Project work by masters students supervised by James Wootton at the University of Basel and IBM Quantum.
Soft Information Quantum Error Correction
Maurice Hanisch
Implementing and Benchmarking a Floquet Code on Superconducting Hardware
Ian Hesner
Quantum Error Correction Benchmark and Diagnostics
Milan Liepelt
With the improvements in the quality and size of quantum computers, the point where quantum error correction (QEC) can be the key-enabling technology for specific real- world applications comes closer. Quantum computing platforms differ in their physical implementation and architectures and have therefore different strengths and weaknesses, which can make QEC more or less effective. To assess the potential that can be reached with QEC reliably, we present a method for quantum error correction diagnostics and benchmarking. The QEC benchmark allows to assess and compare how well a quantum computer retains useful quantum information over time and how well this number scales by adding more qubits to the QEC system. The developed method is based on the anisotropic repetition code (ARC). This codes’ unique property is the combination of the simplicity of a standard repetition code, while encoding neighboring data qubits in different bases, which is a special property of more advanced QEC codes like the Surface code, and might be an additional source of noise. This code allows further data to be gathered for the so-called micro diagnostics/benchmarks to assess a quantum computer down to single qubit properties. Different diagnostic methods based on syndrome data were developed to detect erroneous qubits and leakage during QEC runtime. Such in- formation can be useful for quantum circuit schedulers to optimize which qubits to run an algorithm best, and QEC decoders can also greatly benefit from this information to improve accuracy. Finally, a protocol is proposed under which the ARC might qualify to be taken up in application-oriented quantum computing benchmarking suites.
Universal quantum computation using a hybrid quantum double model
Katharina Laubscher
We present a way to perform universal quantum computation using a hybrid quantum double model consisting of a lattice divided into two half-planes, where one is associated with the D(Z_2) quantum double model and the other one with the D(S_3) quantum double model. Logical information is stored in the D(Z_2) part of the lattice using the usual hole-pair encoding, for which we perform initial- ization processes, measurements and the full set of Clifford operations using the standard procedures. We then use our knowledge of the braiding rules of the D(S_3) quantum double model to prepare a non-stabilizer state in the D(S_3) part of the lattice, and propose a protocol to inject such a state state into the D(Z_2) phase. This allows us to perform universal quantum computation in the D(Z_2) part of the lattice, replacing the standard magic state distillation procedures by the injection of a non-stabilizer state from a foreign phase. We also discuss the reverse process, i.e. the transport of logical information from the D(Z_2) phase to the D(S_3) phase. This enables us to manipulate logical information in the D(S_3) part of the lattice, further enlarging the set of possible operations and providing even more flexibility.
Analysis of noisy gates in minimal surface codes
Andreas Peter
In order to build a useful quantum computer, the problem of noise has to be tackled. A promising way to get noise under control is the use of surface codes. The smallest useful surface code is S 17 , which we will analyse in this work. Using tensor network methods, we analyse the connection between the fidelity of the cnot-gates in a code with the performance of the code itself for one round of error correction. Two scenarios were calculated for different cnot inspired by quantum dot implementations, one starting in a product state with one measurement round and final measurement and one starting in a stabilizer state with one measurement round. For purely decoherent noise we find that the code performance can be predicted well using the channel fidelity for both scenarios. For more complicated unitary gates that approximate a cnot and are derived from floating gate implementations we find that for very small intervals of channel infidelity there is a large spread in code performance. This shows that we can not predict the performance of a surface code that uses specific entangling gates well if we only know the channel infidelity of those entangling gates.
Markus Kesselring
The quantum anonymous broadcast (QAB) is an example of an information protocol not relying on the full universal gate set. It can be carried out with gates in the Clifford group alone. This makes it an interesting candidate for the study of fault tolerant means to achieve it. Systems with a high resilience against errors, such as surface codes or Majorana zeromodes, have the flaw of not trivially having access to the whole universal gate set. We study how to implement the QAB in a variety of fault tolerant systems. In a last section, non-destructive ways to measure the charge of multiple Majorana zeromodes is discussed.
Embedded D(Z_2) Surface Codes & A decoder for imperfectly measured Planar Code
Janos Winkler
New topological error correction codes are defined using embedding techniques, where D(Z_2) Surface Codes serve as the building blocks. The properties of these new codes are thoroughly investigated and we show that they do not all share the same anyon model.
We developed a decoder under the assumption that noiseless measurement of the stabilizers is not possible. This decoder is based on the MWPM algorithm and is designed to fix errors on a Wen style planar code. The decoder was numerically tested and a threshold was obtained for two rounds of measurements, where measurement errors occurred with a probability of p m = 1%. The thresholds for the decoder were found in the range of ≈ 6% for independent noise as well as ≈ 9% for depolarized noise. Furthermore, we show that the decoder is significantly better compared to regular MWPM for very low error rates.
Fault-tolerant Error Correction of non-Abelian Anyons
Patrick Heim
In this thesis a new decoding algorithm (Weasel) was developed for the planar code and compared with other decoders (Bravyi Haah, ABCB and Expanding Diamonds). The algorithm's threshold in the qubit case is around 6%; for d=6 it is 11.5%. Error configurations that cause the decoder to fail were analyzed by applying Kruskal's algorithm to find the minimal spanning tree of errors across the 2D lattice. The scaling behaviour of these error configurations was investigated for the four decoders and the Weasel decoder was found to be competitive in that respect.
Note that, despite the title, no non-Abelian anyons get corrected in this thesis. Plans changed during the project, but changing the title would have needed too much admin.