[Paper Review] Quantum information processing in semiconductor nanostructures

John H. Reina, Luis Quiroga+1 more|arXiv (Cornell University)|Sep 8, 2000

Semiconductor Quantum Structures and Devices1 references3 citations

TL;DR

This paper proposes two quantum information processing schemes in semiconductor quantum dots: (1) all-optical generation of maximally entangled Bell and GHZ states using controlled light pulses in coupled quantum dots, enabling solid-state quantum teleportation; and (2) a nuclear magnetic resonance (NMR)-based quantum switch using electron-nuclear hyperfine coupling tuned via external magnetic fields to implement fault-tolerant quantum logic gates with long decoherence times. The key contribution is demonstrating feasible, coherent control of qubits in solid-state systems under realistic decoherence conditions.

ABSTRACT

A major question for condensed matter physics is whether a solid-state quantum computer can ever be built. Here we discuss two different schemes for quantum information processing using semiconductor nanostructures. First, we show how optically driven coupled quantum dots can be used to prepare maximally entangled Bell and Greenberger-Horne-Zeilinger states by varying the strength and duration of selective light pulses. The setup allows us to perform an all-optical generation of the quantum teleportation of an excitonic state in an array of coupled quantum dots. Second, we give a proposal for reliable implementation of quantum logic gates and long decoherence times in a quantum dots system based on nuclear magnetic resonance (NMR), where the nuclear resonance is controlled by the ground state transitions of few-electron QDs in an external magnetic field. The dynamical evolution of these systems in the presence of environmentally-induced decoherence effects is also discussed.

Motivation & Objective

• To develop a scalable, solid-state platform for quantum information processing using semiconductor nanostructures.
• To enable the generation and control of maximally entangled excitonic states (Bell and GHZ) via optically driven coupled quantum dots.
• To propose a reliable, low-decoherence mechanism for quantum logic gates using nuclear spin qubits in quantum dots via tunable hyperfine coupling.
• To demonstrate that environmental decoherence, particularly from phonons, does not necessarily destroy quantum coherence in driven quantum dot systems.
• To establish a solid-state NMR-based quantum switch capable of performing single-qubit rotations and C-NOT gates with high fidelity.

Proposed method

• Use of selective light pulses to drive coherent Rabi oscillations between electronic states in coupled quantum dots, enabling preparation of Bell and GHZ states.
• Employment of pseudo-spin operators and density matrix formalism to model the dynamics of entangled excitonic states in two- and three-dot systems.
• Application of time-dependent perturbation theory to analyze the unitary evolution of the system under external optical control.
• Utilization of electron ground-state transitions in few-electron quantum dots under an external magnetic field to tune the hyperfine coupling to a nuclear spin-1/2 impurity.
• Design of a quantum switch where the nuclear resonance frequency is controlled by changing the magnetic field, enabling adiabatic tuning of the electron-nuclear interaction.
• Adiabatic gating protocol to ensure that electron system relaxes to a new ground state without disturbing the nuclear spin qubit, preserving coherence.

Experimental results

Research questions

• RQ1 Can maximally entangled Bell and GHZ states be generated in a solid-state system using only optical control?
• RQ2 Can quantum teleportation of excitonic states be realized in an array of coupled quantum dots via all-optical means?
• RQ3 Can nuclear spin qubits in quantum dots be used to implement fault-tolerant quantum logic gates with long decoherence times?
• RQ4 How does phonon-induced decoherence affect the coherence of optically driven excitonic states in quantum dots?
• RQ5 Can the nuclear magnetic resonance frequency in a quantum dot be tuned via external magnetic fields by manipulating electron ground-state transitions?

Key findings

• Maximally entangled Bell and GHZ states can be generated in coupled quantum dots using selective light pulses, with fidelity dependent on pulse duration and strength.
• The proposed scheme enables all-optical quantum teleportation of excitonic states in a solid-state array of quantum dots.
• Phonon-induced decoherence does not necessarily destroy coherence in the driven system, as long as the gating time is sufficiently long compared to the inverse energy splitting.
• The lower limit for the gating time τg is estimated to be ~1 ps, with a decoherence time τdec ≈ 10^9 τg, supporting fault-tolerant quantum computation.
• The number of operations possible before decoherence is estimated at ~10^9, exceeding the 10^4–10^5 threshold required for fault-tolerant quantum error correction.
• The NMR-based quantum switch enables single-qubit rotations and C-NOT gates via adiabatic tuning of the hyperfine coupling through magnetic field changes, with electron relaxation being compatible with nuclear spin coherence.