YSM Issue 93.4 Full Magazine

FOCUS
Quantum Coupling
of different such QEC codes have
been theorized, but not all have been
practically implemented.
Revisiting The GKP Algorithm
IMAGE COURTESY OF THE YALE QUANTRONIC LABS
A photograph of Yale’s Quantronic Laboratory (QLab) Team
All the hype (and troubles) surrounding
quantum computers stems from the
fundamentally different manner in which
a quantum computer operates. While your
laptop (a ‘classical’ computer) uses the
principles of classical physics to operate,
a quantum computer exploits seemingly
unintuitive quantum phenomena to
perform its computations. Investigating
how these quantum phenomena can be
leveraged in a quantum computer is at the
heart of the mission of Yale’s Quantronics
Laboratory (QLab). “The laws of quantum
physics are radically different from the
laws of classical physics, so quantum
computers pose new challenges that
one does not encounter with classical
computers,” said Michel Devoret, F.W.
Beinecke Professor of Applied Physics,
QLab principal investigator, and coauthor
of the research.
Correcting Errors in Quantum Computing
Among the most significant of these
challenges that the QLab attempts to tackle
arises due to the curious phenomenon of
quantum decoherence, wherein quantum
information is lost. Just as classical
computers store information using bits
(binary values of 0 and 1), quantum
computers utilize qubits (quantum
bits). Unintuitively, these qubits can
take on a combination (superposition)
of binary values which are encoded
by their wavefunctions; it is these
wavefunctions that are manipulated
while performing computations.
‘When a qubit is encoded in a physical
system, its wavefunction interacts with
the environment, and the information it
stores tends to get corrupted in a process
known as quantum decoherence,” said
Alec Eickbusch, the co-lead author and
a graduate student at the QLab. Since it
is impossible in practice to completely
isolate a qubit, quantum decoherence
tends to quickly scramble the qubit,
destroying its information in a matter of
microseconds. “In a quantum computer,
we need to find a way to give a qubit a
longer lifetime,” Eickbusch said.
Unsurprisingly, prolonging a qubit’s
lifetime is much easier said than done. This
goal is the focus of quantum error correction
(QEC), which seeks to correct for errors
stemming from quantum decoherence
and other sources. In classical computers,
error correction, in the very unlikely
circumstance that it is required, is relatively
simple: all one needs is redundant copies
of bits. Any error causing a bit to change
value is easily detected and rectified by
observing the values of its copies.
Alas, quantum physics does not allow
for such a straightforward solution.
The aptly named ‘no-cloning theorem’
disallows the creation of independent,
identical copies of quantum states. Even
more frustratingly, checking whether
the encoded information in a qubit has
changed requires one to measure that
state of the qubit, which itself alters the
qubit. With such enormous roadblocks,
QEC seemed an impossible feat, until
MIT professor Peter Shor developed a
roundabout technique (a “code”), which
corrected errors in a “logical qubit” that
was made of a collection of ordinary
(“physical”) qubits. Since then, a number
The QLab team chose to focus on a
particular code devised in 2001 called
the GKP code, rather creatively named
after the initials of its theorists: Daniel
Gottesman, Alexei Kitaev and John
Preskill. “The GKP algorithm was a
very ingenious form of error correction,
developed ahead of its time,” Devoret
said. It relies on the principle that
quantum noise - the cause of errors in a
qubit - is local: it affects different parts
of a system differently. Therefore, if
information is stored non-locally, it
can be recovered in spite of noise.
Devoret uses an analogy to explain
the basis behind the GKP algorithm:
“Suppose you have two boxes put close
together, with a hole in them to allow
them to ‘communicate.’ If a bit is stored
by placing a ball in either the left (0) or
the right (1) box, then shaking the system
(introducing ‘noise’) may cause the ball
to move between boxes, thus changing
the bit stored. However, if the boxes are
placed far away (‘non-local storage’), then
the ball will remain in its box and the bit
will be preserved in spite of the system
being shaken. Similarly, the GKP code
provides a way to put the 0 and 1 of a
logical qubit as far apart in ‘phase space’
as possible, therefore preventing errors to
as large an extent as possible.
Although the GKP code has been around for
nearly two decades, it was believed to be too
impractical to physically realize in a laboratory
setting. However, in the decades since, the
development of better instrumentation has
allowed the QLab team to recognize that
implementing the GKP code was “very
possible, using tricks of superconducting
circuits”—the quantum mechanical apparatus
that hosts the qubits they manipulate.
Eickbusch outlined the two-year research
journey by separating it into three rough
stages. First, the team set about crafting
simulations to determine whether their
idea would work in practice. Then, they
spent time in the cleanroom, building,
tweaking, and debugging their quantum
superconducting circuits. Finally, with
20 Yale Scientific Magazine December 2020 www.yalescientific.org