Nature Achieving fully stable, long coherent, error-correcting logical quantum bits
The ambition to use quanta for computation is inconsistent with the fundamental phenomenon of decoherence. Quantum error correction (QEC) aims to counteract the natural tendency of complex systems to decoherence.
However, whether it is possible to use QEC to extend quantum coherence remains an open question. This time, V. V. Sivak (now at Google AI Quantum), M. H. Devoret, and others at Yale University (USA), in a paper in Nature, answer this question by showing a fully stable and error-corrected logical quantum bit.
Its quantum coherence is much longer than that of all the imperfect quantum components involved in the QEC process: with G = 2.27 ± 0.07 (G is defined as the ratio of the coherence time of an actively error-correcting logical quantum bit in the same system to that of the best passive quantum bit encoded in the same system, with G = 1 i.e. reaching the break-even point) the coherence gain reigns supreme.
The experiment builds on its theoretical foundation and demonstrates that quantum error correction is valid in practice after decades - validating the cornerstone assumptions of quantum computing.
This time, the Yale team demonstrated a new fully stable and error-correcting logical quantum bit with much longer quantum coherence than all incomplete quantum components of the QEC process, with a coherence gain of G = 2.27 ± 0.07.
Specifically, the team achieves this performance by combining innovations from several fields, including superconducting structures.
Achieving a single correctable logic quantum bit requires a physical system with a large state space that should accommodate the code subspace and its redundant copies, and when a physical error occurs, the logic information will be transmitted without distortion. This redundancy is inevitably associated with the additional operational cost of QEC, which is referred to as control overhead.
In order to find an efficient way to mitigate the harmful effects of overhead, the team used bosonic codes in resonant sub-state space as an alternative to the standard approach based on physical quantum bit registers. In the hybrid architecture, the two approaches are complementary, with quantum bit register codes built on logical quantum bits that are protected by effective underlying boson dynamics.
The team demonstrates full code stabilization and error correction for gain G = 2.27 ± 0.07, using Gottesman-Kitaev-Prekiel (GKP) encoding a logical quantum bit to a lattice state of an oscillator. The QEC of this code was previously implemented in superconducting circuits and trapped ions. In this work, the oscillator is the electromagnetic mode of a superconducting cavity whose quantum state is manipulated by transmitting auxiliary quantum bit elements (Figure 1a).
Fig. 1 Experimental system. a) The sample consists of a superconducting aluminum cavity and a sapphire chip with a transmon circuit, readout resonator and Purcell filter. b) The sample is cooled in a dilution chiller, controlled with microwaves and digital electronics. the QEC process is coordinated by a field-programmable gate array (FPGA), whose parameters are implemented on a graphics processing unit (GPU) of the RL agent for field optimization. c) Experimental Wigner function of the grid code for Δ = 0.34 measured after six QEC cycles.
The team then implemented a QEC scheme called "trickle-down" in this system to obtain real-time classical processing and measurement-based feedback, and trained the QEC circuit parameters in the field with reinforcement learning (RL) to ensure that they adapt to real error channels and control system defects.
At peak performance, the logical bubble error probability per QEC cycle is pY = (4.3 ± 0.4) × E-4 and pX = pZ = (1.81 ± 0.04) × E-3. With such low logical error probabilities, the team explores the QEC process on a time scale of thousands of cycles previously unattainable, and scrutinized the standard assumptions of QEC theory, such as the smoothness and correlation of error rates. Finally, the scientists performed error injection experiments to identify the major factors limiting logic performance and mapped the path toward the next generation of logical quantum bits.
Ultimately, the team more than doubled the lifetime of quantum information. Their error-correcting quantum bits survived for 1.8 milliseconds - things happen fast in the quantum realm.
The core idea behind the principle of the experiment is to implement artificial error-correcting dissipation, which effectively removes entropy from the system by preferentially correcting for frequent small errors without ignoring rare large errors. In contrast, trickle dissipation scheme 2 has the ability to correct all the same errors, but it cannot be corrected in a single step. Due to this simplification, this approach reduces the control overhead in the grid code.
Figure 2 QEC implementation and optimization
After training, the experimental team selected the best performing QEC circuit for further characterization and focused on the ability of the QEC to create a good quantum memory (i.e., to convert the effect of time passing into an identity channel that preserves all quantum bit states).
The higher excited states of the oscillator have shorter lifetimes due to spontaneous emission of boson enhancement. Therefore, as with any QEC code, the use of lattice states to encode quantum bits immediately reduces the fidelity.
Figure 3 System coherence.
After describing the logical quantum bits as quantum memory, the team investigated the properties of the QEC process. The measurements of the auxiliary quantum bits, called syndromes, indicate which random path the QEC process takes in each cycle.
From the dataset in Figure 4a, it can be observed that most of the results are g (green), which means that errors are rare. e random pattern of results (yellow) reflects errors that occur randomly. Most errors are small and, when corrected, leave a single isolated e result
The average value of the time function for each result is shown in Figure 4b. After about 10 cycles of initial state correction, the process enters a dynamic equilibrium lasting at least 100,000 cycles (the longest cycle measured here) with no significant increase in error rate over time. Detailed analysis shows that the QEC process is almost smooth.
In this dynamic equilibrium, the physical error excites the quantum state out of the code space. The competition between physical errors and error-correcting dissipation leads to a "hot" distribution among subspaces, the probability of which proves that the use of low-rank error-correcting dissipation in the experimental system is sufficient to prevent the accumulation of physical errors and lead to logical errors.
It was concluded that 97% of the errors were successfully corrected.
In this work, the Yale team used real-time error correction to achieve fully stable logical quantum bits that more than doubled the lifetime compared to the best passive quantum bit encoding in the system, marking the transition of QEC from a proof-of-principle to a practical tool for enhancing quantum memory.
In addition, this work improves on previous QEC experiments, and the keys to this achievement are, among other factors, the adoption of a model-free learning framework, improved transmon assisted quantum bit fabrication techniques and a new lattice-coded QEC protocol. By conducting additional experiments, the team has also identified core challenges that need to be addressed to ensure future progress on Grid Code QEC.
Regarding subsequent progress, the team said, "We expect to obtain considerable improvements by tuning the QEC process to target errors not only in the oscillator but also in the auxiliary quantum bits. Our QEC circuit is designed to be fault-tolerant to phase flipping errors in auxiliary quantum bits. In the transmon class of bits used here, the logic lifetime is 65 times less sensitive to phase flips in the auxiliary class of bits than it is to bit flips in the auxiliary class of bits. Future developments should include improving the robustness of auxiliary quantum bit flips: either through path-independent control or by employing auxiliary quantum bits with bias noise."
[1]https://www.nature.com/articles/s41586-023-05782-6
[2]https://phys.org/news/2023-03-qubit-life-key-theory-quantum.html
