A major research goal in the field of quantum computation is the construction of the universal quantum computer (UQC): a device that can implement any quantum algorithm. Several theoretical schemes for implementing UQC have been developed which require different sets of resources and capabilities with varying implications for the optimum experimental implementations. The ancilla driven quantum computation scheme (ADQC) comprises two subsystems: a memory register of qubits on which information is retained and processed and an ancilla system of qubits which couple to the register. This coupling is represented in the ADQC scheme by a fixed quantum gate.By preparing the ancilla in selected states before applying this gate and then measuring it in selected measurement basis afterwards, quantum gates are enacted on the register qubits. ADQC is deterministic in that the probability of the outcome after performing the entire procedure is 1 but we have to apply corrections to the procedure at each step that depend on the probabilistic outcome of the ancilla measurement. An important resource in this model is the availability of a maximally entangling two-qubit gate between the ancilla and register qubits because if the gate is not maximally entangling,the resulting gates on the register can not be selected with stepwise determinism.It is proven in this thesis that in fact ADQC with non-maximally entangling interaction gates is universal. This requires showing that single- and two-qubit unitary gates can be effciently implemented probabilistically. We also show a relationship between the expected time of the probabilistic implementation of a gate and the ability to control the ancilla. In the ADQC model, the ancilla is controlled with single qubit unitary gates just before interacting with the register and just before measurement.We show that the increase in time caused by a loss of maximally entangling two-qubit gates can be counteracted by control over the ancilla. This needs not be the ability to perform any single qubit unitary to the ancilla but just the ability to perform a specific small finite set of operations.This is important because the resource requirements described by a scheme affect the properties of possible experimental implementations. The ADQC scheme was originally designed to be used with physical implementations of quantum computing that involves qubits coming from different physical systems that have different properties.This may restrict the availability of couplings between the register and ancilla systems equivalent to maximally entangling quantum gates. By further focusing on the model under specific restrictions, such as minimal control of the ancilla system or long distance separation between register qubits, we find certain properties of the physical implementation that may best suit it for ADQC beyond stepwise determinism. Minimal control appears best suited for symmetric ancilla-register interactions; use overlong distances suits a transmitter going to an unknown receiver with possible small errors in the receiver's interaction with the ancilla.
|Date of Award||1 Apr 2014|
- University Of Strathclyde
|Sponsors||EPSRC (Engineering and Physical Sciences Research Council) & University of Strathclyde|
|Supervisor||Daniel Oi (Supervisor) & John Jeffers (Supervisor)|