The device in the photomicrograph was used to run the first solid-state demonstration of Shor’s algorithm. It is made up of four phase qubits and five superconducting resonators, for a total of nine engineered quantum elements. The quantum processor measures one-quarter inch square. Credit: UCSB |
Computing
prime factors may sound like an elementary math problem, but try it
with a large number, say one that contains more than 600 digits, and the
task becomes enormously challenging and impossibly time-consuming. Now,
a group of researchers at UC Santa Barbara has designed and fabricated a
quantum processor capable of factoring a composite number—in this case
the number 15—into its constituent prime factors, 3 and 5.
Although
modest compared to a 600-digit number, the achievement represents a
milestone on the road map to building a quantum computer capable of
factoring much larger numbers, with significant implications for
cryptography and cybersecurity. The results are published in the advance
online issue of the journal Nature Physics.
“Fifteen
is a small number, but what’s important is we’ve shown that we can run a
version of Peter Shor’s prime factoring algorithm on a solid state
quantum processor. This is really exciting and has never been done
before,” said Erik Lucero, the paper’s lead author. Now a postdoctoral
researcher in experimental quantum computing at IBM, Lucero was a
doctoral student in physics at UCSB when the research was conducted and
the paper was written.
“What
is important is that the concepts used in factoring this small number
remain the same when factoring much larger numbers,” said Andrew
Cleland, a professor of physics at UCSB and a collaborator on the
experiment. “We just need to scale up the size of this processor to
something much larger. This won’t be easy, but the path forward is
clear.”
Practical
applications motivated the research, according to Lucero, who explained
that factoring very large numbers is at the heart of cybersecurity
protocols, such as the most common form of encoding, known as RSA
encryption. “Anytime you send a secure transmission—like your credit
card information—you are relying on security that is based on the fact
that it’s really hard to find the prime factors of large numbers,” he
said. Using a classical computer and the best-known classical algorithm,
factoring something like RSA Laboratory’s largest published
number—which contains over 600 decimal digits—would take longer than the
age of the universe, he continued.
A
quantum computer could reduce this wait time to a few tens of minutes.
“A quantum computer can solve this problem faster than a classical
computer by about 15 orders of magnitude,” said Lucero. “This has
widespread effect. A quantum computer will be a game changer in a lot of
ways, and certainly with respect to computer security.”
So,
if quantum computing makes RSA encryption no longer secure, what will
replace it? The answer, Lucero said, is quantum cryptography. “It’s not
only harder to break, but it allows you to know if someone has been
eavesdropping, or listening in on your transmission. Imagine someone
wiretapping your phone, but now, every time that person tries to listen
in on your conversation, the audio gets jumbled. With quantum
cryptography, if someone tries to extract information, it changes the
system, and both the transmitter and the receiver are aware of it.”
To
conduct the research, Lucero and his colleagues designed and fabricated
a quantum processor to map the problem of factoring the number 15 onto a
purpose-built superconducting quantum circuit. “We chose the number 15
because it is the smallest composite number that satisfies the
conditions appropriate to test Shor’s algorithm—it is a product of two
prime numbers, and it’s not even,” he explained.
The
quantum processor was implemented using a quantum circuit composed of
four superconducting phase qubits—the quantum equivalents of
transistors—and five microwave resonators. The complexity of operating
these nine quantum elements required building a control system that
allows for precise operation and a significant degree of automation—a
prototype that will facilitate scaling up to larger and more complex
circuits. The research represents a significant step toward a scalable
quantum architecture while meeting a benchmark for quantum computation,
as well as having historical relevance for quantum information and
cryptography.
“After
repeating the experiment 150,000 times, we showed that our quantum
processor got the right answer just under half the time” Lucero said.
“The best we can expect from Shor’s algorithm is to get the right answer
exactly 50% of the time, so our results were essentially what we’d
expect theoretically.”
The
next step, according to Lucero, is to increase the quantum coherence
times and go from nine quantum elements to hundreds, then thousands, and
on to millions. “Now that we know 15=3×5, we can start thinking about
how to factor larger—dare I say—more practical numbers,” he said.
