INSIGHTS | PERSPECTIVESGRAPHIC: V. ALTOUNIAN/SCIENCEscience.org SCIENCEQUANTUM COMPUTING
Programming a quantum phase of matter
The ability to measure long-range entanglement may enable robust quantum memory
By Stephen D. BartlettA
t very low temperatures, some ma-
terials may condense into exotic
phases of matter, where quantum
entanglement becomes the domi-
nant feature governing their be-
havior. These quantum phases—a
world different from the ordinary states
of solid, liquid, gas, and plasma—exhibit
exotic properties such as quasiparticle ex-
citations that interfere with each other in
unusual ways. From an applica-
tion point of view, these quan-
tum phases may serve a key role
in increasing the robustness of
quantum memory devices—a
key component in quantum
computers. However, although
theorists have predicted the
existence of these quantum
phases under a variety of con-
ditions, quantum phases with
long-range entanglement are
extremely difficult to realize
experimentally. On pages 1237
and 1242 of this issue, Satzinger
et al. ( 1 ) and Semeghini et al.
( 2 ), respectively, provide direct
observation of these phases and
their key features by using a
coupled superconducting cir-
cuit and an array of atoms.
There are many kinds of
quantum phases, with supercon-
ductivity and Bose-Einstein con-
densates being two well-known
examples. Motivated by funda-
mental questions in condensed
matter physics, with potential implications
for quantum information systems, research-
ers have been studying the pattern of long-
range entanglement among spins. The
quantum correlations among spins can be
long range and “topological,” meaning that
the correlations are unchanged under con-
tinuous local deformations. For this reason,
such exotic quantum phases of matter are
said to be “topologically ordered.”
Among the topologically ordered quan-
tum phases, the most well studied are
those that break time-reversal symmetry,meaning that they would behave differ-
ently if time ran backward. A key experi-
mental signature of non–time-symmetric
topological phases is their robust edge
modes, which are persistent currents that
run along the outer edge of the material.
One such example is the fractional quan-
tum Hall effect, which led to the discovery
of a wealth of topological insulators and
superconductors. Conversely, quantum
computer architects are more interested in
topologically ordered phases that are sym-metric under time reversal because such
phases can be used for error correction
and therefore help protect quantum in-
formation from noise, perturbations, and
other deleterious effects.
However, because time-symmetric topo-
logical phases do not have edge modes, tra-
ditional methods cannot be used to probe
their long-range entanglement properties,
which is necessary for realizing their poten-
tial to be used for quantum error correction.
Because of the very nature of long-range
entanglement, one cannot learn about the
material’s properties by examining a local
region but must instead probe quantum
correlations that traverse across the entire
volume. Observing such nonlocal propertiesof a system requires exquisite control of the
individual quantum constituents together
with entangling interactions and precise
measurements. This level of control over
the individual components of a complex,
many-component quantum system has only
recently become possible thanks to state-of-
the-art, albeit still rudimentary, quantum
computing devices.
Satzinger et al. use a nascent quantum
processor that consists of a two-dimen-
sional array of 31 coupled superconducting
quantum devices. The proces-
sor, known as Sycamore, made
headlines in 2019 by claiming
“quantum supremacy,” or the
ability to perform certain com-
puting tasks faster than a con-
ventional supercomputer ( 3 ).
By executing a short quantum
program, Satzinger et al. used
Sycamore to stitch together
the lowest-energy state of the
toric code ( 4 )—the canonical
example of a topologically or-
dered quantum phase that can
be used for quantum error cor-
rection. This together with an-
other short quantum program
allowed long-range entangle-
ment to be measured. They also
created additional programs to
simulate the creation of quasi-
p a r t i c l e s a n d t o p e r f o r m a q u a n -
tum interference experiment
that illustrates the expected
behavior of the quasiparticles.
The authors also demonstrate
that quantum information can
be encoded into the toric code, protect-
ing it from errors, and that this quantum
information can be subsequently read out
again. These properties illustrate how the
toric code may become the central pillar in
an approach to contain errors when scal-
ing up the quantum architecture.
Semeghini et al. report on a different
experiment that shares the goal of creat-
ing and exploring the properties of a topo-
logically ordered phase related to the toric
code. Their experiment uses a quantum
simulator consisting of 219 atoms arranged
on a two-dimensional lattice by using opti-
cal tweezers. By controlling the interaction
between neighboring atoms, the lattice is
coaxed into a topologically ordered phase.Centre for Engineered Quantum Systems, School of
Physics, University of Sydney, Sydney NSW, Australia.
Email: [email protected]1200 3 DECEMBER 2021 • VOL 374 ISSUE 6572Knitting a quantum topology
Shown is an artist’s concept of how topological phases can be
constructed by using quantum processors. The circuitry on the left
represents a quantum circuit, which can be controlled to form specific
patterns of long-range entanglement. The patterns of long-range
entanglement—the hallmark of topological quantum phases—are indicated
on the right by the wavy lines, of which some form closed loops and some
have open strings extending out to the edge.