Designing Quantum Memories with Embedded Control: Photonic Circuits for Autonomous Quantum Error Correction

We propose an approach to quantum error correction based on coding and continuous syndrome readout via scattering of coherent probe fields, in which the usual steps of measurement and discrete restoration are replaced by direct physical processing of the probe beams and coherent feedback to the register qubits. Our approach is well matched to physical implementations that feature solid-state qubits embedded in planar electromagnetic circuits, providing an autonomous and “on-chip” quantum memory design requiring no external clocking or control logic.

Figure 1

Schematic diagram of a coherent-feedback quantum memory showing qubits in cavities ($Q1$, $Q2$, and $Q3$), circulators, beam splitters, steering mirrors, and relays ($R1$ and $R2$).

Figure 2

Level diagrams of (a) $Z$ probe interaction, and (b) $X$ probe interaction.

Figure 3

Details of the cQED relay component model (modified from 11): (a) input and output ports, (b) coupling of input and output fields to resonant modes of two cavities, and (c) relay internal level diagram.

Figure 4

Decay of fidelity, $⟨{\Psi }_0|{\rho }_t|{\Psi }_0⟩$, for several values of the feedback parameter $\Omega =|\beta {|}^2\gamma /2\Delta$ (see 8), $\alpha =\Omega /8$, and $\Gamma =0.1$. The fidelity decay of a single, bare qubit also suffering bit-flip errors at rate $\Gamma =0.1$ is also shown.