# Quantinuum sheds light on the way to error-free quantum computing

*By André Saraiva, Diraq*

The most mind-blowing applications for quantum computers require trillions or more of qubit operations. But even the best engineering plus the best error mitigation strategies will only give you about a thousand operations before all the quantum “goodness” in your computer is gone. The only solution to this conundrum is to sacrifice several qubits to form a large cluster that cooperates to better protect quantum information. This collective entity is called a logical qubit.

Creating and controlling good logical qubits is no easy feat. Poorly controlled qubits will work against each other, instead of protecting each other. Moreover, to identify possible errors and correct them, it is necessary to be able to repeatedly measure certain qubits while keeping others alive.

Quantinuum, resulting from the merger between Honeywell Quantum Solutions and Cambridge Quantum, had already been working on error correction for a while. Their quantum processors are getting large and precise enough that they can now meaningfully test some of these techniques. Last year, they created unique logic qubits equipped to track errors in real time. They have now advanced and entangled two of these logical qubits.

To understand the precise value of this progress, one must understand the stakes of error correction. In its blog, Quantinuum describes the main achievements of this survey as follows

*1. The first demonstration of entangled gates between two logical qubits performed in a fully fault-tolerant manner using real-time error correction*

*2. The first demonstration of a logical entanglement circuit that has higher fidelity than the corresponding physical circuit*

Non-experts will agree – there’s a lot to unpack here. The key term is “fault tolerance”. Quantum error correction does not completely remove errors – it simply reduces the likelihood of an error occurring. Error correction schemes, called “codes”, may or may not be able to cause error rates to become as low as the user wants. A code capable of systematically reducing the error rate by sacrificing an increasingly large number of qubits is said to be fault-tolerant.

Quantinuum’s first achievement was to perform an entanglement between two groups of physical qubits (or logical qubits); and they did it by respecting the rules which make it possible to protect more and more the logical qubits by enlarging these groups.

Importantly, the operations on the individual physical qubits were good enough for the concerted dynamics of the whole group to work better than the individual qubits, confirming the key ingredient of error correction – error removal with redundant encoding of quantum information in a logic qubit.

Quantinuum even went so far as to test two different error correction strategies, using two different quantum processors – the 20 qubit H1-1 and the 12 qubit H1-2. The codes tested were the five-qubit code and the color code. The five-qubit code – one of the most economical codes in terms of the number of physical qubits needed – has been surpassed by the color code. Indeed, color coding requires fewer operations per error correction cycle, which leads to a better error budget and ultimately more competitive compared to noisy qubits.

This is the tip of the iceberg. The H1-series processors consist of ions floating on reconfigurable traps made from electrodes in a CMOS chip, which means it is able to mix qubits. This characteristic makes it possible to reorganize the connectivity between the qubits and to test more advanced codes. Moreover, the real-time measurement and decision-making of qubits should allow exciting anticipated applications in the near future.

This result was based not only on the exceptional quality of Quantinuum processors, but also on significant advances in classical computing in support of quantum operations. Tight integration between the quantum processor and a classical processor and the development of fast software optimized for the characteristics of H1 processors will enable significant advances in the science of error correction.

**What is the next?**

One of the main challenges facing error correction is not the quantum side of things, but the classical processing that goes along with it. Quantinuum has made excellent progress in this direction with its reconfigurable traps enabling real-time measurement of qubits, rapid decision-making based on tightly integrated classical processing, and active error correction over multiple cycles. However, when all of these ingredients come together, the advantage of the collective logic qubit over individual qubits is hindered. Indeed, interpreting where the errors occurred and deciding how to correct them requires a few precious milliseconds, enough for the qubits to lose some of their coherence.

Another important challenge moving forward is maintaining malleable connectivity between qubits while increasing the number of qubits enough for large-scale quantum computing. It’s unclear to what extent this is simply an engineering issue, or if there is a fundamental limitation to the ability to shuffle qubits, at which point the processor will need to be broken down into cells with a certain number qubits and interact with neighbors. cells, effectively limiting the range of qubit connectivity.

Additional information on this research can be found in a blog post on the Quantinuum website here and a preprint of the full technical article published on arXiv here.

*Dr. Saraiva has worked for more than a decade providing theoretical solutions to the quantum computing problems of silicon spin, as well as other quantum technologies. He is currently Solid State Theory Lead for Diraq, an Australian start-up developing a scalable quantum processor based on CMOS quantum dots.*

August 4, 2022