Pseudospin Quantum Computation in Semiconductor Nanostructures

We theoretically show that spontaneously interlayer-coherent bilayer quantum Hall droplets should allow robust and fault-tolerant pseudospin quantum computation in semiconductor nanostructures with voltage-tuned external gates providing qubit control and a quantum Ising Hamiltonian providing qubit entanglement. Using a spin-boson model, we estimate decoherence to be small $(\sim {10}^{-5})$.

Figure 1

Schematic representation of two bilayer quantum Hall droplets separated by a center-to-center distance $R$. Individual droplets are vertically separated by a distance $d$. The left set of droplets has one extra electron in the top layer giving it a net pseudospin, $S_z=+1/2$. The right set of droplets has pseudospin $S_z=-1/2$. This configuration corresponds to the basis state $\mid \uparrow \downarrow ⟩$. ${\Delta }_z^1$ and ${\Delta }_z^2$ are the relative bias voltages between the layers in the left and right set of droplets, respectively.

Figure 2

The exchange splitting, $J$, between the pseudospin singlet and triplet states of a pair of bilayer quantum Hall droplets versus lateral separation $R$. $J$ is evaluated for systems with a total of 6, 10, and 14 electrons. The vertical separation between droplets is $d=a$. The droplet diameter is below $7.5a$ for each curve. ${\epsilon }^{\prime }$ is the dielectric constant between bilayer quantum Hall droplets.

Figure 3

The probability, $T$, that a perturbation of the electron density will excite a bilayer quantum Hall droplet from the ground, maximum density droplet state to an edge state as a function of wave vector, $k$. The vertical separation between droplets is $d=a$. The particle number, $N$, is increased from 1 to 9, showing a dramatic decrease in $T$.