Chart Showing Improvement in Error Rates with this Latest Research. Credit: Quantinuum

The race to achieve fault tolerant quantum computing (FTQC) will need many steps in order to cross the goal line and provide a usable capability so that end users can take advantage of it for their applications. But Quantinuum and Microsoft have moved the ball further downfield with their latest experiment.

Basic quantum error correction groups together a bunch of error prone physical qubits with a coding scheme to form a logical qubit that shows a greatly decreased error rate. More advanced schemes increase the rate of encoding. A key metric that shows how effective the error correction has been is the separation between resulting physical and logical circuit error rates.  And in this latest demonstration, Quantinuum and Microsoft have achieved an improvement of up to 800X.

In particular, the team has created a circuit that creates four logical qubits from 30 physical qubits on Quantinuum’s H2 processor. This circuit reduces a physical error rate for the circuit from 0.008 (8×10-3) to 0.00001 (1×10-5) for the 800X improvement with pre-selection and post-selection. Of course, it helps to start with a good physical error rate and Quantinuum’s H2 machine is the best available today in this regard. But still, we should remind everyone that a 10-5 error rate is still far away from Microsoft’s goal of 10-8 or better error rate for a hybrid quantum/classical system that would be truly useful. This level of error rate will need to be achieved through continued improvement in the physical qubit error rate as well as larger codes that use a higher number of physical qubits per logical qubit to provide a greater distance between codewords.

Technical Details
The technical details are that the team experimented with two different codes to achieve this result. The first is the well-known Steane code which has characteristics [[7,1,3]] while the second one is a version of a CSS code they call the Carbon code and has characteristics [[12,2,4]]. (In this notation the first number represents the number of physical qubits, the second is the number of logical qubits, and the first is the distance between codewords. The greater the codeword distance the better the protection against errors.) The 10-5 error rate allowed the team to run over 14,000 experiments without error. They were also able to demonstrate repeated error correction with the Carbon code. Microsoft has defined Criteria for Resilient Quantum Computation and this advance moves them into the starting gate of what they call Level 2 resilient quantum computing. However, further refinements are necessary to make this resilience flexible and universal. Further they will still need to move to Level 3 to provide scale and this will be the long term objective of their research. For customers wishing to try out fault tolerant quantum computing, Microsoft has indicated that they will make these logical qubits available soon for private preview to Azure Quantum Elements customers. Though with only a handful of qubits available applications will remain limited.

Next Steps
As we’ve indicated above, this work represents a new milestone for quantum error correction, but it is still far from the ultimate goal. The most immediate work should be to show how this approach can be implemented to provide more logical qubits. Quantinuum has indicated they will be expanding their H2 processor to support up to 50 physical qubits so perhaps they will be able to support a few more logical qubits when this occurs.

Also, they will need to show they can support a universal quantum computer that can provide all the gate types necessary to be able to run any quantum algorithm. This research only used gates from the Clifford group, but they will need to also have support for non-Clifford gates like the T-gate or a Toffoli-gate. To do this, the team will need to build circuits known as magic state factories in order to implement those non-Clifford gates. These magic state factories will also require more qubits.

The H2 processor can support mid-circuit measure and feed forward capability which will ultimately be essential for large scale error correction. This experiment does not take advantage of feed forward, but such systems will ultimately require this to make corrections in real time.

But beyond the current generation H2, Quantinuum’s next generation Helios processor will come online in 2025 and we expect it will have roughly 90 physical qubits and provide even better physical qubit fidelity. The Helios processor will introduce, for the first time in a commercial QCCD device, a X-junction as part of the 2D surface electrode trap that the company recently described at the APS Conference. The company expects they will be able to have 10 or more logical qubits with this machine and moving from their current linear topology to two or three dimensions provides them with a pathway for scaling even further.

And, of course, Microsoft is continuing to research their topological based qubits which might provide advantages in coming years due to their potential advantages in qubit error rates, gate speeds, and small physical size. (See our previous writeup in the QCR about Microsoft’s research in topological qubits.)

GQI’s Thoughts
So, to summarize this announcement, GQI believes that while it is not yet  a Sputnik  moment for fault tolerant quantum computing, at 800X it’s the first time we’ve seen a rocket engine really ignite.

The Quantinuum H2 hardware is the highest fidelity truly commercial quantum kit available today. Quantinuum has consistently delivered on the promises of its quantum roadmap and it’s no surprise that this breakthrough has been achieved using this system. Their next generation  Helios architecture is expected to provide continuing vigor in their plans to scale up.

And for Microsoft, their major initiatives in quantum may seem diverse: topological qubits, quantum networking, programming frameworks and quantum chemistry software. But experts will see a common thread of quantum error correction know-how running behind them all.

Additional Information
More information is available in a Quantinuum press release here and a Quantinuum blog post here. Microsoft has published two blogs about this research that can be seen here and here. In addition, a short video produced by Microsoft can be seen here. And finally, a technical paper describing this research in detail has been posted on arXiv here.

April 3, 2024