# Quantum bus

A quantum bus is a device which can be used to store or transfer information between independent qubits in a quantum computer, or combine two qubits into a superposition. It is the quantum analog of a classical bus.

### History

The concept was first demonstrated by researchers at Yale University and the National Institute of Standards and Technology (NIST) in 2007.[1][2][3] Prior to this experimental demonstration, the quantum bus had been described by scientists at NIST as one of the possible cornerstone building blocks in quantum computing architectures.[4]

### Mathematical Description

A quantum bus for superconducting qubits can be built with a resonance cavity. The hamiltonian for a system with qubit A, qubit B, and the resonance cavity or quantum bus connecting the two is ${\displaystyle {\hat {H}}={\hat {H}}_{r}+\sum \limits _{j=A,B}{\hat {H}}_{j}+\sum \limits _{j=A,B}hg_{i}\left({\hat {a}}^{\dagger }{\hat {\sigma }}_{-}^{j}+{\hat {a}}{\hat {\sigma }}_{\text{+}}^{j}\right)}$ where ${\displaystyle {\hat {H}}={\frac {1}{2}}\hbar \omega _{j}{\hat {\sigma }}_{+}^{j}{\hat {\sigma }}_{-}^{j}}$ is the single qubit hamiltonian, ${\displaystyle {\hat {\sigma }}_{+}^{j}{\hat {\sigma }}_{-}^{j}}$ is the raising or lowering operator for creating or destroying excitations in the ${\displaystyle j}$th qubit, and ${\displaystyle \hbar \omega _{j}}$ is controlled by the amplitude of the D.C. and radio frequency flux bias.[5]

### References

1. ^ J. Majer; J. M. Chow; J. M. Gambetta; Jens Koch; B. R. Johnson; J. A. Schreier; L. Frunzio; D. I. Schuster; A. A. Houck; A. Wallraff; A. Blais; M. H. Devoret; S. M. Girvin; R. J. Schoelkopf (2007-09-27). "Coupling superconducting qubits via a cavity bus". Nature. 449 (7161): 443–447. arXiv:0709.2135. Bibcode:2007Natur.449..443M. doi:10.1038/nature06184. PMID 17898763.
2. ^ M. A. Sillanpää; J. I. Park; R. W. Simmonds (2007-09-27). "Coherent quantum state storage and transfer between two phase qubits via a resonant cavity". Nature. 449 (7161): 438–42. arXiv:0709.2341. Bibcode:2007Natur.449..438S. doi:10.1038/nature06124. PMID 17898762.
3. ^ "All Aboard the Quantum 'Bus'". 2007-09-27. Retrieved 2008-12-12.
4. ^ G.K. Brennen; D. Song; C.J. Williams (2003). "Quantum-computer architecture using nonlocal interactions". Physical Review A. 67 (5): 050302. arXiv:quant-ph/0301012. Bibcode:2003PhRvA..67e0302B. doi:10.1103/PhysRevA.67.050302.
5. ^ Sillanpää, Mika A.; Park, Jae I.; Simmonds, Raymond W. (2007). "Coherent quantum state storage and transfer between two phase qubits via a resonant cavity". Nature. 449 (7161): 438–442. arXiv:0709.2341. Bibcode:2007Natur.449..438S. doi:10.1038/nature06124. PMID 17898762.