Robust Ion Trap Quantum Computation Enabled by Quantum Control

Abstract

The advent of quantum computation foretells a new era in science and technology, but the fragility of quantum bits (qubits) and the unreliability of gates hinder the realization of functioning quantum computers. For ion trap quantum computers in particular, 2-qubit operations relying on the M\o lmer-S\o rensen interaction have the greatest error rates. This dissertation introduces frequency-modulated (FM) pulses as a measure to maximize 2-qubit gate fidelity and a way to calibrate gate errors through the measurement of circuit performance.A key challenge of two-qubit gates in ion chains is unwanted residual entanglement between the ion spin and its motion. Frequency-modulated pulses are developed to achieve such goal. This theoretical advance has led to high-fidelity 2-qubit gates that are robust against small frequency drifts in a 5-ion experiment. Combining frequency and amplitude modulation, numerical calculations suggest that entanglement between an arbitrary pair of qubits are possible in a lattice with up to 50 ions. More recently, long-distance 2-qubit gates have been realized within a 17-ion chain. Quantum circuit calibration is proposed to improve quantum circuits using feedback from measurement results. A relationship between the error parameters and measured observables can be established to identify systematic circuit errors. The calibration of a 6-qubit parity check circuit targeting 2-qubit overrotations has been implemented using measurement results from an experimental 15-ion trap. This improvement is conducive to quantum error correction protocols which involve high-weight stabilizers. A 4-bit Toffoli circuit with an error vector of length 6 is calibrated using a custom circuit simulator, reducing the average error size by a factor of 4. Using linear and quadratic approximation, a 6-bit Toffoli circuit with 12 error parameters is calibrated in the presence of 3 ancilla qubits.