Erasure Qubits without Erasure Checks
Quantum computers will need quantum error correction to perform computations at a useful scale. It is well known that heralded erasure errors are easier to correct than Pauli errors in quantum error correction (QEC). In particular, a QEC code can correct twice as many erasure errors as Pauli errors. For this reason, there is significant interest in developing qubits whose dominant physical error channel can be converted into erasures. This erasure conversion may be accomplished either by mid-circuit erasure checks or by end-of-the-line erasure-resolving logical measurement. This dissertation presents two quantum computing architecture proposals that use erasure qubits without requiring mid-circuit erasure checks.
The first proposed architecture builds on linear optical quantum computing with fusion-based error correction. This QEC paradigm requires single photons which are entangled into small resource states before being fed into a fusion network. We show how optomechanics enables reliable production of quantum resources (single photons and small entangled states) for linear optical quantum computing. Specifically, acoustic modes can cache these quantum resources with on-demand readout. This proposed architecture uses dual-rail-encoded qubits and implements erasure-resolving qubit measurement via photon-counting detection. This combination converts excitation loss, which is the dominant error mechanism, into erasure errors.
The second architecture proposal is based on transmons, weakly anharmonic superconducting oscillators. In this work, we systematically study the conditions required to enable erasure performance—the ability to correct twice as many errors as one would under a stochastic Pauli error model—in the surface code with and without mid-circuit erasure checks. We introduce the moonwalking surface code, and show that it enables zero-overhead erasure performance when combined with three-state measurement—an implementation of erasure-resolving qubit measurement—if the two-qubit gate and the decoding algorithm meet certain conditions. We show that a qubit encoded into the ground (g) and second excited (f) states of a transmon can meet the gate-design requirements. Our decoder is based on a branch-and-bound algorithm and incorporates the noise structure of the two-qubit gate in the presence of leakage, meeting the second condition for zero-overhead erasure performance. This architecture allows the g-f qubit to function as an erasure qubit without requiring mid-circuit erasure checks.
Advisor: Shruti Puri
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