Scientists triple the lifetime of a quantum state through error correction
Recently, ETH Zurich improved a quantum error correction scheme based on Gottesman-Kitaev-Preskill (GKP) codes, thereby extending the lifetime of quantum states by a factor of three, which is of great significance for the realization of large-scale quantum computers in the future. The related results have been published in the journal Nature Physics [1]. This is also the second quantum error correction progress ZTH has made in two months. In December last year, another team at ZTH achieved the first automatic correction of errors in a quantum system.
The experimental platform in this paper
Quantum computers process information in fundamentally different ways than classical computers. This brings unique computing power, but also requires new strategies to deal with errors in the process. More specifically, quantum information cannot be fully replicated because measurements inevitably change fragile quantum states. With some creative rethinking, however, it may be possible to devise measurements that can tell us whether quantum information has been perturbed. As with classical error correction, the key is to exploit redundancy.
Among the innovative ideas for quantum error correction, so-called GKP codes are a particularly promising approach. In general, error-correcting codes implemented using a single physical qubit require the control of many independent systems, but codes built using quantum oscillators offer the possibility to perform error correction using a single physical entity. GKP codes use flexible control of a single oscillator to avoid controlling many different physical carriers of quantum information. Using GKP codes, discrete quantum information can be encoded in the continuous space of a quantum system, forcing it to lie at regularly spaced points, forming a regularly spaced comb of teeth, effectively digitizing the space (see figure below). Information is stored in comb size. Small shifts in comb position can be corrected as long as they do not cause adjacent combs to overlap.
Practical improvements to GKP codes
In GKP codes, discrete quantum information is encoded in the continuous space of the quantum system, forcing it to be positioned at regularly spaced points, forming regularly spaced comb teeth, effectively digitizing space. Image: Christa Flühmann, ETH Zurich / Shutterstock
This scheme was proposed in 2001, but experimental demonstrations of error correction using GKP codes did not appear until 2020, and the degree of error correction that can be achieved is limited. This is because GKP codes only apply to quantum states of infinite energy, whereas finite energy states are naturally involved in experiments. Doctoral student Brennan de Neeve, postdoctoral researcher Dr. Thanh-Long Nguyen and another doctoral student Tanja Behrle from the team of Professor Jonathan Home at the ETH Institute for Quantum Electronics have now solved the problem.
On the platform used by the team, quantum information is encoded in the mechanical oscillator motion of individual trapped ions. This is the same system for generating and controlling the logic states of GKP codes pioneered by the Home team in 2019 [2]. Building on these capabilities, de Neeve et al. designed and implemented a novel measurement scheme optimized for finite energy states. This method is relatively simple to implement because it exploits a damping process that avoids having to measure the quantum state and then apply classical control feedback. Using this method, they demonstrated efficient correction of excess displacements in the motion of quantum oscillators.
Quantum state lifetime tripled
The results showed that the team used square and hexagonal GKP codes to triple the coherence time of logical states (essentially the lifetime of quantum states).
For square codes, without error correction, each dataset X, Y, Z gets coherence times of 2.5(2), 2.2(2), and 2.5(2) ms, respectively, while with error correction, coherence times The time increased to 12.6(4), 8.6(3) and 12.3(5) ms. The shortest coherence time of the latter is 3.4 times the longest coherence time of the former, as shown in the figure below. For hexagonal codes, this number is also closer to 3 times.
For (a) square and (b) hexagonal finite GKP codes, <XL> (orange), <YL> (green) and <XL> (orange), <YL> (green), with stability (circle) and without stability (cross). ZL> (blue) logical readout. Each dataset is fitted with exponential decay. a) The quantum state lifetimes of square codes are 12.6(4), 8.6(3) and 12.3(5) ms (with error correction) and 2.5(2), 2.2(2) and 2.5(2) ms (without error correction) . b) For hexagonal codes, the corresponding lifetimes are 8.9(3), 6.2(3) and 9.6(4) milliseconds (with error correction) and 2.2(1), 2.1(2) and 2.4(2) milliseconds ( No error correction).
This extended coherence time is important because it directly represents more time to perform quantum computations. Therefore, this work addresses a major challenge in the field of quantum computing. In addition, this new approach uses variants of well-established techniques in the toolbox of experimental quantum physics. Combined with other advances, this brings us closer to finally enabling a quantum computer to perform computations with arbitrary precision, even if it is made of error-prone components.
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