YSM Issue 93.2

second approach: engineering qubits
to have properties that make them less
susceptible to noise.
Building Better Qubits
Ultimately, the researchers would develop
a novel type of superconducting qubit better
protected against noise, which Devoret
and coworkers recently reported. The
new design is based on a proposed circuit
element that allows only pairs of Cooperpairs
of electrons to tunnel across the circuit.
“It is an elaboration on the transmon and
fluxonium qubits that we had previously
worked on,” noted Devoret.
The idea of building qubits from
superconducting circuits was first proposed
in 1997; progress in the field followed
rapidly. In such quantum electromagnetic
circuits, charge carriers are pairs of bound
electrons—known as Cooper pairs—which
may quantum mechanically tunnel through
a junction. The quantum mechanical states
of the circuit can be labelled by the number
N of Cooper pairs that tunnel. Although
these circuits are macroscopic objects—
made up of many millions of electrons and
atoms—the number of effective degrees
of freedom is quite small. This gives
superconducting qubits a relatively simple
energy spectrum and is why these systems
are often referred to as artificial atoms.
The transmon qubit is one such type of
superconducting qubit, and it is the qubit
of choice for many of the commercial
players in the field of quantum information,
including IBM, Rigetti, and Google. It
consists of a nonlinear inductance—the
Josephson junction, marked by a crossed
box—in parallel with a capacitor, where
the charging energy of the circuit is much
smaller than the so-called tunnelling energy.
The transmon has a oscillating potential
energy U = EJ cos(φ), where φ is the
superconducting phase in the circuit, and E J
is the tunneling energy for the Cooper pairs
across the junction. “The Josephson junction
is very precious [in superconducting
quantum computing] because it is the
only non-dissipative [lossless] nonlinear
element we have,” explained Xu Xiao, one
of the researchers on the project. “The
cosine potential is therefore the only kind of
nonlinearity we usually have access to,” Xiao
continued. This nonlinearity—stemming
from the cosine potential of the Josephson
junction—is necessary to ensure that the
(frequency) level-spacing is unequal; this
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makes it possible to address only the lowest
two-levels as a qubit, without exciting the
higher energy level states.
The proposed “two-Cooper-pair” qubit
includes a novel circuit element which is
itself composed of two Josephson junctions
in a loop. The current through this loop is
controlled by an external magnetic field
or flux, which, when tuned carefully, gives
rise to an effective potential energy term
of the form U = E J
cos(2φ), i.e., it now has
two energy wells, rather than one. Thus, by
connecting several Josephson junctions, it
is possible to engineer an effective potential
that would not otherwise have been realizable
using a single transmon qubit alone.
The “cos(2φ)” potential reflects the feature
that only pairs of Cooper-pair electrons can
tunnel across the circuit element at a time.
It follows that the number N of Cooperpairs
that have tunneled must have constant
parity (i.e., be even or odd), leading to two
different ground states (of equal energy but
opposite parity). These degenerate ground
states—of equal energy—can be used to
store quantum information in a way that
is resistant towards noise. Like discussed
earlier, this system protects its quantum
information by distributing it across more
than one state. “In experiments, there are
various noise channels, which couple to
the system via some operator. Because of
the special parity of this new potential,
transitions via many such noise channels
between the logical zero and one states are
prohibited,” Xiao said. The researchers at
Qulab tested this new design in simulations
to show that the characteristic lifetimes of
the “two-Cooper-pair” qubit are competitive
with other state-of-the-art implementations,
at around one millisecond. “This [result]
shows how much we can gain … it seems
like if we build more complex circuits, we
could go a long way towards building better
qubits,” Devoret said.
Outlook and Implications
“I think the field as a whole is realizing
how to exploit the specific features of a
quantum system to store information,” said
Xiao, when reflecting on the significance
of their result. “This work is theoretically
quite a successful tactic in understanding
how we go from a circuit design to a
desired Hamiltonian [a mathematical
description of a quantum system], and
then to understanding why it is robust,”
he continued. “Even though this may not
be the ultimate qubit used in a generic
quantum computer, it still educates us a lot
about what types of resources we have.”
Engineering qubits with better coherence
properties can be thought of as a passive form
of error correction, in contrast to the explicit
active quantum error correction protocols
described earlier. “Actually, both methods
are needed,” Devoret said, referring to two
other articles from Qulab to be published
soon. These both try to implement an active
QEC, via two other types of qubit: the Kerr-
Cat qubit (that encodes information in
the phase space of a harmonic oscillator)
and the bridge-state qubit. “This research
takes place on various fronts; you get here
an example of a concerted effort [in our
group] to improve quantum information
science,” Devoret continued. Indeed, as the
field continues to progress, each of these
developments will be crucial steps towards
ultimately realizing a scalable and faulttolerant
quantum computing architecture—
an idea which, unlike in decades prior, now
seems within reach. ■
A R T B Y E L L I E G A B R I E L
ABOUT THE AUTHOR
Physics
SHOUMIK CHOWDHURY
SHOUMIK CHOWDHURY is a junior in Saybrook College studying Mathematics
and Physics. In addition to writing for YSM, he works on research at the Yale
Quantum Institute and Yale Quantronics Lab and is also co-president of the
Society of Physics Students at Yale.
THE AUTHOR WOULD LIKE TO THANK Professor Michel Devoret and Xu Xiao for
their time and enthusiasm for talking about their research.
FURTHER READING
Smith, W.C., Kou, A., Xiao, X., Vool, U., & Devoret, M.H. (2020). Superconducting circuit
protected by two-Cooper-pair tunneling. npj Quantum Inf 6(8). https://doi.org/10.1038/
s41534-019-0231-2
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September 2020 Yale Scientific Magazine 19