SHF: Small: Fault-Tolerant Quantum Computation in Multi-Qubit Block Codes

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Quantum computers use the peculiar properties of quantum mechanics---superposition, entanglement, and interference---to do new kinds of information processing. Large scale quantum computers could solve certain difficult problems that are beyond the ability of standard classical computers. Building quantum computers is challenging due to decoherence---quantum noise---which disrupts the needed quantum effects. The solution is fault-tolerant quantum computation: quantum information is encoded in quantum error-correcting codes, and shielded from the effects of noise. Theory shows that this will work if the decoherence rate is not too high, but most constructions require a daunting amount of overhead to do computation. The number of quantum bits (qubits) and basic operations (quantum gates) needed are multiplied by a very large factor.This research will minimize the overhead required by encoding the qubits of the computation in multi-qubit storage blocks that achieve higher rates than most codes that have been studied before. A small number of additional processor blocks will also be constructed, using a different quantum code. These different codes allow different types of quantum gates to be done efficiently, so by choosing the right combination of codes, any quantum computation can be done: such a quantum computer is called universal. Qubits are transferred between the code blocks by quantum teleportation, and are protected from decoherence at all times.This project also takes a somewhat different tack on fault tolerance. Rather than study conditions that allow quantum computations of arbitrarily large size, this research will ask, for a fixed choice of codes and a given level of decoherence, how large a quantum computation can be done. Since in reality only computations up to a certain size can actually be done, this is the most immediately practical question.This project will support two Ph.D. students at USC, and will be an active strand of research at USC's Center for Quantum Information Science and Technology (CQIST). CQIST, and the PI, support education and outreach in the Los Angeles area and elsewhere, and also organize and sponsor international conferences on quantum information science.