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Creating a roadmap to fault tolerant quantum computing

Dr Harry Buhrman

Credit: Quantinuum

Quantinuum recently published an accelerated roadmap to universal, fault-tolerant quantum computing, which the company aims to achieve by 2030. The updated roadmap accelerates the path to commercial quantum computing systems and unveils plans for its fifth-generation quantum computer, Apollo. This new system will be a fully fault-tolerant and universal quantum computer capable of executing circuits with millions of gates, delivering scientific advantage and enabling a commercial tipping point.

The roadmap is built on the foundations of Quantinuum’s fully scalable quantum charge-coupled device (QCCD) architecture, including a universal gate set and high-fidelity physical qubits uniquely capable of supporting reliable logical qubits. For four years now, Quantinuum has remained steadfast in providing data and peer-reviewed papers to show the science and engineering work behind these methodical advances.

In a recently published preprint research paper: “Scalable Multispecies Ion Transport in a Grid Based Surface-Electrode Trap” the company outlines the scientific advancements that led to this accelerated technology development.

What specific advancements have enabled the acceleration of your hardware roadmap towards a commercial quantum advantage?

Buhrman: "Our new roadmap is an acceleration of what we were previously planning. The benefits of this are obvious: Apollo brings the commercial tipping point sooner than we previously thought possible. This acceleration is made possible by a set of recent breakthroughs."

"First, we solved the “wiring problem”: we demonstrated that trap chip control is scalable using our novel center-to-left-right (C2LR) protocol and broadcasting shared control signals to multiple electrodes. This demonstration of qubit rearrangement in a 2D geometry marks the most advanced ion trap built, containing approximately 40 junctions. This trap was deployed to 3 different testbeds in two different cities and operated with two different collections of dual-ion-species, and all 3 cases were a success. These demonstrations showed that the footprint of the most complex parts of the trap control stay constant as the number of qubits scales up. This gives us the confidence that Sol, with approximately 100 junctions, will be a success."

"Second, we continue to reduce our two-qubit physical gate errors. Today, H1 and H2 have two-qubit gate errors less than 1x10-3 across all pairs of qubits. This is the best in the industry and is a key ingredient in our record >2 million quantum volume. Our systems are the most benchmarked in the industry, and we stand by our data - making it all publicly available. Recently, we observed an 8x10-4 two-qubit gate error in our Helios development test stand in 137Ba+, and we’ve seen even better error rates in other testbeds. We are well on the path to meeting the 5x10-4 spec in Helios next year."

Stutz: "By leveraging our all-to-all connectivity and low error rates, we expect to enjoy significant efficiency gains in terms of fault tolerance, including single-shot error correction (which saves time) and high-rate and high-distance Quantum Error Correction (QEC) codes (which mean more logical qubits, with stronger error correction capabilities, can be made from a smaller number of physical qubits)."

"Studies of several efficient QEC codes already suggest we can enjoy logical error rates much lower than our target of 10-6 – we may even reach 10-10, which enables exploration of even more complex problems of both industrial and scientific interest."

"Error-correcting code exploration is only the beginning – we anticipate discoveries of even more efficient codes. As new codes are developed, Apollo can accommodate them, thanks to our flexible high-fidelity architecture. The bottom line is that Apollo promises fault-tolerant quantum advantage sooner, with fewer resources."

How does achieving logical error rates better than 10-6, and what are the implications of possibly reaching 10-10 in future systems?

Stutz: "Apollo will achieve error rates of 10-6 and lower via quantum error correction. Reaching these error rates means that we can run circuits deep enough to solve problems of both industrial and scientific interest. This is enabled by starting with physical error rates at the 10-4 level, well below the “threshold” where quantum error correction starts working. Our lower physical error rate makes it easier to reach a logical error rate of 10-6 and beyond.  Reducing the logical error rate to 10-10 in future systems means you could run quantum circuits with order 1010 gates and still receive the correct answer with a reasonable probability. This opens up many more applications for quantum computers."

How do features like all-to-all connectivity, mid-circuit measurement, and real-time classical co-compute improve Apollo's performance and flexibility?

Stutz: "Many error correction codes require connectivity beyond the basic nearest neighbour connectivity offered by other quantum computing architectures.  Our ability to move our qubits around in space gives us all-to-all connectivity because we can bring any two qubits into contact with each other. With our all-to-all connectivity, we can explore many more QEC codes than those with limited connectivity."  

"Mid-circuit measurements enable you to perform quantum error correction during a circuit, so without it you can’t perform fault-tolerant quantum computing. 
The ability to make real-time corrections is also a requirement for fault-tolerant quantum computing; thus, there is a need for real-time classical co-compute to determine the corrections to perform." 

"Beyond the ability to perform quantum error correction, these features also enable applications run on the physical layer (i.e. do not require logical qubits and QEC).  Almost all applications require gating qubits that are not nearest neighbours, so in fixed qubit geometries logical “swaps” are needed. Those drive up the number of entangling gates you must perform, reducing the probability of getting the correct answer.  Our algorithm teams have devised clever ways to take advantage of these added features (mid-circuit measurement and real-time classical co-compute) for applications that are being run on the physical layer."

What role do Quantum Error Correction (QEC) codes play in advancing towards fully fault-tolerant quantum computing, and what is "single-shot error correction"?

Stutz: "All fault tolerance is based on QEC, but not all QEC is fully fault-tolerant. We “tolerate” faults, or errors, by detecting and correcting them. QEC is a necessary but insufficient condition for creating a fault-tolerant computer."

"Quantum error correction is essential for bringing the error rates lower than their physical limits. QEC is what allows for error rates of 10^-5 and lower. Low error rates mean that you can run deeper circuits – which means solving more complex problems."

"Single-shot error correction: For a fixed physical error rate, you can scale the logical (aka “corrected”) error rate down by increasing the “size” of the code, i.e. by using more physical qubits per logical qubit.  The most studied QEC code, the surface code, requires increased numbers of measurements (recall, mid-circuit measurement discussion above) as you increase the code size. Many quantum computing modalities favour the surface code since it only requires nearest-neighbour interactions.  By relaxing this requirement and allowing codes with higher qubit connectivity, you can find QEC codes that only require a single round of measurements per QEC round, independent of the code size. Our all-to-all connectivity enables us to run these efficient single-shot codes." 

"Because of our connectivity, low crosstalk mid-circuit measurement, qubit reuse, ability to do real time corrections enabled by long qubit coherence times, and low physical error rates, our architecture allows for virtually any error correcting code to be run. This flexibility will be crucial as we scale up towards fault-tolerant quantum computing."

What scientific applications do you foresee Apollo driving forward, particularly in fields like materials science, chemistry, and high-energy physics?

Stutz: "Apollo will give us the ability to simulate complex quantum mechanical systems beyond the reach of classical computers, which will have important impacts on fundamental science. Nobody could have predicted the internet when classical computers were first developed. We don’t know everything that quantum computers will be used for, but we are excited about the future potential of solving important problems."

How did you overcome the "wiring problem" for scalable quantum systems?

Stutz: "Full details can be found in this preprint research paper. In summary, we were able to perform low heating “junction transport” (meaning having qubits cross an intersection). We were able to do this across a grid of junctions.We co-wired different sections of the trap such that all corresponding electrodes in the different sections used a single analog voltage signal. We then devised a clever control system that minimised the signals required to arbitrarily rearrange the qubits (or ions) on the grid."

"Both of these techniques combined allowed us to drastically reduce the number of physical wires in the system. This means we can increase the number of qubits and grow the size of the quantum computer while keeping the number of unique analogue electrical signals constant, or near constant."

Dr Harry Buhrman is the Chief Scientist for Algorithms and Innovation at Quantinuum

Russell Stutz is the Director, Commercial Hardware, Quantinuum

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