Logical Gates and Read-Out of Superconducting Gottesman-Kitaev-Preskill Qubits

  1. Mackenzie H. Shaw,
  2. Andrew C. Doherty,
  3. and Arne L. Grimsmo
The Gottesman-Kitaev-Preskill (GKP) code is an exciting route to fault-tolerant quantum computing since Gaussian resources and GKP Pauli-eigenstate preparation are sufficient to achieve
universal quantum computing. In this work, we provide a practical proposal to perform Clifford gates and state read-out in GKP codes implemented with active error correction in superconducting circuits. We present a method of performing Clifford circuits without physically implementing any single-qubit gates, reducing the potential for them to spread errors in the system. In superconducting circuits, all the required two-qubit gates can be implemented with a single piece of hardware. We analyze the error-spreading properties of GKP Clifford gates and describe how a modification in the decoder following the implementation of each gate can reduce the gate infidelity by multiple orders of magnitude. Moreover, we develop a simple analytical technique to estimate the effect of loss and dephasing on GKP codes that matches well with numerics. Finally, we consider the effect of homodyne measurement inefficiencies on logical state read-out and present a scheme that implements a measurement with a 0.1% error rate in 630 ns assuming an efficiency of just~75%.

Universal flux-based control of a π-SQUID

  1. J. Wilson Staples,
  2. Thomas B. Smith,
  3. and Andrew C. Doherty
We describe a protocol for the universal control of non-ideal π-periodic superconducting qubits. Our proposal relies on a π-SQUID: a superconducting loop formed by two π-periodic
circuit elements, with an external magnetic flux threading the circuit. The system exhibits an extensive sweet spot around half-flux where residual 2π-periodic Cooper pair tunneling is highly suppressed. We demonstrate that universal single-qubit operations can be realised by tuning the flux adiabatically and diabatically within this broad sweet spot. We also assess how residual 2π-periodicity in π-SQUIDs impacts holonomic phase gates.