Assessing the Progress of Trapped-Ion Processors Towards Fault-Tolerant Quantum Computation

Abstract

A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the well-known QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trapped-ion quantum processors and, more importantly, to guide the future hardware developments that shall be required in order to demonstrate beneficial QEC with small topological quantum codes. In doing so, we present a thorough description of a realistic trapped-ion toolbox for QEC, and a physically-motivated error model that goes beyond standard simplifications in the QEC literature. We focus on laser-based quantum gates realised in two-species trapped-ion crystals in high-optical aperture segmented traps. Our large-scale numerical analysis shows that, with the foreseen technological improvements hereby described, this platform is a very promising candidate for fault-tolerant quantum computation.

Use of global interactions in efficient quantum circuit constructions

“…[[ ] ]encoding circuit is used to distill the Añ | state [26], its efficient GMS-enabled implementation may potentially be used to synthesize the logical-level T gate efficiently, constituting an important optimization for fault-tolerant quantum computing. We note, however, that GMS gates may be difficult to use fault-tolerantly [14].…”

“…We revisit the implementation of fan-in in section 3.1, since it is relevant to our more advanced constructions. Reference [14], figure 5 shows a two-GMS gate decomposition of the number excitation operator used in quantum chemistry simulations [15,16]. References [7,17] study the ways to implement quantum algorithms efficiently on a trapped ion quantum computer with the two-qubit gates enabled by the global entangling operator, concentrating on the case featuring anywhere between two to four qubits.…”

Quantum Computers as Universal Quantum Simulators: State‐of‐the‐Art and Perspectives

“…Generally speaking, a trade‐off between speed and fidelity has to be found, where faster usually means more error prone. Considering also that the reported coherence times of trapped ion qubits vary between few hundred ms and hundreds of seconds (i.e., up to several minutes), depending on the type of qubit, the trapped ion quantum hardware is the one currently allowing to achieve the highest coherence vs. gating time ratio, ideally in the order of 10 5 to 10 6 (e.g., assuming two‐qubit gate times in the order of 100‐200 µs, and depending on the qubit type).…”

The dynamical-decoupling-based spatiotemporal noise spectroscopy

“…Such investigations are currently of high importance for ongoing and nearfuture development of multi-qubit quantum registers for various applications. The cross-correlations of local noises are known to have significant influence on quantum metrological applications of systems of multiple entangled qubits [45][46][47][48][49][50][51][52], and quantum error correction [53,54]-a central issue for long-term prospects of quantum computation-that crucially relies on assumptions about correlations in decoherence processes of multiple qubits [55][56][57][58][59][60].…”