Microsoft Technology Licensing, LLC

Zhenghan Wang

Parsa Hassan Bonderson

Michael Hartley Freedman

Chetan Vasudeo Nayak

Roman Mykolayovych Lutchyn

Matthew Benjamin Hastings

David Alexander Aasen

Alexei V Bocharov

Jeongwan Haah

Vadym Kliuchnikov

Xingshan Cui

Aspects of the disclosure include removing a faulty qubit in a quantum circuit. The faulty qubit is determined to be in the quantum circuit, the faulty qubit being associated with a plaquette having other qubits, where adjacent plaquettes are neighboring the plaquette. A route is determined to isolate the plaquette from the adjacent plaquettes. Measurements are caused to be performed on the quantum circuit for the route that isolates the plaquette having the faulty qubit and the other qubits.

Fault tolerant Hastings-Haah codes in the presence of dead qubits

A method and apparatus for performing quantum error correction using an automorphism code related to the honeycomb code. The automorphism code is based on Kramers-Wannier (KW) duality. For embodiments on a hexagonal lattice using three repeated time steps, ⅓ of the pixels are active in a given time steps. In a given time step r, a KW circuit is applied to plaquettes labeled r mod 3, transferring quantum information from the active qubits at the beginning to a new set of active qubits at the end of the time step. Each of the three plaquette types is associated with one stabilizer either given by a product of six Z operators or three X operators. The KW circuit maps the product of X operators to the product of Z operators and vice-versa. The stabilizer group of the superlattice toric code changes every round.

Quantum code with simpler pairwise checks

Certain ensembles of metapletic anyons allow for topologically protected encoding and processing of quantum information. Such processing is done by sequences of gates (circuits) drawn from a certain basis of unitary metaplectic gates. A subject unitary operator required for the desired processing can be approximated to any desired precision by a circuit that has to be effectively and efficiently synthesized on a classical computer. Synthesis methods use unitary reflection operators that can be represented either exactly or by ancilla-assisted approximation over the basis of metaplectic gates based on cost-optimizing determinations made by the synthesis algorithm.

Efficient topological compilation for metaplectic anyon model

A fusion outcome quasiparticle may be trapped in a potential well of a topological segment. The fusion outcome quasiparticle may be the product of fusion of a first quasiparticle and a second quasiparticle, where the first and the second quasiparticles are localized at ends of a topological segment. The potential well having the fusion outcome quasiparticle trapped therein and a third quasiparticle may be moved relative to each other such that the potential well and the third quasiparticle are brought toward each other. The quasiparticles may be Majorana modes of a nanowire.

Topological qubit fusion

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Zhenghan Wang