Measurement-only topological quantum computation without forced measurements

Abstract

We investigate the measurement-only topological quantum computation (MOTQC) approach proposed by Bonderson et al (2008 Phys. Rev. Lett. 101 010501) where the braiding operation is shown to be equivalent to a series of topological charge 'forced measurements' of anyons. In a forced measurement, the charge measurement is forced to yield the desired outcome (e.g. charge 0) via repeatedly measuring charges in different bases. This is a probabilistic process with a certain success probability for each trial. In practice, the number of measurements needed will vary from run to run. We show that such an uncertainty associated with forced measurements can be removed by simulating the braiding operation using a fixed number of three measurements supplemented by a correction operator. Furthermore, we demonstrate that in practice we can avoid applying the correction operator in hardware by implementing it in software. Our findings greatly simplify the MOTQC proposal and only require the capability of performing charge measurements to implement topologically protected transformations generated by braiding exchanges without physically moving anyons.

Poking Holes and Cutting Corners to Achieve Clifford Gates with the Surface Code

“…We use this entangling operation to perform a controlled-not gate between qubits encoded with twist defects. We point out that this scheme is much of a likeness to a measurement-only topological quantum computation scheme [39,40,65,69,[86][87][88] presented by Bravyi in Ref. [69].…”

Optimizing Clifford gate generation for measurement-only topological quantum computation with Majorana zero modes

“…when using Parafendleyons (parafermion zero modes), as was applied for measurement-only braiding transformations in Ref. [26]. The tracking methods allow for the use of fewer physical measurement operations and makes the sequence of measurement operations used for topological gate operations completely deterministic.…”

“…The procrastination and tracking methods can only be applied when the measurement outcomes correspond to fusion channels that are Abelian [26,29], e.g. for Ising anyons, MZMs, and Parafendleyons (parafermionic zero modes).…”

Holonomic implementation of CNOT gate on topological Majorana qubits

“…Importantly, the braiding of a single pair of MZMs can be realized in several ways, which are all equivalent to a physical exchange of the two non-Abelian anyons [24][25][26][27][28][29][30]. Indeed, by considering the presence of additional (hybridized) ancilla Majoranas, we can perform braiding by properly tuning pair-wise couplings between different MZMs [31,32], or by performing sequential projective parity measurements [8,[33][34][35][36][37][38]. Non-Clifford operations such as the T gate cannot be realized via Majorana braiding and necessarily rely on implementations that are not topologically protected and require additional error correction schemes such as magic state distillation [23,39].…”