Nature Shenzhen Institute of Quantum Research makes international first quantum error correction major breakthrough!

Quantum error correction (QEC) aims to protect logical quantum bits from noise by exploiting the redundancy of Hilbert space, which allows errors to be detected and corrected in real time. In most QEC codes, the logical quantum bits are encoded as some discrete variables, such as photon numbers, so that the encoded quantum information can be extracted unambiguously after processing.

Reproducibility of QEC based on various discrete variable encoding schemes has been demonstrated in the last decade. However, extending the lifetime of the logical quantum bits so encoded beyond the best available physical quantum bits remains elusive, representing a trade-off point for judging the practical utility of QEC.

This time, the SUSTech team, led by Academician Yu Dapeng, and Xu Yuan's group, an assistant researcher at the Superconductivity Laboratory of the Shenzhen Institute of Quantum Research, together with Professor Zheng Shibiao of Fuzhou University and Professor Sun Lu Yan of Tsinghua University, have overcome the difficulties and achieved a breakthrough and significant experimental progress in the field of quantum error correction based on superconducting quantum line systems.

This work illustrates the potential of hardware-efficient discrete-variable encoding for fault-tolerant quantum computing, and the related research results are published online as "Beating the break-even point with a discrete-variable-encoded logical qubit". The research results were published online in Nature, a leading international academic journal, under the title "Beating the break-even point with a discrete-variable-encoded logical qubit.

One of the main obstacles to building quantum computers is environment-induced decoherence, which destroys the quantum information stored in the quantum bits.

Errors caused by decoherence can be corrected by repeatedly applying a quantum error correction (QEC) procedure, in which logical quantum bits are encoded in a high-dimensional Hilbert space so that different errors project the system into different orthogonal subspaces, which in turn can be unambiguously identified and corrected without disturbing the stored quantum information.

In the traditional QEC scheme, the codeword of logical quantum bits is formed by two highly symmetric entangled states of several physical quantum bits, encoded in some discrete variables. In the last two decades, significant progress has been made in the experimental demonstration of this QEC coding in different systems, including nuclear spins, diamond nitrogen vacancy centers, trapped ions, optical quantum bits, silicon spin quantum bits, and superconducting circuits.

In these experiments, the lifetime of the logical quantum bits still needs to be greatly extended to achieve the best available physical component lifetime, which is considered to be the balance point to judge whether QEC encoding can benefit quantum information storage and processing.

Another QEC encoding scheme is the use of the large space of simple harmonic oscillator (oscillator), which can be used to encode either continuous-variable or discrete-variable quantum bits.

Both types of coding can tolerate errors due to loss and gain of energy quanta, allowing quantum error correction to be performed in a hardware efficient manner. Circuit quantum electrodynamics (QED) systems represent an ideal platform for implementing such encoding schemes: in existing experiments, the break-even point has been exceeded by distributing quantum information over an infinite dimensional Hilbert space of light quantum bits encoded in continuous variables; however, the encoding of such light quantum bits is not strictly orthogonal.

Schematic diagram of the QEC procedure using the lowest order binary encoded logical quantum bits.

This inherent limitation can be overcome with a discrete-variable coding scheme. Therefore, such discrete-variable quantum bits are promising in fault-tolerant quantum computing. These advantages can be translated into practical benefits in real quantum information processing only when the lifetime of the encoded logical quantum bits exceeds the break-even point. However, this remains an elusive scientific result, although scholars have made sustained efforts toward this goal.

This time, the SDSU team has demonstrated a break-even point beyond QEC by performing a real-time feedback correction for discrete variable photonic quantum bits in a microwave cavity.

The main error of the logical quantum bit, i.e., the single photon loss, is mapped to the state of a nonlinear oscillator based on a Josephson junction that is decentrally coupled into the cavity and implemented as an auxiliary quantum bit by a continuous pulse involving a cleverly tailored combination of frequency components.

Since the driving frequency is targeted to the error space where the photon loss event occurs, perturbations on the logic quantum bits are highly suppressed when they remain in the encoded logic space. Another inherent advantage of this error syndrome detection is that the continuous drive protects the system from the dephasing noise of the auxiliary quantum bits.

Control of measurement error syndrome with frequency combs

The joint research team exploits the infinite-dimensional Hilbert space in microwave simple harmonic oscillator or bosonic mode systems to achieve redundant encoding and quantum error correction of quantum information. In superconducting quantum line systems, the quantum error correction scheme based on bosonic coding has the advantages of simple error types, easy error detection, good coherence performance, more efficient hardware, and easy implementation of feedback control.

In this research work, the research team has finally achieved logical quantum bits in the bosonic mode based on binomial encoding of discrete variables by developing quantum systems with high coherence performance, designing and implementing error symptom detection methods with low error rates, and improving and optimizing quantum error correction techniques experimentally, and extending the storage time of quantum information through a quantum error correction process repeated in real time, and the related results for the first time exceeds the best value in this system without error correction, i.e., breaks the break-even point.

This is also the first time in the world that the prolonged storage time of quantum information beyond the break-even point is achieved by active repetitive error detection and error correction process, which is of milestone importance.

The team demonstrated this procedure with the lowest-order binomial encoding and extended the lifetime of stored quantum information by 16% over the best physical quantum bits. A more important feature associated with this error detection procedure is that neither the logical space nor the error space needs to have definite parity, which allows for QEC encoding that can tolerate more than one photon loss.

Experimental performance of QEC operation. (a)-(d), Histograms of the real part of the process matrix for the encoding and decoding process. (b) Waiting time without QEC is about 105 μs; (c) cycle time for single-layer QEC operation is about 90 μs; (d) cycle time for two-layer QEC operation is about 180 μs. Compared with the uncorrected Fock state {|0⟩,|1⟩} encoding (black squares) with one layer of QEC (red triangles) and the corrected binomial encoding with two layers of QEC (blue circles) both exhibit a slow decay in process fidelity, which defines the break-even point of the system. The corrected binomial encoding with two layers of QEC improves the break-even point by a factor of 1.2, also by a factor of 2.9 over the uncorrected binomial encoding (yellow star), and by a factor of 8.8 over the uncorrected inverse quantum bits (green diamond).

In this research work, Zhongchu Ni, a PhD student at SUSTech, is the first author of the paper. Assistant Researcher Xu Yuan from SUSTech's Graduate School is the main corresponding author of the paper, Prof. Sun Lu Yan from Tsinghua University and Prof. Zheng Shibiao from Fuzhou University are the co-corresponding authors of the paper, and Academician Yu Dapeng from SUSTech is the final corresponding author. Other co-authors include Associate Researcher Song Liu, Associate Researcher Fei Yan, and Assistant Researcher Xiaowei Deng from SUSTech, Professor Changling Zou from University of Science and Technology of China, Researcher Haifeng Yu from Beijing Institute of Quantum Information Science, and Professor Zhenbiao Yang from Fuzhou University. The Institute of Quantum Science and Engineering, Southern University of Science and Technology is the first completer of the paper. The research work was supported by the Department of Science and Technology of Guangdong Province, Shenzhen Science and Technology Commission, National Natural Science Foundation of China, and Southern University of Science and Technology.

Link to the paper:

https://www.nature.com/articles/s41586-023-05782-6