If you think testing a chip with a gazillion transistors is a challenge, try testing a handful of qubits in the quantum computing world. To confirm all the possible states of just eight qubits needs four billion or so measurements.
The problem of characterization, as it is known, is the target of a technique developed by a team from three universities (Queensland University, MIT and Princeton), along with SC Solutions. In a paper published in March’s Physical Review Letters, the researchers described an algorithm to drastically reduce the number of characterizations needed to test qubit state using a statistical sampling technique.
UQ’s Dr Allesandro Fedrizzi, co-author of the paper, says the research has “found a way to test quantum devices efficiently, which will help transform them from small-scale laboratory experiments to real-world applications.”
The problem arises, he told El Reg, because unlike a bit that can only have two values (one and zero), a qubit can live in a superposition of the two, simultaneously possessing both values.
Even worse: “They [qubits] can also be entangled, which means that any number of qubits can be in a superposition of different states.”
It is this property that makes quantum computers highly efficient for certain classes of problems – most notably factoring very large prime numbers, because it can process simultaneously a large number of inputs that would have to be given one-by-one to a “classical” computer.
“The fact that a quantum computer (or any quantum device – a quantum sensor, for example) can be in so many states means that, if one is to fully characterize it, one has to feed it all the possible input states and measure all possible output states.”
For an eight-bit – sorry, eight qubit – machine, we arrive at billions of measurements required because, as Dr Fedrizzi told El Reg: “Every qubit added to the system increases the exponent of the required measurements by 4 (the scaling goes as o(2^(4N)), where N is the number of qubits.”
(Since someone else is bound to ask this question, El Reg also asked Dr Fedrizzi this question: Isn’t the number of possible states of a quantum such as a photon pretty much infinite? His response: “Yes … the photon can be in any superposition of its basis states. We would write that as α|0>+exp(iφ)β|1>, where the parameters α, β and φ can be anything between 0 and 1. A photon, encoded as a qubit, can only carry one bit of information, though.”
I think that means you can get away with assuming less-than-infinite possible states to test.)
Instead of testing all possible states, the University of Queensland researchers used a statistical sampling approach to characterization. In their “compressive testing”, he said they reduced the 576 test needed for a two-qubit photonic computer down to 18.
“We picked 18 random configurations, and were still able to get almost the same information as if we had used all 576,” he said.
Think of it as analogous to product testing: rather than check every single product coming off a manufacturing line, a manufacturer tests sufficient products to yield a good statistical sample.
“The largest systems that anyone has characterized so far are just two or three qubits,” Dr Fedrizzi told El Reg. By compressing the number of measurements required to characterize a quantum system, he said, full characterization of an eight-bit laboratory system is now feasible.
As quantum computers move slowly out of the laboratory, they’ll also need to be characterized to perform real-world applications, so techniques such as this will grow in importance as quantum computers become more feasible.
Members of the team which developed the compressive testing also included Dr Marcelo de Almeida, Professor Andrew White and PhD student Matthew Broome from Queensland University, along with the study’s main author, Dr Alireza Shabani from Princeton University, Dr Robert Koust from SC Solutions, Dr Masoud Mohseni from MIT, and Professor Hershel Rabitz of Princeton.
*Not Safe For Maths-Phobics ®