Quantum computing with LDPC codes

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Errors in quantum computers are unavoidable. Controlling quantum bits (qubits)stored in individual electrons or photons is significantly more challenging thancontrolling bits in traditional computers. Direct use of physical qubits typicallyonly yields very short lifetimes such that information is lost before anymeaningful computation can be executed. Fortunately, we can use quantumerror correcting codes to make a logical qubit that is protected against errors.This approach allows us to extend the lifetime as long as is needed to completea computation. Although, the longer we extend the lifetime the more physicalqubits will be needed per logical qubit. Maybe hundreds or thousands of physicalqubits will be needed per logical qubit. Current quantum hardware supportsfewer than 50 qubits so this cost is substantial. Therefore, a fundamentalrethinking of how we design quantum computers is a pressing near-future issue.The most efficient codes in conventional information technology systems arecalled low-density parity check codes and are used in all Wi-Fi networks andmobile communication networks. This theoretical PhD project will explore thedifferent ways that these highly efficient classical techniques can be convertedinto highly efficient quantum codes.