Holonomic Quantum Computation with Electron Spins in Quantum Dots

Abstract

With the help of the spin-orbit interaction, we propose a scheme to perform holonomic single qubit gates on the electron spin confined to a quantum dot. The manipulation is done in the absence (or presence) of an applied magnetic field. By adiabatic changing the position of the confinement potential, one can rotate the spin state of the electron around the Bloch sphere in semiconductor heterostructures. The dynamics of the system is equivalent to employing an effective non-Abelian gauge potential whose structure depends on the type of the spin-orbit interaction. As an example, we find an analytic expression for the electron spin dynamics when the dot is moved around a circular path (with radius R) on the two dimensional electron gas (2DEG), and show that all single qubit gates can be realized by tuning the radius and orientation of the circular paths. Moreover, using the Heisenberg exchange interaction, we demonstrate how one can generate two-qubit gates by bringing two quantum dots near each other, yielding a scalable scheme to perform quantum computing on arbitrary N qubits. This proposal shows a way of realizing holonomic quantum computers in solid-state systems.

References in corpus (8)

• Measurement-based quantum computation
• Orbital mechanisms of electron spin manipulation by an electric field
• Electric Dipole Spin Resonance for Heavy Holes in Quantum Dots
• Spin-Orbit Mediated Control of Spin Qubits
• Universal set of quantum gates for double-dot spin qubits with fixed interdot coupling
• Electric Dipole Induced Spin Resonance in Disordered Semiconductors
• Geometric phases in semiconductor spin qubits: Manipulations and decoherence
• Measurement, control, and decay of quantum-dot spins

Cited by in corpus (30)

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• Coherent long-distance displacement of individual electron spins
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• On the stability of quantum holonomic gates
• Exact Nonadiabatic Holonomic Transformations of Spin-Orbit Qubits
• Fast shuttling of a particle under weak spring-constant noise of the moving trap
• All-electric qubit control in heavy hole quantum dots via non-Abelian geometric phases
• Non-adiabatically driven electron in quantum wire with spin-orbit interaction
• Nonadiabatic Holonomic Quantum Computation and Its Optimal Control
• Arbitrary qubit transformations on tuneable Rashba rings
• Manipulation of two spin qubits in a double quantum dot using an electric field
• Exact analysis of gate noise effects on non-adiabatic transformations of spin-orbit qubits
• Exact spin-orbit qubit manipulation
• Protocols to measure the non-Abelian Berry phase by pumping a spin qubit through a quantum-dot loop
• Stellar Representation of Grassmannians
• Thermal effects on a nonadiabatic spin-flip protocol of spin-orbit qubits
• A simpel and versatile cold-atom simulator of non-Abelian gauge potentials
• Fast electron spin flips via strong subcycle electric excitation
• Longitudinal coupling between electrically driven spin-qubits and a resonator
• Berry-phase induced entanglement of hole-spin qubits in a microwave cavity
• Qubit transformations on Rashba ring with periodic potential
• Suppression of Hyperfine Dephasing by Spatial Exchange of Double Quantum Dots
• Effects of geometry on spin-orbit Kramers states in semiconducting nanorings
• Solitonic Andreev spin qubits from Andreev states in Corbino Josephson junctions
• Noise Effects on the Wilczek-Zee Geometric Phase
• Geometric and holonomic quantum computation
• Entanglement And Non-Trivial Topologies