Fault-tolerant quantum error correction with trapped-ion quantum bits
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Abstract
Trapped-ion quantum information processing is among the most promising candidates
to realize a scalable quantum computer. A segmented Paul trap can be used to move
ions in and out of storage and processing regions via dynamic register reconfiguration
operations, enabling effective all-to-all connectivity. The processing region is dedicated
to perform laser-driven operations, such as single-qubit rotations and two-qubit
entangling gates. To achieve the long-term goal of a large-scale fault-tolerant quantum
computer, it is of crucial importance to realize quantum error correction.
This thesis focuses on the experimental realization of a fault-tolerant (FT) weight-
4 parity check measurement (PCM) scheme on a trapped-ion quantum processor
node. The scheme presented here uses only minimal resource overhead in the form
of one additional ’flag’ qubit, to detect errors that would proliferate onto the data
qubit register as uncorrectable weight-2 errors. This parity check measurement is an
important building block in a broad class of resource-efficient flag-based quantum
error correction protocols, such as the topological color code. The experimental
result presented is one of the first realizations of the FT PCM scheme on a shuttlingbased
trapped-ion quantum computing architecture. A parity measurement fidelity
of 92.3(2)% is achieved, which is increased to 93.2(2)% upon flag-qubit conditioning,
exceeding the bare parity fidelity by 4.5 standard errors. Injection of bit- and phaseflip
errors shows that the scheme is able to reliably intercept faults. For holistic
benchmarking, an entanglement witnessing scheme is used, to verify the generation
of six-qubit multipartite entanglement, involving all ions participating in the faulttolerant
parity measurement.
Within the work presented here, improvements of the register reconfiguration
operations were carried out, in order to reduce the motional excitation in quantum
circuits with a high number of transport, separation/merge and positional ion swap
operations, such as the parity measurement scheme.
Taking into account the architectural features of the shuttling-based trapped-ion
quantum processor, such as effective all-to-all connectivity and no operational crosstalk,
the demonstrated building block of flag-based fault-tolerant quantum error
correction lays out a clear path towards scalable fault-tolerant quantum computing.