Protected superconducting qubits such as the 0-π qubit promise to substantially suppress error rates, facilitating fault-tolerant quantum computing with fewer qubits. Measuring thesequbits is challenging due to their protected nature, and thus far no concrete proposal exists for how to measure them without breaking their protection. Here we show how to perform protected measurements of the 0-π qubit in two orthogonal bases. The protection of these measurements is facilitated by their quantum non-demolition nature, allowing faults on ancillary measurement qubits to be tolerated. As experimental progress pushes protected qubits further into the low error-rate regime, our techniques will be crucial for fault-tolerant universal control.
Protected superconducting qubits such as the 0-π qubit promise to substantially reduce physical error rates through a multi-mode encoding. This protection comes at the cost of controllability,as standard techniques for quantum gates are ineffective. We propose a protected phase gate for the 0-π qubit that utilises an internal mode of the circuit as an ancilla. The gate is achieved by varying the qubit-ancilla coupling via a tunable Josephson element. Our scheme is a modified version of a protected gate proposed by Brooks, Kitaev and Preskill that uses an external oscillator as an ancilla. We find that our scheme is compatible with the protected regime of the 0-π qubit, and does not suffer from spurious coupling to additional modes of the 0-π circuit. Through numerical simulations, we study how the gate error scales with the circuit parameters of the 0-π qubit and the tunable Josephson element that enacts the gate.
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-periodiccircuit 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.