A
photon-based method for demonstrating the advantage of quantum over
classical machines can handle photon loss, facilitating experiments.
A
race is on to build a quantum computer that solves difficult problems
much faster than a classical computer—a milestone dubbed quantum
supremacy [1].
Runners in this race, however, are faced with a hazy finish line, which
can move closer as quantum machines and algorithms improve or further
away as their classical counterparts catch up. An experiment led by
Jian-Wei Pan of the University of Science and Technology in China [2]
nudges the racers forward for now. Inspired by a theoretical proposal,
the researchers confirmed that a promising method for demonstrating
quantum supremacy, known as boson sampling with photons (Fig. 1),
produces useful output even as photons leak from the system. This means
that researchers don’t have to “toss away” the output of a sampling
experiment when photons are lost, as was previously assumed [3], allowing for faster computations and bringing a demonstration of quantum supremacy closer to reality.
When
will we have a useful quantum computer? To make the answer concrete,
consider the most famous quantum-computing algorithm—factoring large
prime numbers [4].
This task will likely require millions, and possibly billions, of
quantum bits (qubits) and an even larger number of the devices, or
“gates,” that manipulate the qubits. Since today’s most advanced quantum
computers have around 50 qubits, a quantum computer that could quickly
factor large numbers is probably a long way off.
APS/Alan Stonebraker
Figure 1: Boson sampling is a task that’s much more efficiently done on a quantum computer than a classical one. A boson-sampling device with photons takes an input of photons, allows them to interact for a period of time, and then measures their positions
But
a question with a more encouraging answer is this: what's the bare
minimum of quantum resources required to demonstrate the power of
quantum computing? Researchers have approached this question by using
so-called quantum sampling problems. These tasks generate random
outputs, or “samples,” with a particular probability distribution. While
this distribution isn’t necessarily useful, producing the samples is
relatively simple on a quantum machine. And, crucially, simulating the
same distribution of random outputs with purely classical computing
resources is proven (under some plausible conjectures) to be
exponentially slower.
Boson sampling [5], the subject of the Pan team’s work, is one of two main quantum-sampling approaches [6]. It involves three steps: prepare N
single bosons (usually photons), create a linear interaction among
them, and detect the locations of the bosons after the interaction (Fig.
1).
The boson positions measured after each experiment provide a random
sample, and the statistical distribution of multiple samples depends on
the nature of the interactions. The challenge for a classical simulation
would be to generate the same distribution as the quantum machine
assuming the same interactions between the bosons. Estimates suggest
that a boson-sampling device would need only about 100 photons before it
could produce a random output that would be impractical for a classical
device to simulate [7].
The current estimate, however, depends on a few factors. One is the
choice of algorithm for generating the sample on a classical computer;
such algorithms are continually being improved, which makes classical
machines tougher to beat. Another factor is that experimentalists are
getting better at eliminating the imperfections in a quantum machine
that slow it down. Finally, the proof that the boson-sampling problem is
exponentially hard for a classical computer can be adapted to describe
imperfect quantum machines. These modified proofs make demonstrations of
quantum supremacy involving many bosons more practical.
Pan and colleagues’ experiments are inspired by just such a modification [8].
In 2016, Scott Aaronson and Daniel Brod showed that a boson sampling
distribution with a fixed number of lost photons could still outperform
classical devices. Pan and colleagues’ work is a small-scale
proof-of-principle demonstration that boson sampling with this kind of
loss can still be done successfully on a quantum device. As a photon
source, the researchers used a semiconductor quantum dot embedded in a
multilayered cavity. The dot behaves like an artificial atom, emitting
single photons when excited by a laser; the cavity improves the rate and
quality of the single photons produced. The photons are then sent
through an array of 16 trapezoidal optical elements that are bonded
together. This array creates an effective network of pathways for the
photons, which experience a linear interaction with one another at
various points. Finally, single-photon detectors at the exit ports of
the network determine the positions of the arriving photons (the
sample). The network is expressly designed to prevent practically any
photon loss, with the majority of lost photons coming from
inefficiencies in the photon source and detectors.
Previous
boson sampling experiments like this one avoided the issue of loss by
postprocessing the data and rejecting samples that had too few photons [3].
Pan’s group, by contrast, analyzes samples made up of fewer photons
than had been sent by the source. By adjusting the way the photons are
fed into the optical network, the researchers could inject from 1 to 7
single photons. They then ensured the sampling task was working
correctly by assessing the distribution of detected photons with
statistical tests, adjusting these tests to apply to cases where fewer
photons arrive at the detector than left the source. The researchers
showed that many of these “lost photon” samples are useful, leading to a
dramatic improvement in the data acquisition rate. For example,
allowing for 2 out of 7 photons lost, the team can collect samples 1000
times per second—at least 10,000 times faster than if they had only
collected samples with zero photons lost.
As it
stands, this experiment is still far from producing an output that is
intractable for a classical computer to generate. More photons and lower
loss rates are required to reach that goal. In addition, Aaronson and
Brod’s proof rests on the assumption that a fixed number of photons are
lost in an experiment, a condition Pan’s team was able to meet in their
small-scale setup. But doing so with more photons may be tough, as
fixing the fraction, rather than the number, of photons lost is
experimentally more realistic. The real message of this experiment is to
not fear optical loss in boson sampling. With further theoretical and
experimental work, researchers will have a more complete picture of
boson sampling with loss, allowing them to forge new paths to a
demonstration of quantum supremacy.
This research is published in Physical Review Letters.
