levels represent discrete nodes of the quantum walk.
• Employs multi-photon Stimulated Raman Adiabatic Passage (STIRAP) to coherently transfer population between energy levels, simulating the walk steps.
• Designs the quantum dot potential to enable selective coupling between specific energy levels, ensuring controlled dynamics.
• Applies adiabatic control via laser pulses to maintain coherence and minimize population leakage during walk evolution.
• Models the system using quantum optical techniques to simulate the time evolution of the quantum walk.
• Validates the implementation by comparing simulated dynamics with theoretical predictions of quantum random walks.

Experimental results

Research questions

• RQ1 Can a solid-state quantum dot system be engineered to physically realize a discrete-time quantum random walk with controllable step operations?
• RQ2 How well do the simulated dynamics of the quantum walk in the proposed system match the theoretical predictions of quantum random walks?
• RQ3 To what extent is the proposed implementation robust against noise and variations in system parameters such as laser intensity or detuning?
• RQ4 Can multi-photon STIRAP processes be effectively used to mediate coherent transitions between non-adjacent energy levels in a controlled manner?
• RQ5 What are the limitations of the scheme in terms of decoherence and fidelity under realistic experimental conditions?

Key findings

• The simulated quantum walk dynamics closely match the theoretical predictions of discrete-time quantum random walks, confirming the feasibility of the proposed scheme.
• The system exhibits modest robustness against noise disturbances, maintaining coherent evolution under perturbations.
• Parameter uncertainty in laser intensity and detuning has a limited impact on the overall fidelity of the walk evolution.
• Selective coupling between energy levels is successfully achieved through tailored quantum dot design, enabling precise control over walk steps.
• The use of multi-photon STIRAP allows for coherent, non-adiabatic population transfer between levels with high fidelity.
• The results suggest that the quantum dot platform is a viable candidate for experimental realization of quantum random walks.