[Paper Review] Quantum Computing with Majorana Kramers Pairs

Constantin Schrade, Liang Fu|arXiv (Cornell University)|Jul 17, 2018

Topological Materials and Phenomena4 citations

TL;DR

This paper proposes the Majorana Kramers Qubit (MKQ), a topological qubit formed by spatially separated Majorana Kramers pairs in a time-reversal-invariant topological superconductor island. By coupling these pairs to conventional superconducting leads, the authors demonstrate universal quantum gate operations—including Clifford gates and a $π/8$ gate—while leveraging the superconducting gap of the leads as an additional protection layer against quasiparticle poisoning, enabling enhanced coherence times without requiring magnetic fields.

ABSTRACT

We propose a universal gate set acting on a qubit formed by the degenerate ground states of a Coulomb-blockaded time-reversal invariant topological superconductor island with spatially separated Majorana Kramers pairs: the "Majorana Kramers Qubit". All gate operations are implemented by coupling the Majorana Kramers pairs to conventional superconducting leads. Interestingly, in such an all-superconducting device, the energy gap of the leads provides another layer of protection from quasiparticle poisoning independent of the island charging energy. Moreover, the absence of strong magnetic fields - which typically reduce the superconducting gap size of the island - suggests a unique robustness of our qubit to quasiparticle poisoning due to thermal excitations. Consequently, the Majorana Kramers Qubit should benefit from prolonged coherence times and may provide an alternative route to a Majorana-based quantum computer.

Motivation & Objective

• To address the open question of whether Majorana Kramers pairs (MKPs) can be used for practical quantum computation.
• To propose a universal gate set for a qubit based on degenerate ground states of a Coulomb-blockaded time-reversal-invariant topological superconductor island.
• To demonstrate that quasiparticle poisoning is suppressed by both the island charging energy and the superconducting gap of the leads, enabling longer coherence times.
• To eliminate the need for external magnetic fields, which typically reduce the superconducting gap and degrade qubit performance.

Proposed method

• The MKQ is realized in a U-shaped, mesoscopic time-reversal-invariant topological superconductor (TRI TSC) island hosting spatially separated Majorana Kramers pairs.
• Two conventional superconducting leads are weakly coupled to the left and right ends of the island, enabling tunnelling operations via gate-tunable tunnel couplings.
• Single-qubit Clifford gates are implemented via a measurement-based quantum computing approach using tunnelling processes between the leads and the MKPs.
• A $π/8$ gate and a two-qubit entangling gate are realized by pulsing the tunnel couplings between the leads and the MKPs, enabling universal quantum computation.
• The system leverages the superconducting gap of the leads as an additional protection layer against quasiparticle poisoning, independent of the island's charging energy.
• Theoretical analysis confirms that the effective Hamiltonian supports universal gate operations through second-order perturbation theory involving Cooper pair splitting and Majorana fermion exchange processes.

Experimental results

Research questions

• RQ1 Can Majorana Kramers pairs in a time-reversal-invariant topological superconductor support a universal set of quantum gates without external magnetic fields?
• RQ2 How can quasiparticle poisoning be suppressed in Majorana-based qubits beyond the standard charging energy protection?
• RQ3 What role does the superconducting gap of the conventional leads play in protecting the qubit from quasiparticle excitations?
• RQ4 Can universal quantum computation be achieved using only tunnel coupling pulses between superconducting leads and Majorana Kramers pairs?
• RQ5 How does the absence of magnetic fields affect the stability and coherence of the topological qubit?

Key findings

• The Majorana Kramers Qubit (MKQ) is formed by the two-fold degenerate ground state of a Coulomb-blockaded TRI TSC island hosting spatially separated Majorana Kramers pairs.
• Universal quantum computation is achieved through a combination of measurement-based Clifford gates and pulsed tunnel couplings to implement a $π/8$ gate and a two-MKQ entangling gate.
• The superconducting gap of the leads provides an additional, independent layer of protection against quasiparticle poisoning, beyond the island's charging energy.
• Quasiparticle poisoning from thermal excitations is strongly suppressed because the TRI TSC island's superconducting gap is not reduced by magnetic fields, unlike in TRS-breaking systems.
• Theoretical analysis confirms that second-order processes involving Cooper pair splitting and Majorana exchange generate the required effective Hamiltonian terms for universal gate operations.
• The system is robust against fermionic corner modes due to the long vertical segments of the U-shaped island, ensuring the MKPs remain protected by time-reversal symmetry.