Universal quantum computation with hybrid spin-Majorana qubits

Abstract

We theoretically propose a set of universal quantum gates acting on a hybrid qubit formed by coupling a quantum-dot spin qubit and Majorana fermion qubit. First, we consider a quantum dot that is tunnel coupled to two topological superconductors. The effective spin-Majorana exchange facilitates a hybrid CNOT gate for which either qubit can be the control or target. The second setup is a modular scalable network of topological superconductors and quantum dots. As a result of the exchange interaction between adjacent spin qubits, a CNOT gate is implemented that acts on neighboring Majorana qubits and eliminates the necessity of interqubit braiding. In both setups, the spin-Majorana exchange interaction allows for a phase gate, acting on either the spin or the Majorana qubit, and for a SWAP or hybrid SWAP gate which is sufficient for universal quantum computation without projective measurements.

Spin-dependent coupling between quantum dots and topological quantum wires

“…Alternatively, if the relative positions are fixed or the SOI length is smaller than the experimental precision, the spin dependence cannot be adjusted and thus may be a source of error. This is especially problematic when combining braiding and readout of MBS qubits using quantum dots [19]. That is, after a braiding operation, the distance between the MBS and quantum dot must be brought back to a precise position.…”

“…However, these properties that make them a desirable element for information storage make readout problematic. Nonetheless, there have been several schemes for storage, manipulation, and readout of topological quantum computers using MBSs modeled as a Kitaev chain [13], which is largely phenomenological [14][15][16][17][18][19][20][21][22]. A theoretical analysis of physically realized MBSs for quantum information storage has yet to be rigorously studied; the details of which, as we show in this paper, are critical for quantum operations.…”

“…Following Ref. [19], we find that a Schrieffer-Wolff transformation yields [48], to second order in tunneling,…”

“…If a quantum dot [26,27], which can be electrically defined in experiments within the same quantum wire, is brought into proximity of these Majorana end states, the charge or spin coupling can be used to readout the parity of the quantum wire junction; such a scheme was proposed in Ref. [19] wherein MBSs, described by a Kitaev chain, were coupled to a spinful single-level quantum dot and later adapted to a spinless single-level dot in Refs. [21,22].…”

“…In the presence of two MBSs, the spin-dependent tunneling induces an effective magnetic field on the dot which changes direction when the occupation of the nonlocal fermion, formed from the two MBSs, changes parity. Thus, this setup allows the readout of MBS qubits via reading out the spin of the electron on the quantum dot [19].…”