Quantum gates for superconducting qubits

Quantum Gates for Superconducting Qubits Chad Tyler Rigetti 2009 Josephson junction-based devices o¤er the potential to process information with the electromagnetic modes of an engineered quantum circuit. Doing so requires the subtle application of control signals to induce arbitrary transformations of the associated Hilbert space –or quantum gates –without causing the system to decohere. But there are strict constraints on the dynamical control we can exert over the circuit Hamiltonian, and given a practical set of controls, it is in general di¢ cult to extract a particular desired transformation. Of the possible strategies to address this quantum gate problem, those requiring the fewest control parameters, the least relative control bandwidth, and the minimal number of non-linear circuit elements are particularly interesting, as they would reduce experimental complexity and minimize unwanted interactions with degrees of freedom in the environment. We show how microwave signals and …xed weak linear coupling elements can be used to e¤ectively switch on and o¤an interaction and tune its strength and direction in the on state, and we derive speci…c irradiation protocols that use these interactions to implement universal two-qubit gates. These results emerge from Fourier analysis of the circuit Hamiltonian in a particular multiply-rotating reference frame. We develop and formalize this approach, then apply it to twoand three-qubit systems. In the two-qubit case, the theory succinctly reproduces many earlier results, and reveals new methods of entangling pairs of superconducting quantum bits. For example, a static weak linear coupling reactance can give rise to an e¤ective interaction that turns on linearly with the drive amplitude when one qubit is simply irradiated at the transition frequency of the other. In the three-qubit case, it describes how a very weak o¤-diagonal three-body coupling Hamiltonian can be exploited to controllably and directly produce pure tripartite entanglement, even when the qubits are far detuned from one another. We describe e¤orts to experimentally observe some of these e¤ects in two-qubit systems. The results provide preliminary evidence for the microwave-tuned interaction of qubits with …xed linear couplings.