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132 10 JULY 2020 • VOL 369 ISSUE 6500 sciencemag.org SCIENCE
their bits are so reliable that error
correction isn’t much used.
But a quantum computer will de-
pend on it, at least if it’s made of super-
conducting qubits. (Qubits made of
individual ions suffer less from noise,
but are harder to integrate.) Unfortu-
nately for developers, quantum me-
chanics itself makes their task much
harder by depriving them of their
simplest error-correcting tool, copy-
ing. In quantum mechanics, a no-
cloning theorem says it’s not possible
to copy the state of one qubit onto
another without altering the state
of the first one. “This means that
it’s not possible to directly translate
our classical error correction codes
to quantum error correction codes,”
says Joschka Roffe, a theorist at the
University of Sheffield.
Even worse, quantum mechanics
requires researchers to find errors
blindfolded. Although a qubit can
have a state that is both 0 and 1 at
the same time, according to quan-
tum theory, experimenters can’t
measure that two-way state with-
out collapsing it into either 0 or 1.
Checking a state obliterates it. “The
simplest [classical error] correction
is that you look at all the bits to see
what’s gone wrong,” Kuperberg says.
“But if it’s qubits then you have to find the
error without looking.”
Those hurdles may sound insurmount-
able, but quantum mechanics points to a
potential solution. Researchers cannot copy
a qubit’s state, but they can extend it to
other qubits using a mysterious quantum
connection called entanglement.
How the entangling is done shows just
how subtle quantum computing is. Prod-
ded with microwaves, the original qubit in-
teracts with another that must start in the
0 state through a “controlled not” (CNOT)
operation. The CNOT will change the state
of the second qubit if the state of the first
is 1 and leave it unchanged if the first qubit
is 0. However, the maneuver doesn’t actu-
ally measure the first qubit and collapse its
state. Instead, it maintains the both-ways
state of the first qubit while both changing
and not changing the second qubit at the
same time. It leaves the two qubits in a state
in which, simultaneously, they are both 0
and both 1.
If the original qubit is in, for example, a
30% 0 and 70% 1 state, physicists can link it
to other qubits to make a chain of, say, three
qubits that share an entangled state that’s
30% all three are 0 and 70% all three are 1.
That state is distinct from three copies of
the original qubit. In fact, none of the three
entangled qubits in the string possesses a
well defined quantum state of its own. But
now, the three qubits are completely cor-
related: If you measure the first one and it
collapses to 1, then the other two must also
instantly collapse to 1. If the first collapses
to 0, the others must also. That correlation
is the essence of entanglement.
With that bigger entangled state, scien-
tists can now keep an eye out for errors. To
do that, they entangle still other “ancillary”
qubits with the chain of three, one with first
and second qubits in the string and another
with the second and third. They then use
measurements on the ancillas to make the
quantum mechanical equivalent of parity
checks. For example, without breaking the
entanglement, noise can flip any one of
the three coding qubits so that its 0 and 1
parts get switched, changing the latent cor-
relations among all three. If researchers set
things up right, they can make “stabilizer”
measurements on the ancillary qubits to
probe those correlations.
Although measuring the ancillary qubits
collapses their states, it leaves the coding
qubits unperturbed. “These are specially
designed parity measurements that don’t
collapse the information encoded in the
logical state,” Roffe says. For example, if the
measurement shows the first ancilla is 0, itreveals only that the first and second
coding qubits must be in the same
state, but not which state that is. If
the ancilla is 1, then the measure-
ment reveals only that the coding
qubits must be in opposite states. If
researchers can find a flipped qubit
more quickly than the qubits tend to
fuzz out, they can use microwaves to
flip it back to its original state and
restore its coherence.
That’s just the basic idea. The
state of a qubit is more complex
than just a combination of 0 and 1.
It also depends on exactly how those
two parts mesh, which, in turn, de-
pends on an abstract angle called
the phase. The phase can range from
0° to 360° and is key to the wave-
like interference effects that give a
quantum computer its power. Quan-
tum mechanically, any error in a qu-
bit’s state can be thought of as some
combination of a bit-flip error that
swaps 0 and 1 and a phase flip that
changes the phase by 180°.
To correct both types, researchers
can expand into another dimension—
literally. Whereas a string of three
entangled qubits, with two ancillas
woven between them, is the small-
est array that can detect and correct
a bit-flip error, a three-by-three grid
of qubits, with eight interspersed ancillas, is
the simplest one that can detect and correct
both bit-flip and phase-flip errors. The logi-
cal qubit now resides in an entangled state
of the nine qubits—be thankful you don’t
have to write it out mathematically! Stabi-
lizer measurements along one dimension
of the grid check for bit-flip errors, while
slightly different stabilizer measurements
along the other dimension check for phase-
flip errors.
Schemes for pushing into two dimen-
sions vary, depending on the geometric ar-
rangement of the qubits and the details of
the stabilizer measurements. Nevertheless,
researchers’ road to error correction is now
clear: Encode a single logical qubit in a grid
of physical qubits and show that the fidelity
of the logical qubit gets better as the size of
the grid increases.
Experimenters have already made a start.
For example, in a Nature Physics study pub-
lished on 8 June, Andreas Wallraff at ETH
Zurich and colleagues demonstrated that
they could detect—but not correct—errors
in a logical qubit encoded in a square of
four qubits with three ancillary qubits.
But experimenters face a daunting chal-
lenge. Manipulating individual qubits
can introduce errors, and unless that er-
ror rate falls below a certain level, then GRAPHIC: C. BICKEL/SCIENCE0 1 0 1 0 10 10 1 0 1 0 10 1 0 1 0 1Parity measurementsError
correctionNoiseFlipped bitCopyingAn easy fix
In a conventional computer, a bit is a switch that can be set to either
0 or 1. To protect a bit, a computer can copy it. If noise then flips a
copy, the machine can find the error by making parity measurements:
comparing pairs of bits to see whether they’re the same or different.