In a sign that the wave of error correction research we saw in 2024 will not only continue but accelerate in 2025, three new error correction papers, two from Google AI and one from a Harvard/MIT/QuEra team, have been posted on arXiv showing continued advancements from some of their previous research.

The first paper from Google is titled Scaling and logic in the color code on a superconducting quantum processor which shows the results of their implementation of a different error code on their recently announced Willow chip. Unlike the previous error correction experiment on the Willow chip which used the surface code, this one uses the Color code. An advantage of the Color code is that is can enable much more efficient logic but it also makes the measurement and error decoding more complex. In this new experiment, they also achieved error correction performance below the threshold, meaning the logical error rate is lower than the physical error rate and achieved a Λ3/5 factor of 1.56 indicating an improvement in the error rate when scaling the code distance from three to five. Although this Λ3/5 factor reported was not quite as good as the 2.14 they previously reported with the surface code, this work shows that this approach has potential and warrants additional exploration to see if can it can be further optimized. In addition, the team implemented transversal Clifford gates on the logical qubits, injected magic states with high fidelity, and was able to teleport logical states using lattice surgery. The team was also able to perform randomized benchmarking with logical qubits for the first time in this new experiment with good results. You can access the paper posted on arXiv here.

A second paper from Google Quantum AI and Collaborators is titled Demonstrating dynamic surface codes which implements demonstrate three time-dynamic implements variations of the surface code on the Willow and Sycamore chips. The first variation, called Hexagonal Lattice Surface Code, implements the surface code on a hexagonal array that only requires couplings to three neighboring qubits instead of the traditional square lattice which needs coupling to four neighboring qubits. This approach could potentially simplify future quantum chip designs. The second variation titled Walking Surface Code swaps the role of the data and the measure qubits for each round. In the normal surface code, each qubit remains in its role as a data or measure qubit which can result in accumulating non-computational errors. In the Walking Surface Code, because a qubit is set as a measure qubit every two cycles it will be reset or replaced every two cycles which will reduce issues associated with leakage and other errors. The third variation, known as iSWAP Surface Code, replaces the traditional CNOT/CZ two-qubit gates with the iSWAP gate. An advantage of this approach is that it minimizes leakage generation. The team reported improvement results for each of the variations of Λ35,hex = 2.15(2), Λ35,walk = 1.69(6), and Λ35,iSWAP = 1.56(2). Note that these results were achieved on the standard Willow and/or Sycamore chips where were designed and optimized for the standard surface code in a square grid topology. This leaves open the opportunity for Google to design new chips which are specifically optimized for one of these codes and achieve even better performance. The technical paper that describes these experiments is also posted on arXiv and can be found here.

The third paper from a team from Harvard, MIT, and QuEra is titled Experimental Demonstration of Logical Magic State Distillation. One of the requirements of achieving a true fault tolerant quantum computer is the ability to implement a full universal gate set. That is to provide a set of gates that can implement any conceivable quantum program. This requires providing a way to implement the Clifford group of quantum gates such as the Hadamard (H), Phase Gate (S), an CNOT gate which is often straightforward in an error corrected system. Using these three basic gate types, one can generate many of the common gates such as the Pauli gates (X, Y, Z) and others. However, this is not enough. A true FTQC that provides a universal gate set must also implement non-Clifford gate types such as the T-gate or the Toffoli gate. It turns out that generating these non-Clifford gates in an FTQC is quite difficult and requires a significant amount of resources using a method like magic state distillation. This method creates a purified non-Clifford gate by combining and distilling it through multiple noisy quantum states. This paper describes how the team was able to achieve this with distance 3 and distance 5 color codes using QuEra’s neutral atom quantum computer. Although there have been several announcements of successful error correction experiments in the past year (see our articles here, here, here, and here), most of them have not yet demonstrated this very critical process of magic state distillation so this remains a very significant hurdle. The team describing this research has also been posted on arXiv and is available here. In addition, QuEra has posted a blog on their website describing this research that can be accessed here.

To reiterate what we have previously said, GQI believes that the three challenges which need to be met for a full FTQC for creating a useful quantum computer are the following:

  • Challenge 1: Platform capable of scaling to commercially relevant size
  • Challenge 2: Code scaling for systematically suppressing logical errors
  • Challenge 3: Universal fault-tolerant circuits with realistic clock times

So these three papers make us optimistic that a true FTQC can be implemented, but there is still much work to be done. As an example, in our The Road to Shor Era Quantum Computing, we state that a Λ factor of 10 would be needed to create an error corrected quantum processor capable of running Shor’s algorithm on a 2048 bit number. So the Λ result of 2.14 ± 0.02 still appears quite modest by this standard. In addition, the teams must show that their approaches are scalable for systems that contain thousands of qubits as well as provide continuous improvement in logical error rates as the code distance is increased to much higher levels than the 3 or 5 distances shown in these papers. And all this needs to occur while the teams are also improving the physical gate fidelities to the 99.9% or 99.99% or higher levels. The more the physical error rates improve, the easier it is to implement an error correction code that provides the necessary logical gate fidelity.

But overall, there has been excellent progress in error correction research in 2024 and we look forward to seeing more great progress in 2025.

December 28, 2024