[Paper Review] Robust Quantum Computation with Quantum Dots

C. Stephen Hellberg|ArXiv.org|Apr 23, 2003

Quantum Computing Algorithms and Architecture2 references3 citations

TL;DR

This paper proposes a robust quantum computation scheme using a five-quantum-dot system where qubits are encoded in the degenerate singlet ground state of four or six electrons, enabling immunity to collective and local decoherence. Universal quantum gates are implemented by tuning tunneling barriers between dots, eliminating the need for local magnetic fields, with a controlled-phase gate achievable in a single pulse via adiabatic control of tunneling rates.

ABSTRACT

Quantum computation in solid state quantum dots faces two significant challenges: Decoherence from interactions with the environment and the difficulty of generating local magnetic fields for the single qubit rotations. This paper presents a design of composite qubits to overcome both challenges. Each qubit is encoded in the degenerate ground-state of four (or six) electrons in a system of five quantum dots arranged in a two-dimensional pattern. This decoherence-free subspace is immune to both collective and local decoherence, and resists other forms of decoherence, which must raise the energy. The gate operations for universal computation are simple and physically intuitive, and are controlled by modifying the tunneling barriers between the dots--Control of local magnetic fields is not required. A controlled-phase gate can be implemented in a single pulse.

Motivation & Objective

• To address decoherence in solid-state quantum dot quantum computers by encoding qubits in a decoherence-free subspace.
• To eliminate the need for precise local magnetic fields in single-qubit rotations, which are experimentally challenging.
• To design a physically intuitive and robust gate operation mechanism using tunable tunneling barriers between quantum dots.
• To ensure universal quantum computation is achievable in a two-dimensional, scalable architecture with enhanced stability against parameter fluctuations.

Proposed method

• Encoding each qubit in the degenerate singlet ground state of four or six electrons in a five-dot square arrangement with a central dot.
• Using a Hubbard Hamiltonian model with tunable hopping amplitudes $ t_{ij} $, Coulomb repulsion $ U_i $, and chemical potential $ \mu_i $ to describe electron dynamics.
• Implementing single-qubit rotations via adiabatic tuning of tunneling rates between the central dot and outer dots, generating effective pseudospin rotations.
• Realizing a controlled-phase gate by simultaneously turning on tunneling between outer dots of adjacent qubits, preserving total singlet symmetry.
• Ensuring gate operations commute and remain within the degenerate singlet subspace to maintain decoherence protection.
• Verifying the stability and degeneracy of the ground state through exact diagonalization of the 10-dot, 8-electron Hubbard model.

Experimental results

Research questions

• RQ1 Can a five-quantum-dot architecture with a central mediator dot provide a robust, decoherence-free subspace for quantum computation?
• RQ2 Can universal quantum gates be implemented without applying local magnetic fields by tuning tunneling barriers?
• RQ3 How does the stability of the degenerate ground state respond to variations in tunneling parameters compared to a four-dot design?
• RQ4 Can a controlled-phase gate be implemented in a single pulse using only tunneling control?
• RQ5 Does the presence of an auxiliary central dot enable equal effective exchange interactions between outer dots despite geometric separation?

Key findings

• The five-dot system exhibits a doubly degenerate singlet ground state for both four- and six-electron configurations, enabling robust qubit encoding.
• The ground state remains degenerate under variation of a single tunneling rate, indicating enhanced robustness compared to the four-dot design, which splits the degeneracy under similar perturbations.
• Single-qubit operations are achieved via adiabatic tuning of tunneling rates between the central dot and outer dots, generating effective pseudospin rotations without magnetic fields.
• A controlled-phase gate is implemented in a single pulse by coherently varying six tunneling rates, with the gate matrix matching the ideal $ \bar{\mathbf{C}}_P $ operation.
• The system remains within the total singlet subspace during all gate operations, preserving immunity to collective and local decoherence.
• Exact diagonalization of the 10-dot, 8-electron system confirms the two-qubit gate has the expected diagonal form with symmetric eigenvalues, validating the gate design.