Majorana fermions arising in superconducting nanowires are of interest both for fundamental reasons and due to their potential use as building blocks for a topological quantum computer. While recent experiments have reported strong evidence of Majorana fermions in the form of occupation of a zero-energy fermionic mode, there is still disagreement about whether the observed data can be explained by other mechanisms. Furthermore, to be useful for quantum computation, the fermionic parities of zero-energy modes must be measured with high fidelity. In this thesis, we apply a quantum information protocol known as self-testing to a system of Majorana fermions. A self-testing protocol is a statistical test for certifying a quantum state and a set of measurement operators from experimentally determined expectation values, under minimal physical assumptions. Such a test treats the system as a black-box and relies only on the distributions of measurement outcomes given device settings. For the protocol described in this thesis, if the test is passed, then a set of measurements that ideally are of fermionic parities are certified to have the exact anticommutation relations as determined by the anticommutativity of Majorana fermion operators. The protocol is robust in the sense that bounds on the state and operator fidelities can still be established in the presence of small experimental imperfections. Finally, a rigorous statistical analysis is used to derive a confidence interval for the certified fidelities given a finite experimental data set.Majorana fermions arising in superconducting nanowires are of interest both for fundamental reasons and due to their potential use as building blocks for a topological quantum computer. While recent experiments have reported strong evidence of Majorana fermions in the form of occupation of a zero-energy fermionic mode, there is still disagreement about whether the observed data can be explained by other mechanisms. Furthermore, to be useful for quantum computation, the fermionic parities of zero-energy modes must be measured with high fidelity. In this thesis, we apply a quantum information protocol known as self-testing to a system of Majorana fermions. A self-testing protocol is a statistical test for certifying a quantum state and a set of measurement operators from experimentally determined expectation values, under minimal physical assumptions. Such a test treats the system as a black-box and relies only on the distributions of measurement outcomes given device settings. For the protocol described in this thesis, if the test is passed, then a set of measurements that ideally are of fermionic parities are certified to have the exact anticommutation relations as determined by the anticommutativity of Majorana fermion operators. The protocol is robust in the sense that bounds on the state and operator fidelities can still be established in the presence of small experimental imperfections. Finally, a rigorous statistical analysis is used to derive a confidence interval for the certified fidelities given a finite experimental data set.

Jan 1, 20190 citations

Quantum Engineering of Majorana Fermions

Dirk K. Morr

Bulletin of the American Physical SocietyMar 8, 20192 citations

High-fidelity realisation of CNOT gate in Majorana-based optical platform

Jia-Kun Li, Kai Sun, Ze-Yan Hao +7 more

We present the experimental realisation of a robust CNOT quantum gate using Majorana zero modes simulated on a photonic platform. Three Kitaev chains supporting Majorana zero modes at their endpoints are used to encode two logical qubits, and both intra-chain and inter-chain braiding operations are performed to implement the CNOT gate. While the topological encoding of quantum information in Majorana fermions does not offer full topological protection in our non-interacting photonic setting, it nevertheless exhibits a natural resilience to the dominant noise and decoherence effects present in the experiment. Consequently, the fidelity of the CNOT gate is significantly enhanced, surpassing 0.992 and addressing a key limitation in the path toward scalable quantum computation. These results represent a major advancement in topological quantum computing with Majorana fermions and underscore the potential of photonic platforms for realising high-fidelity quantum gates.We present the experimental realisation of a robust CNOT quantum gate using Majorana zero modes simulated on a photonic platform. Three Kitaev chains supporting Majorana zero modes at their endpoints are used to encode two logical qubits, and both intra-chain and inter-chain braiding operations are performed to implement the CNOT gate. While the topological encoding of quantum information in Majorana fermions does not offer full topological protection in our non-interacting photonic setting, it nevertheless exhibits a natural resilience to the dominant noise and decoherence effects present in the experiment. Consequently, the fidelity of the CNOT gate is significantly enhanced, surpassing 0.992 and addressing a key limitation in the path toward scalable quantum computation. These results represent a major advancement in topological quantum computing with Majorana fermions and underscore the potential of photonic platforms for realising high-fidelity quantum gates.

arXiv:2508.14641Aug 20, 20250 citations

Certified quantum measurement of Majorana fermions

Abu Ashik Irfan, Karl Mayer, Gerardo Ortíz +1 more

We present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We show that observing a set of ideal measurement statistics implies anticommutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of the state and measurement operators that are linear in the errors. We propose to analyze experimental outcomes in terms of a contextuality witness $W$ , which satisfies $\ensuremath{\langle}W\ensuremath{\rangle}\ensuremath{\le}3$ for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value $\ensuremath{\langle}W\ensuremath{\rangle}=5$ indicates the degree of confidence in the detection of Majorana fermions.We present a quantum self-testing protocol to certify measurements of fermion parity involving Majorana fermion modes. We show that observing a set of ideal measurement statistics implies anticommutativity of the implemented Majorana fermion parity operators, a necessary prerequisite for Majorana detection. Our protocol is robust to experimental errors. We obtain lower bounds on the fidelities of the state and measurement operators that are linear in the errors. We propose to analyze experimental outcomes in terms of a contextuality witness $W$, which satisfies $\ensuremath{\langle}W\ensuremath{\rangle}\ensuremath{\le}3$ for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value $\ensuremath{\langle}W\ensuremath{\rangle}=5$ indicates the degree of confidence in the detection of Majorana fermions.

arXiv:1904.12207Physical Review AMar 12, 202014 citations

W

, which satisfies $\ensuremath{\langle}W\ensuremath{\rangle}\ensuremath{\le}3$ for any classical probabilistic model of the data. A violation of the inequality witnesses quantum contextuality, and the closeness to the maximum ideal value $\ensuremath{\langle}W\ensuremath{\rangle}=5$ indicates the degree of confidence in the detection of Majorana fermions.