Logical qubits start outperforming physical qubits

‍Broomfield, Colorado, August 4^th, 2022 — Quantinuum researchers have hit a significant milestone by entangling logical qubits in a fault-tolerant circuit using real-time quantum error correction. The research, published in a new scientific paper that was released on August 3^rd, is the first experimental comparison study of different quantum error correction codes in similar environments and presents a collection of several different experiments. These experiments include:

1. The first demonstration of entangling gates between two logical qubits done in a fully fault-tolerant manner using real-time error correction
2. The first demonstration of a logical entangling circuit that has higher fidelity than the corresponding physical circuit.

This milestone achievement is important because it marks the first time that logical qubits have been shown to outperform physical qubits — a critical step towards fault-tolerant quantum computers.

“Quantinuum’s trapped-ion quantum computing roadmap is designed around continuous upgrades, enabled our flexible architecture and our precision control capabilities. This combination provides for outstanding, first-of-its-kind achievements that help accelerate the entire industry,” said Tony Uttley, President and COO of Quantinuum.

David Hayes, a Theory and Architecture Technical Manager at Quantinuum and co-author of the new research paper, said the research moves quantum computing closer to the point where encoded circuits outperform more primitive operations.

“People have worked with error corrected qubits before, but they haven't reached this sort of special point where the encoded operation is working better than the primitive operation,” Hayes said. “The other thing that's new here is that in other experiments we're doing the error correction while we're doing the operations. An important next step for us is to get the error rate induced by the error correction itself down further." 

The findings are described in the new research paper, “Implementing Fault-tolerant Entangling Gates on the Five-Qubit code and the Color Code”. The paper was recently published on the arXiv. Scientists used both the H1-1 and the H1-2 quantum computers, Powered by Honeywell, to compare the Five-Qubit error code and the Distance Three Color Code in these tests.

Quantum researchers are in the early days of experimental quantum error correction with a multitude of codes to test. Quantinuum researchers can explore a wider range of quantum error codes, compared to other quantum hardware designs, due to the architecture of the machine. 

The System Model H1 uses a trapped-ion design and a quantum charged coupled device architecture (QCCD). Along with the inherent flexibility of this design, another strength is all-to-all connectivity. All the qubits are connected to each other which makes it easy to move information through chains of ions without creating multiple errors along the way.

“Instead of having to build a new machine every time we want to try a new code, we can just program the machine to run a different code, make the measurements and weigh the different pros and cons,” Hayes said.

Advancing quantum error correction

All forms of technology need error correction including servers in data centers and space probes sending transmissions back to Earth. For Quantinuum and other companies in the quantum computing sector, quantum error correction is one of the most important pillars of progress. Errors prevent quantum computers from producing reliable results before they are overwhelmed. Quantinuum’s researchers are working toward the milestone of fault tolerance, meaning the errors can be suppressed to arbitrarily low levels. 

Natalie Brown, another co-author of the paper and an Advanced Physicist at Quantinuum, said that most classical error correction principles fail with quantum computers because of the basic nature of quantum mechanics. 

“It becomes very difficult to suppress noise to very small levels, and that becomes a problem in quantum computing,” she said. “The most promising candidate was this quantum error correction, where we take the physical qubits, make a logical qubit.”

Logical qubits are groups of physical qubits working together to perform a computation. For each physical qubit used in a computation, other ancillary qubits perform a range of tasks such as spotting and correcting errors as they occur.

Ciaran Ryan-Anderson, a Senior Advanced Physicist at Quantinuum and also a co-author of the new paper, said the newest research paper builds on research performed in 2021 and published in Physical Review X. That work explained how researchers at Honeywell Quantum Solutions applied multiple rounds of quantum error correction to a single logical qubit. 

“One of the first really important things to demonstrate was these repeated rounds of quantum error correction cycles,” he said.

That is one of several milestones on Ryan-Anderson’s quantum error correction checklist:

1. Conduct repeated rounds of fault tolerant quantum error correction 
2. Feed forward and conditionally apply syndrome extraction
3. Enable real-time determination of correction for a quantum error correction code 
4. Demonstrate general algorithmic real-time decoding
5. Scale up quantum error correction with two logical qubits
6. Hit the breakeven point when logical quantum computing starts to outperform physical quantum computing

“Quantinuum has achieved some of the milestones required to accomplish this now,” Ryan-Anderson said.

Five-Qubit Code vs. Color Code

Building upon the 2021 research involving one logical qubit, the newest research illustrates the Quantinuum team’s progress with quantum error correction and two logical qubits. The team tested two error codes familiar to quantum experts: the Five-Qubit Code and the Color Code. The Five-Qubit Code does not allow for a fault tolerant transversal gate using only two logical qubits. Researchers used “pieceable” fault tolerance to decompose an initially non-fault tolerant logical gate operation into pieces that are individually fault-tolerant. The Color Code, however, does allow the use of a transversal CNOT gate which is naturally fault-tolerant.

How the experiment worked

H1-2 can use up to 12 qubits and H1-1 can use up to 20. The Five-Qubit Code tested on H1-2 while the Color Code tested on H1-1. Both computers use the same surface electrode ion trap to control ytterbium ions as qubits. Ion transport to isolated gate zones with focused laser beams provides low crosstalk gate and mid-circuit measurement operations.

The researchers ran five experiments with different combinations of circuit elements to test the Five-Qubit Code and to understand the impact of fault tolerant design and circuit depth. The team found that the extra circuitry designed to increase fault tolerance had a negative impact on the overall fidelity of the logical operation, due to the large number of CNOT operations required. 

The Color Code showed much better results due in part to the ability to use a transversal CNOT gate. The team ran seven experiments to investigate the fault tolerant potential of these codes. With the Color Code, the researchers found that the State Preparation and Measurement circuits benefitted from the addition of fault tolerant circuitry with a significant reduction of error rates: 99.94% for the logical qubits compared to 99.68% for the physical qubits. This was the only additional circuitry required to make the circuit fault tolerant from end-to-end, since the logical CNOT is transversal and naturally fault tolerant.

The researchers concluded that the “relatively economical fault tolerant circuitry of the Color Code will provide a better platform for computation than the qubit efficient five-qubit code.” Also, the researchers found that the Five-Qubit Code would be useful only in systems with far lower physical error rates than quantum computers have at this point in time. 

Hayes said the team’s next step will be to surpass the breakeven point and provide proof of the work. “We are getting evidence that we're really darn close to that point, but there's a lot of work that needs to be done to actually prove it,” he said. “Just getting right there is not good enough, you have to actually get past it.”

A new classical+quantum connection

Another advance from this experiment is a new classical processor with enhanced capabilities which will be essential to scalable algorithmic decoders. The data from the classical functions were used to dictate the control flow and operations executed in the quantum program.

The decoders used in these experiments were partially written in Rust and compiled to WebAssembly (Wasm). The choice of Wasm provides an efficient, safe, and portable classical language to have functions that are callable from quantum programs. 

The decoder implemented in Rust uses many high-level program constructs. The support for these features means that various scalable algorithmic decoders can be ergonomically implemented in various high-level languages that compile to Wasm (such as Rust, C, and C++) and called from quantum programs.

“It was pretty enabling for this particular experiment, and it'll be even more important for future experiments as these things get more and more complicated,” Hayes said.

Another advantage of the trapped ion architecture is the ability to do real-time decision making during the execution of the quantum circuit thanks to long coherence times and the ability to do mid-circuit measurement and reset qubits as needed. 

“Our systems have very long coherence times which is super advantageous when integrating in the classical compute real-time decision making,” Hayes said. 

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