## Landscape of Quantum Computing in 2023

In 2021 I wrote a brief explainer of where quantum computing was and where it needs to go, specifically to break crypto. I updated the chart below to reflect recent progress in quantum computing:

Check the original post for the explaination of the chart. This year I coloured the dots of existing quantum computers to reflect how recent they are (dark grey = very recent, white = ancient history, i.e., before 2017), and connected dots from the same organization(s) with arrows. Progress continues, slowly.

2023 had two big advances in quantum computing that are relevant to this chart.

Firstly, a new quantum factoring algorithm! The new algorithm needs *asymptotically* fewer gates, but it is unclear right now if that translates into fewer resources in practice. It is a big task to create a complete, optimized circuit that accounts for all necessary error correction overheads, so no one has finished that yet. The proposed improvement is proportional to the square root of the bitlength, so it might be approximately a 45x improvement for an attack against RSA-2048. However, saving 45x in number of operations will not save 45x in qubits, so the red lines on the chart may not move that much.

Still, I said in 2021, "An asymptotic improvement is highly unlikely". Whoops!

The biggest experimental news came out just before the end of the year, with a collection of impressive error correction results. Like Google's result last year, this group (from QuERA, Harvard, JQI, and MIT) show that the logical qubits improve as the code gets larger, but the new result goes up to distance 7 (for context, error correction in Shor's algorithm would need distance around 25-30). They were also able to perform an operation between two logical qubits.

Other results from that paper use a colour code. Colour codes share many of the good properties of surface codes (they fit on a flat chip and suppress errors well), and either type of code could lead us to breaking RSA.

They also perform a number of algorithms on logical qubits with smaller codes. These results are less relevant to this chart and breaking RSA, as the smaller codes do not have the scaling guarantees that a surface code does.

While Google and IBM use superconducting qubits, this group used neutral atoms. It was harder to find a specific number for fidelity from their paper, so take the dot on the chart with a grain of salt (as in previous years, compressing qubit quality to a single dot is imprecise and loses a lot of information). For more discussion on this result, see Scott Aaronson's blog (note especially Craig Gidney's critique in the comments that they do not do multiple rounds of error correction, something that is absolutely necessary for quantum computation at large scales).

Finally, based on a good suggestion from Paul Hoffman, here's the same chart with *non*-logarithmic axes. On this chart, the distance from today's quantum computers to breaking RSA is about 10,000 chart-widths.