Quantum computing with an electron spin ensemble (0903.3506v2)

Abstract: We propose to encode a register of quantum bits in different collective electron spin wave excitations in a solid medium. Coupling to spins is enabled by locating them in the vicinity of a superconducting transmission line cavity, and making use of their strong collective coupling to the quantized radiation field. The transformation between different spin waves is achieved by applying gradient magnetic fields across the sample, while a Cooper Pair Box, resonant with the cavity field, may be used to carry out one- and two-qubit gate operations.

Quantum Computing with an Electron Spin Ensemble

This paper explores a novel approach to quantum computing using a hybrid system that employs an ensemble of electron spins coupled to a superconducting transmission line cavity. The primary focus is on encoding quantum bits, or qubits, within collective electron spin wave excitations rather than relying on conventional single-ion or single-atom systems.

Theoretical Framework and Experimental Setup

The authors propose encoding qubits in different spatial modes of excitation within a solid-state electron spin ensemble, comprising approximately $10^{10} - 10^{12}$ spins. These spins are positioned in proximity to a superconducting transmission line cavity, enabling strong collective coupling with the quantized radiation field. The transformation between different spin waves is achieved through the application of gradient magnetic fields, allowing the controlled manipulation of the qubits. A Cooper Pair Box, resonant with the cavity field, facilitates one- and two-qubit gate operations.

The system's physical configuration includes a superconducting transmission line cavity integrated with a transmon Cooper Pair Box (CPB). This setup allows for efficient coupling of electron spins, enabling collective modes to interact effectively with the cavity field. The average coupling strength is characterized by $\bar{g} \approx 2\pi \times 20 \, \text{Hz}$, with the collective coupling enhanced by a factor of $\sqrt{N}$, resulting in an effective coupling frequency of $\sim 2\pi \times 6 \, \text{MHz}$.

Key Results and Observations

• Mode Independence and Coupling: One of the significant results is the demonstration that different spatial modes, identified by their wave numbers $k$, act as independent harmonic oscillators. This independence is crucial for using the ensemble to store multiple qubits reliably. By applying magnetic field gradients, these modes can be addressed and manipulated without disturbing the others.
• High Coherence Time Materials: The paper identifies materials like phosphorus-doped silicon and endohedral fullerene (N@C$_{60}$) as potential candidates for the spin ensemble. These materials exhibit long spin coherence times, enhancing the viability of storing quantum information stably.
• Practical Quantum Gates: The combination of the spin ensemble with a Cooper Pair Box allows the implementation of both classical and quantum two-qubit gates. The authors detail methods for qubit initialization, gate operations, and readout, demonstrating the practical potential of this approach.

Implications and Future Directions

This hybrid quantum computing approach offers promising implications for scaling up quantum computers. The ability to hold substantial numbers of qubits within a single ensemble, combined with the accessibility of these qubits via applied gradients, positions the setup as a potentially scalable quantum computing framework.

Future research might focus on addressing and mitigating potential errors related to thermal excitations and dipole-dipole interactions within the spin ensemble. Investigating more robust materials with longer coherence times and exploring enhanced cavity designs could further optimize performance. There is also room to refine the techniques used to ensure the independence of collective modes across varying doped geometries.

In conclusion, the paper provides a comprehensive design for a quantum register capable of efficiently storing and processing quantum information at a scale suitable for further development toward practical quantum computational devices. This indicates a clear path forward in the exploration and realization of feasible quantum computing technologies leveraging electron spin ensembles.