P H O T O B Y L I N D A A . C I C E R O / S T A N F O R D U N I V E R S I T Y N E W S S E R V I C E

The machine at Stanford is far from the first to attack optimization problems by emulating the behavior of Ising spin glasses. D-Wave Systems, Google, Microsoft, and a number of universities and computing companies are focusing on designs that use quantum effects to drive the annealing process.

Explains McMahon, “Quantum an-
nealers are types of Ising machine. The
leading quantum-annealing technologies
are these superconducting circuits that use
magnetic flux and circulating current
rather than photons as the information
in their systems. It’s now a fairly advanced
technology compared to ours: D-Wave has
been around for almost 20 years now.”
The major problems facing build-
ers of computers that use the Ising
model are scale and connectivity. With-
out scale, digital computers will eas-
ily outpace quantum annealers and
other machines that exploit spin-glass
behavior. At the beginning of 2017, D-
Wave unveiled a machine that doubles
the number of qubits to several thou-
sand. Yet the D-Wave design is limited
in terms of connectivity.

A20TH-CENTURY THEORETICAL model of the way magne- tism develops in cooling solids is driving the devel- opment of analog computers that could deliver results with much less electrical power than today’s super-computers. But the work may instead yield improved digital algorithms rather than a mainstream analog architecture.

Helmut Katzgraber, associate pro-
fessor at Texas A&M in College Station,
TX, argues, “There is a deep synergy
between classical optimization, statisti-
cal physics, high-performance comput-
ing, and quantum computing. Those
things really go hand in hand. Nature is
the best optimizer out there. Lightning
typically chooses the path of least re-
sistance. A soap bubble will always give
you the minimal surface.”
“Maybe we should go back to what
we did in the 1930s and 1940s: we
built special-purpose computers,” adds
Katzgraber. The problem with such alter-
native architectures, he notes, is that the
technology for such analog machines is
at the level of digital computing in the
1940s. “Today we only have very limited
machines and limited experience.”
One physical process that lies at the
heart of a number of experimental ma-
chines is the annealing of a spin glass.
The focus of a model developed by phys-
icist Ernst Ising in the 1920s, a spin glass
represents the highly disordered state of
a hot magnetic material. In the initial
state, the spins are not aligned with each
other, but as the material cools, an an-
nealing process leads to the spins slowly
becoming aligned as the spins of indi-
vidual atoms flip up and down.

In Ising’s model, a cost matrix that
links each simulated atom to each of
the others influences how the spins
will align. The overall energy is cap-
tured in a Hamiltonian, a mathemati-
cal operator used in quantum me-
chanics. The operator represents the
sum of individual energy states in the
system. A prototype for one special-
purpose computer that uses the Ising
model is a long loop of fiber-optic ca-
ble in the E.L. Ginzton Laboratory at
Stanford University in California.
The photonic machine at Stanford
finds “approximate or exact solutions
to the Ising problem,” says Stanford
University researcher Peter McMahon.
“Phrased this way, it sounds very re-
strictive. It’s more general than that
one specific problem: it can be used for
quadratic binary optimization prob-
lems, but it’s not so general that it can
solve any optimization problem.”
The key is to develop a cost matrix
that encapsulates the parameters to
be optimized, and use that to drive the
Hamiltonian to its lowest energy state.
In principle, the physics-based simu-
lation can find optimal solutions to
certain problems in many fewer steps
than classical digital techniques, but it
is far from clear that the analog accel-
erators will prove to be faster than their
digital counterparts.
Optimization Search
Finds a Heart of Glass

Analog computing could provide greater efficiency, improved digital algorithms.

Technology | DOI: 10.1145/3077233 Chris Edwards

Stanford University visiting researcher Alireza Marandi (right) and post-doctoral scholar Peter McMahon inspect a prototype of a new light-based computer.