Universal Quantum Computation using Exchange Interactions and Measurements of Single- and Two-Spin Observables

David Peter Divincenzo, Dave Bacon, Julia Kempe +2 more

Lian-Ao Wu, Daniel A. Lidar

We show how to construct a universal set of quantum logic gates using control over exchange interactions and single- and two-spin measurements only. Single-spin unitary operations are teleported between neighboring spins instead of being executed directly, thus potentially eliminating a major difficulty in the construction of several of the most promising proposals for solid-state quantum computation, such as spin-coupled quantum dots, donor-atom nuclear spins in silicon, and electrons on helium. Contrary to previous proposals dealing with this difficulty, our scheme requires no encoding redundancy. We also discuss an application to superconducting phase qubits.

S. D. Barrett, Thomas M. Stace

We propose and analyze a method for single shot measurement of the total spin of a two electron system in a coupled quantum dot or donor impurity structure, which can be used for readout in a quantum computer. The spin can be inferred by observing spin-dependent fluctuations of charge between the two sites, via a nearby electrometer. Realistic experimental parameters indicate that the fidelity of the measurement can be larger than 0.999 with existing or near-future technology. We also describe how our scheme can be used to implement various one- and two-qubit measurements, and hence to implement universal quantum computation.

David Peter Divincenzo, Guido Burkard, Daniel Loss +1 more

Junya Kasahara

Niklas Rohling, Guido Burkard

We investigate a two-electron double quantum dot with both spin and valley degrees of freedom as they occur in graphene, carbon nanotubes or silicon and regard the 16-dimensional space with one electron per dot as a four-qubit logic space. In the spin-only case, it is well known that the exchange coupling between the dots combined with arbitrary single-qubit operations is sufficient for universal quantum computation. The presence of valley degeneracy in the electronic band structure alters the form of the exchange coupling and, in general, leads to spin–valley entanglement. Here, we show that universal quantum computation can still be performed by exchange interaction and single-qubit gates in the presence of an additional (valley) degree of freedom. We present an explicit pulse sequence for a spin-only controlled-NOT consisting of the generalized exchange coupling and single-electron spin and valley rotations. We also propose state preparations and projective measurements with the use of adiabatic transitions between states with (1,1) and (0,2) charge distributions similar to the spin-only case, but with the additional requirement of controlling the spin and valley Zeeman energies by an external magnetic field. Finally, we demonstrate a universal two-qubit gate between a spin and a valley qubit, allowing universal gate operations on the combined spin and valley quantum register.