Abstract
Measurement-based quantum computing (MBQC) is a promising alternative to traditional circuit-based quantum computing predicated on the construction and measurement of cluster states. Recent work has demonstrated that MBQC provides a more general framework for fault-tolerance that extends beyond foliated quantum error-correcting codes. We systematically expand on that paradigm, and use combinatorial tiling theory to study and construct new examples of fault-tolerant cluster states derived from crystal structures. Included among these is a robust self-dual cluster state requiring only degree-3connectivity. We benchmark several of these cluster states in the presence of circuit-level noise, and find a variety of promising candidates whose performance depends on the specifics of the noise model. By eschewing the distinction between data and ancilla, this malleable framework lays a foundation for the development of creative and competitive fault-tolerance schemes beyond conventional error-correcting codes.
Highlights
Fault-tolerant quantum computation is possible, provided that error processes are sufficiently weak and uncorrelated [1,2,3,4,5]
There is an alternative to circuit-based quantum computation (CBQC) that is built on the adaptive measurement of highly-entangled resource states [23, 24]
There are many similarities between them, fault-tolerant measurement-based quantum computation (MBQC) has certain freedoms that CBQC with error-correcting codes lacks
Summary
Fault-tolerant quantum computation is possible, provided that error processes are sufficiently weak and uncorrelated [1,2,3,4,5]. The essential property of this state is that it can both propagate highly non-local correlations, which carry the logical information being manipulated, while supporting local correlations, which act as consistency checks to catch errors This permits the sharing of long-range entanglement in the presence of noise, which is essential for any fault-tolerance scheme [27]. This stands in contrast to a quantum error-correcting code, in which the logical information is held statically in data qubits that remain unmeasured until the end of the computation, while only the ancilla qubits search for errors Relaxing this division of labor opens up a new design space to explore, and [31] employed a splitting technique reminiscent of approaches in network theory [32, 33] to construct new cluster states that were resilient to both dephasing and erasure noise [34].
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