Two physicists, from EPFL and Columbia University, have introduced an
approach for simulating the quantum approximate optimization algorithm using
a traditional computer. Instead of running the algorithm on advanced quantum
processors, the new approach uses a classical machine-learning algorithm
that closely mimics the behavior of near-term quantum computers.

In a paper published in Nature Quantum Information, EPFL professor Giuseppe
Carleo and Matija MedvidoviÄ‡, a graduate student at Columbia University and
at the Flatiron Institute in New York, have found a way to execute a complex
quantum computing algorithm on traditional computers instead of quantum
ones.

The specific “quantum software” they are considering is known as Quantum
Approximate Optimization Algorithm (QAOA) and is used to solve classical
optimization problems in mathematics; it’s essentially a way of picking the
best solution to a problem out of a set of possible solutions. “There is a
lot of interest in understanding what problems can be solved efficiently by
a quantum computer, and QAOA is one of the more prominent candidates,” says
Carleo.

Ultimately, QAOA is meant to help us on the way to the famed “quantum
speedup”, the predicted boost in processing speed that we can achieve with
quantum computers instead of conventional ones. Understandably, QAOA has a
number of proponents, including Google, who have their sights set on quantum
technologies and computing in the near future: in 2019 they created
Sycamore, a 53-qubit quantum processor, and used it to run a task it
estimated it would take a state-of-the-art classical supercomputer around
10,000 years to complete. Sycamore ran the same task in 200 seconds.

“But the barrier of “quantum speedup” is all but rigid and it is being
continuously reshaped by new research, also thanks to the progress in the
development of more efficient classical algorithms,” says Carleo.

In their study, Carleo and MedvidoviÄ‡ address a key open question in the
field: can algorithms running on current and near-term quantum computers
offer a significant advantage over classical algorithms for tasks of
practical interest? “If we are to answer that question, we first need to
understand the limits of classical computing in simulating quantum systems,”
says Carleo. This is especially important since the current generation of
quantum processors operate in a regime where they make errors when running
quantum “software”, and can therefore only run algorithms of limited
complexity.

Using conventional computers, the two researchers developed a method that
can approximately simulate the behavior of a special class of algorithms
known as variational quantum algorithms, which are ways of working out the
lowest energy state, or “ground state” of a quantum system. QAOA is one
important example of such family of quantum algorithms, that researchers
believe are among the most promising candidates for “quantum advantage” in
near-term quantum computers.

The approach is based on the idea that modern machine-learning tools, e.g.
the ones used in learning complex games like Go, can also be used to learn
and emulate the inner workings of a quantum computer. The key tool for these
simulations are Neural Network Quantum States, an artificial neural network
that Carleo developed in 2016 with Matthias Troyer, and that was now used
for the first time to simulate QAOA. The results are considered the province
of quantum computing, and set a new benchmark for the future development of
quantum hardware.

“Our work shows that the QAOA you can run on current and near-term quantum
computers can be simulated, with good accuracy, on a classical computer
too,” says Carleo. “However, this does not mean that alluseful quantum
algorithms that can be run on near-term quantum processors can be emulated
classically. In fact, we hope that our approach will serve as a guide to
devise new quantum algorithms that are both useful and hard to simulate for
classical computers.”

## Reference:

MedvidoviÄ‡ M, Carleo G. Classical variational simulation of the Quantum
Approximate Optimization Algorithm. npj Quantum Inf. 2021;7(1):1-7.
doi:10.1038/s41534-021-00440-z

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