I am biased, but they do say Copenhagen is one of the best cities in the world... ;)

While the two codes are pretty similar, the CSS version keeps things a little simpler for the physical fusion circuits and is probably more resilient to measurement errors, since each detection cell needs half the number of measurements

@dulwichquantum.bsky.social 😜

A big thank you to Ming-Lai at Sparrow Quantum for the huge effort he put into this paper, as well as the other authors at The Niels Bohr Institute for all their input – I am very lucky to work with such exceptional people.

What’s cool is that we’ve already successfully demonstrated the resource state generation and fusion gates in the lab. As a result, our blueprint is able to focus on feasibility and practicality, with components we know how to implement and improve towards real fault-tolerance.

While our fusion measurements are indeed adaptive, we offload the adaptive part to the photon source using excitation-based feedback pulses – this means we have fewer optical bits and thus fewer losses.

There are a few clever tricks we get to play in our architecture that I encourage you to read about, but the one I think is particularly fun is the fact that we can make all our fusion gates fully passive.

We also calculate space + time resource costs, down to the number of optical elements; thanks to the choice of lattice and temporal encoding, we achieve an ultra-low optical depth for each photon. A single logical clock cycle takes on the order of microseconds, scaling linearly with code distance.

We then benchmark the whole thing with some realistic error models inherent to quantum dots, providing thresholds that should help guide the experimentalists.

We give a very detailed outline of the hardware components of the photon sources and fusion measurement chip with fusion measurement circuits. Like a good recipe should, we show how these are integrated, and precisely what the experimental sequence looks like.

These states are fantastically compatible with our sFFCC fusion network, which measures the fusions sequentially along these chains.

The resource states we use are the so-called “caterpillar” states, with a chain of qubits where we encode each qubit with up to *N* physical photons. Each fusion then gets to try up to *N* times for a successful measurement (hence, “repeat-until-success”).

...tailored quantum error correction in the form of the mouthful that is the synchronous foliated Floquet colour code (sFFCC), which suits fusions very well with its weight-2 checks.

We try to directly address these problems by using deterministic quantum dot emitters that produce high-fidelity entangled photonic resource states from time-bin encoded photons, adaptive repeat-until-success (RUS) fusion gates to significantly boost loss tolerance, and...

1. Successful resource state generation is pretty inefficient
2. Photonic architectures generally use a tonne of multiplexing and fibre delays, which result in…
3. Loss. Loss rates right now far from what we need for fault-tolerance

A potential solution? A beautiful combo of ideas.

A typical approach to photonic quantum computing is to use small resource cluster states that are fused together by projective bell measurements to build a larger lattice for computation (fusion-based quantum computation, or FBQC).

Currently, the field runs into a few stubborn problems...

What does a recipe for building a quantum computer look like?

Not only should it list the exact ingredients we need, but we also need to know how to put them together and in what order. We then need to test how good it might be, and how much it’s going to cost us.