Designing and Simulating Quantum LDPC Codes for Superconducting Qubits

Sammanfattning

Quantum computers are predicted to be able to solve problems impossible for a classical supercomputer. The quantum computers that we have now are however very sensitive to noise from their environment, which makes their results unreliable. This necessitates quantum error correction, the main topic of this thesis. Specifically, this thesis concerns quantum Low Density Parity Check (qLDPC) codes for superconducting qubits. Superconducting qubits are one of the ways to implement a quantum computer, used for example by Google and IBM. qLDPC codes are error-correcting codes whose classical counterpart is used in 5G and Wi-Fi, among other applications. They are a type of stabilizer code, meaning that the quantum state we wish to store is subjected to a sequence of non-destructive measurements, whose results can tell if an error has occurred or not. Explaining this more in-depth is the bulk of this thesis. The qLDPC code chosen as most fitting for superconducting qubits is the bivariate bicycle (BB) code. In it, each qubit interacts with its four nearest neighbours as well as with two qubits further away, which allows for fewer qubits to be needed for the same error-correcting performance. The results were collected in the following order: First, different decoders (classical algorithms that determine the most likely error based on the results of the non-destructive measurements mentioned above) are compared to determine which performs best. That turned out to be relay Belief Propagation (BP-relay), which is a version of standard BP that uses information from failed decoding rounds to initialize new rounds. BP-relay is then used to compare BB codes with the surface code, another error-correcting code, with the result that the BB code outperforms the surface code. In addition, the feasibility of implementing BB codes on current hardware is explored, with the error rates of IBM's latest chip showing promising performance, even for much worse non-local connections. This implies that qLDPC codes could be used in the near term to increase the fault tolerance of current quantum computers.