Charge qubits and limitations of electrostatic quantum gates

TL;DR

This paper analyzes the limitations of electrostatic quantum gates in charge qubits, revealing that while single gates are feasible, implementing full control often compromises the qubit's two-level system, requiring additional tunable parameters.

Contribution

It demonstrates that electrostatic interactions alone are insufficient for complete qubit control without system modifications, highlighting fundamental limitations in electrostatic quantum gate design.

Findings

Single quantum gate realization is straightforward.

Second gate implementation compromises the qubit’s two-level system.

Full control requires tunable tunneling or magnetic fields.

Abstract

We investigate the characteristics of purely electrostatic interactions with external gates in constructing full single qubit manipulations. The quantum bit is naturally encoded in the spatial wave function of the electron system. Single-electron{transistor arrays based on quantum dots or insulating interfaces typically allow for electrostatic controls where the inter-island tunneling is considered constant, e.g. determined by the thickness of an insulating layer. A representative array of 3x3 quantum dots with two mobile electrons is analyzed using a Hubbard Hamiltonian and a capacitance matrix formalism. Our study shows that it is easy to realize the first quantum gate for single qubit operations, but that a second quantum gate only comes at the cost of compromising the low-energy two-level system needed to encode the qubit. We use perturbative arguments and the Feshbach formalism to show that the compromising of the two-level system is a rather general feature for electrostatically interacting qubits and is not just related to the specific details of the system chosen. We show further that full implementation requires tunable tunneling or external magnetic fields.