Optimizing control of quantum information in higher dimensions

Sahel Ashhab from the National Institute of Information and Communications Technology (@NICTchannel) presents at the QuDits for Quantum Technology workshop, hosted by the Quantum Interactions Theory Group at the Institute for Quantum Computing, University of Waterloo. Learn more: quantum-intera...
Optimizing control of quantum information in higher dimensions: (1) qutrit control and (2) speed limits for two-qubit gates with weakly anharmonic qubits. We consider two aspects of quantum information processing when the physical system used to encode the quantum information possesses more than two quantum states in the accessible energy range, as is the case for superconducting devices. On one hand, these devices can be used to encode qudits. In this context, we investigate the optimal implementation of single-qudit gates with superconducting qudits. In particular, we show that it is possible to perform an arbitrary gate using a single pulse with resonant drive frequencies. We also consider the implementation of qubit gates when the presence of higher energy levels cannot be ignored. We use optimal control theory to determine the maximum achievable gate speed for two-qubit gates in the qubit subspace of the many-level Hilbert space. We identify two competing mechanisms. On one hand, higher energy levels are generally more strongly coupled to each other. Under suitable conditions, this stronger coupling can be utilized to make two-qubit gates significantly faster than the reference value based on simple qubits. On the other hand, a weak anharmonicity typically constrains the speed at which a quantum system can be adequately controlled. In order to account for this constraint, we modify the pulse optimization algorithm to avoid pulses that lead to appreciable population of the higher levels. In this case, we find that the presence of the higher levels can lead to a significant reduction in the gate speed. These results can help the search for optimized gate implementations and provide guidelines for desirable conditions on anharmonicity to enable the utilization of the higher levels in realistic systems. This work was supported by MEXT Quantum Leap Flagship Program Grant No. JPMXS0120319794.