ETH physicists have modified one of the major schemes for quantum error
correction and put it into practice, demonstrating that they can
substantially prolong the lifetime of quantum states—a crucial ingredient
for future large-scale quantum computers.

In modern computing devices, literally billions of transistors work
restlessly in almost perfect harmony. The keys to producing near-perfect
computation from devices made from imperfect components are the use of
digitisation and error correction, with the latter encompassing procedures
to detect and rectify inaccuracies as they occur. The challenge of
preventing errors from accumulating is one that future quantum computers
have to face as well—in fact it forms the main barrier to realizing useful
computations. Alas, the tools that have been perfected for classical
computers cannot be applied directly to quantum computers, which play by
another set of rules, those of quantum mechanics. Ingenious solutions for
quantum error correction have been proposed over the past couple of decades,
and recently there has been encouraging progress towards implementing such
methods in state-of-the-art quantum computers. Writing in Nature Physics,
the group of Prof. Jonathan Home at the Institute for Quantum Electronics
report such an experimental realization—one that stands out by factoring in
important limitations of physically realistic devices and by being
relatively easy to implement compared to other proposed error-correction
schemes, thus increasing the relevance of the demonstration for practical
quantum computation.

### Allowing a quantum of error

The way information is processed in quantum computers differs fundamentally
from that in their classical counterparts. This opens up unique
computational capabilities, but also calls for novel strategies to deal with
errors that occur in the process. More specifically, quantum information
cannot be perfectly duplicated, and measurements inevitably alter the
fragile quantum states. Nevertheless, with some creative rethinking it is
possible to devise measurements that can tell us whether the quantum
information has been disturbed. As with classical error correction, the key
is to harness redundancy.

Among the innovative ideas that have emerged for quantum error correction,
the so-called Gottesman–Kitaev–Preskill (GKP) code is a particularly
promising one, using flexible control of a single oscillator to avoid having
to control many different individual physical carriers of quantum
information. It encodes discrete quantum information in the continuous space
of a quantum system, forcing it to be positioned at regularly spaced points
forming a comb with teeth at fixed intervals, effectively digitizing space
(see image below). Information is stored in the size of the comb teeth.
Small displacements of the comb in position can be corrected, so long as
they do not cause neighboring teeth to overlap. While this scheme was
proposed in 2001, an experimental demonstration of error correction with GKP
codes came only in 2020, but the degree of error correction that could be
achieved was somewhat limited. This is because the GKP code is exact only
for quantum states of infinite energy, whereas experiments naturally involve
finite-energy states. Brennan de Neeve, a doctoral student in the Home
group, Dr. Thanh-Long Nguyen, a postdoctoral researcher there, and Tanja
Behrle, another doctoral student, have now tackled just that issue.

### Coping with finiteness

The team used a platform in which quantum information is encoded in the
mechanical oscillator motion of a single trapped ion. This was the same
system in which the Home group pioneered the generation and control of
logical states of the GKP code. Building on these capabilities, de Neeve et
al. now designed and implemented a novel measurement scheme that is
optimized for finite-energy states. Their approach is relatively simple to
realize, in that it makes use of damping processes which avoid having to
measure the quantum state and subsequently apply classically controlled
feedback. Putting the new method into practice, they demonstrated efficient
correction of unwanted displacements in the motion of their quantum
oscillator. As a result, they extended the coherence time (in essence the
lifetime of the quantum state) by a factor of three, setting a benchmark for
quantum computing systems.

Such prolonged coherence times are important, as they translate directly
into more time for executing quantum computations, a key 'currency' when it
comes to practical devices. The work therefore addresses one of the grand
challenges in the field of quantum computing. Moreover, the new approach
uses variants of well-established techniques in the tool chest of
experimental quantum physics, inspiring confidence that it can be pushed
even further. Combined with progress on other fronts, this brings us ever
closer to eventually enabling quantum computers to perform calculations with
arbitrary precision, even if constructed from fault-prone components.

## Reference:

Brennan de Neeve et al, Error correction of a logical grid state qubit by
dissipative pumping, Nature Physics (2022).
DOI: 10.1038/s41567-021-01487-7

C. FlÃ¼hmann et al, Encoding a qubit in a trapped-ion mechanical oscillator,
Nature (2019).
DOI: 10.1038/s41586-019-0960-6

Shruti Puri, Noise phased out, Nature Physics (2022).
DOI: 10.1038/s41567-021-01486-8

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Physics