Quantum computing with LDPC codes

Errors in quantum computers are unavoidable. Controlling quantum bits (qubits)
stored in individual electrons or photons is significantly more challenging than
controlling bits in traditional computers. Direct use of physical qubits typically
only yields very short lifetimes such that information is lost before any
meaningful computation can be executed. Fortunately, we can use quantum
error 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 complete
a computation. Although, the longer we extend the lifetime the more physical
qubits will be needed per logical qubit. Maybe hundreds or thousands of physical
qubits will be needed per logical qubit. Current quantum hardware supports
fewer than 50 qubits so this cost is substantial. Therefore, a fundamental
rethinking of how we design quantum computers is a pressing near-future issue.
The most efficient codes in conventional information technology systems are
called low-density parity check codes and are used in all Wi-Fi networks and
mobile communication networks. This theoretical PhD project will explore the
different ways that these highly efficient classical techniques can be converted
into highly efficient quantum codes.