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Geometric Approach to Quantum Error Correction Improves Efficiency

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Reviewed by Danielle Ellis, B.Sc.Sep 13 2024

In a study published in Science Advances, Hayato Goto of Japan's RIKEN Center for Quantum Computing developed a novel quantum error-correcting technique called "many-hypercube codes."

This technique, which has an elegant geometry, might aid in the realization of extremely efficient mistake corrections as well as the development of highly parallel approaches that would enable fault-tolerant quantum computing, the next step in quantum computer evolution.

Thanks to recent experimental progress, there is now great hope that we will be able to build fault-tolerant quantum computers, meaning quantum computers that can correct errors and surpass the power of conventional computers on certain tasks. To achieve this, however, it is important to develop efficient quantum error correction.

Hayato Goto, RIKEN Center for Quantum Computing

Over the last few decades, scientists have presented a variety of strategies for error correction. The traditional technique for quantum error correction is to encode a single logical qubit—the equivalent of a bit on a classical computer—onto several entangled physical ones and then use a decoder to extract the logical qubit from the physical ones.

However, scalability is a challenge with this strategy since the number of physical qubits required increases significantly, resulting in significant resource overheads. To address this issue, high-rate quantum codes, such as quantum low-density parity-check codes, have been proposed. However, using this technique, the logical gates that enable computations must be configured sequentially rather than in complete parallel, making them less time efficient.

To address this, Goto advocated utilizing what he refers to as "many-hypercube codes." This method has a complex name—high-rate concatenated quantum codes—and what is novel is that the logical qubits can be mathematically visualized as forming a "hypercube"—a type of shape that includes squares, cubes, and higher-order shapes such as the tesseract. The code's exquisite mathematical and geometric structure is surprising, especially given that most high-rate quantum codes have complex architectures.

Goto highlights that for the new codes to perform better, he was required to create a novel specialized decoder capable of interpreting the results from physical qubits. This novel approach is based on level-by-level minimum distance decoding, resulting in great performance.

Unlike other similar methods, it also allows logical gates to be placed in parallel rather than in series, making the system analogous to parallel processing in classical computers. This prompts Goto to refer to it as "high-performance fault tolerant computing" as opposed to "high-performance computing," which is used for massively parallel computing.

The efforts paid off. According to Goto, the codes reach an encoding rate—a statistic that reflects the ratio of logical and physical qubits—of up to 30%, which looks to be the highest among fault-tolerant quantum computing algorithms. Despite this high rate, the performance is equivalent to traditional low-rate codes.

Goto concluded, “In practice, this code could be implementing with physical qubit systems such as laser-trapped neutral-atom qubits.”