The News: On April 3, Microsoft and quantum computing company Quantinuum announced a significant breakthrough in achieving real logical qubits with error detection and correction. They ran more than 14,000 qubit-entangling quantum circuits without observing a single error.
See the press release from Quantinuum; the Microsoft, Quantinuum, and Azure Quantum technical blogs; and the technical preprint for more information.
Quantum in Context: Microsoft & Quantinuum Create Real Logical Qubits
Analyst Take: I believe this result firmly moves the industry into the middle and second era of quantum computing, which Microsoft calls Level 2 Resilient quantum computing. The third era will be when we have achieved Practical Quantum Advantage and real commercial value for problems big enough and hard enough that we require quantum systems for their solution. We have years to go before we get to that point. This result puts other vendors on notice not to play fast and loose with their definitions of logical qubit, and they must back up their claims with reproducible and quantified results.
Why Do We Care about Logical Qubits?
When we speak about classical data stored in bits and bytes, we think of the values as numbers, text, music, images, videos, and so forth. We call the values held in one or more qubits quantum states.
If qubits held their quantum states forever and never had errors introduced by the environment or our operations (initialization, gates, and measurement) on the qubits, we would have perfect qubits and gates. This assumption of perfection is often present when you read quantum computing books and articles. Instead, errors introduced from the operating environment or manufacturing defects in real quantum computers are the reality. We aspire to have perfect qubits, which is probably too much to obtain. Instead, we build quantum computers from physical qubits and combine them with hardware control and software to make logical qubits. There are many ways to make physical qubits, including superconducting materials, photonics, neutral atoms, diamond defects, quantum dots, silicon spin, and trapped ions.
Quantinuum is known for its high-quality trapped ion qubits. They are relatively long-lasting, have reasonable gate speeds, and very low error rates. Is there some way to correct errors on the qubits if something goes wrong? The answer is yes, but the process is non-trivial. For example, we can’t simply copy a quantum state as a backup, comparison, or redundant version. This is a rule of nature according to quantum mechanics and not a failure in our implementations. We combine multiple physical qubits with software to create a virtual logical qubit.
A logical qubit must be able to detect and correct some errors so that the error rates are orders of magnitude lower than the physical qubits that comprise it. Suppose I have a quantum algorithm with a depth of 10,000: I must run 10,000 operations on at least one qubit. If my error rate is 1 in 1,000, I will see mistakes in the quantum computation with high probability, rendering the result useless. If my error rate is 1 in 1 million, I may not see any errors when I run the algorithm. In any case, I can compute how many times I must run the algorithm to have a high enough certainty that I will get the correct answer. Probability is integral to quantum computing, even if you assume your qubits are perfect. Adding error rates into the mix complicates the execution model and your confidence in the computed answers.
You are not a logical qubit if you:
- Are a physical qubit
- Only detect errors without correcting them
- Can’t detect and correct enough errors
- Do not have logical implementations of quantum gates
- Can’t specify your logical versus physical error rates
Quantum Entanglement
The quantum computing model does not allow us to copy quantum states, but it does allow us to entangle qubits. Once entangled, we cannot consider the qubits separate, independent entities. Entanglement links the behavior of one qubit to another. Entanglement is what Einstein called “spooky action at a distance, “ in a now somewhat over-used phrase.
Here is a classical analogy. Suppose you and I each hold a coin in one of our hands, and we can identify one side of each coin as a head and the other as a tail. Under normal circumstances, whether my coin is heads or tails is independent of the state of your coin. The coins are not entangled.
If we could somehow link the coins so that knowing the state of my coin automatically tells me the state of yours, then the coins are entangled. For example, one example is if my coin is heads or tails, yours must be the same. The coins are entangled.
For the universal quantum computing models, you are not doing quantum computation if you cannot perform entanglement on at least two qubits.
Some Technical Details on Quantum Entanglement
Many quantum computing textbooks, including mine, demonstrate entanglement via the creation of the four 2-qubit Bell states:
These involve a lot of symbols, but the two on the left correspond to the coin example where my coin’s state must be the same as your coin’s state.
We create these states via quantum circuits on two qubits that look like:
The H is a Hadamard gate, and the dot-and-circle gate is a controlled-NOT (also known as CNOT, controlled-X, and CX). The H gate puts the first qubit into a balanced superposition, and the controlled-NOT creates the entanglement.
To properly create entanglement without error, we must perform the superposition exactly, followed by the 2-qubit gate. The error rates on 2-qubit gates are often ten times worse than those for 1-qubit gates, so if imprecision were to creep in, this is an excellent circuit to test.
So What Did Microsoft and Quantinuum Do to Create Logical Qubits?
Using the Quantinuum 32-qubit Model H2 quantum computer, they created 4 logical qubits using 30 physical trapped ion qubits. This gave them 2 pairs of qubits, and they entangled each pair into a Bell state. Their error rates running the entanglement circuit were 800 times better than the underlying physical qubits. They ran the circuit 14,000 times without observing any errors. The circuits were each of depth 2, and the error rate is lower than 1 in 14,000, or 7.1 × 10–5. They demonstrated logical qubits and logical gates via error detection, error correction, and entanglement.
Quantinuum provided the hardware within the collaboration, while Microsoft largely provided the software for virtualizing the logical qubits.
Key Takeaway
Microsoft and Quantinuum have precisely set the bar for achieving logical qubits within quantum computation. It’s an early but significant step that moves us closer to Practical Quantum Advantage.
Ultimately, we need thousands of logical qubits. We will virtualize each logical qubit from several physical qubits. How many is “several”? For many years, I and others assumed we would need approximately 1,000 physical qubits per logical qubits. Recent results have lowered that number significantly, but no one has yet proven the relative scale by implementation. This announcement’s “30 physical qubits make 4 logical qubits” comes with many technical details, but this strong result advances the state of the art.
Whereas IBM demonstrated an experimental quantum chip with over 1,100 qubits, Quantinuum must increase the size of the ion traps to closer to 100 qubits and begin to link the traps via quantum networking. Once they do this, we may see logical qubits spanning multiple traps, if necessary, and logical multi-qubit gates across traps.
Finally, as a general note, I do not define a “commercial quantum computer” as something that someone will pay money to use or own to solve useless problems. For me, we will see the true commercialization of quantum computing when the systems are large enough that people will use them in production alongside other advanced platforms such as HPC.
Disclosure: The Futurum Group is a research and advisory firm that engages or has engaged in research, analysis, and advisory services with many technology companies, including those mentioned in this article. The author is a former employee of IBM and holds an equity position in the company.
Analysis and opinions expressed herein are specific to the analyst individually and data and other information that might have been provided for validation, not those of The Futurum Group as a whole.
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Author Information
Dr. Bob Sutor is a Consulting Analyst for Futurum and an expert in quantum technologies with 40+ years of experience. He is an accomplished author of the quantum computing book Dancing with Qubits, Second Edition. Bob is dedicated to evolving quantum to help solve society's critical computational problems. For Futurum, he helps clients understand sophisticated technologies and how to make the best use of them for success in their organizations and industries.
He’s the author of a book about quantum computing called Dancing with Qubits, which was published in 2019, with the Second Edition released in March 2024. He is also the author of the 2021 book Dancing with Python, an introduction to Python coding for classical and quantum computing. Areas in which he’s worked: quantum computing, AI, blockchain, mathematics and mathematical software, Linux, open source, standards management, product management and marketing, computer algebra, and web standards.
