After spending the past two months on sabbatical, I've returned to a deluge of science that I had missed out on. Almost three years ago, a company called D-Wave made waves by announcing that it was about to unveil one of the first-ever functioning adiabatic quantum computers, a device it heralded as being capable of solving NP problems in P time—a claim that doesn't really hold up to scrutiny.

This piqued the interest of many about the actual applications and science behind quantum computers, and we at Nobel Intent dove in and tried to shine some light on the discussion. Even with a fully functional, scalable quantum computer, nobody's large integers are in danger of being factored in polynomial time—it has been shown that integer factorization, via Shor's algorithm, is solvable in bounded error quantum polynomial (BQP) time. So, quantum mechanicists and quantum computer theorists started looking for ways to improve upon the performance of quantum computers and arrived at a question only a theorist could come up with. What if the quantum computer was capable of traveling through time?

A paper that was published in the October 21st edition of Physical Review Letters (PRL) examines this very question. The writers attempt to see if a quantum computer that exists on a closed timelike circuit (CTC)—a timeline that travels to the past before looping back onto itself—experiences an increase in its computational ability. A previous paper in PRL this year suggested that it was possible for a CTC-assisted quantum computer to map a set of pure states into an orthogonal set of states, an impossibility in standard quantum mechanics. This would imply that a CTC would allow a quantum computer to distinguish two identical quantum states—the philosophical or physical meaning and implication of this being entirely unclear.

Aware that something must have been wrong—either with the procedure or assumptions of the previous work—the authors of this paper from the IBM Watson Research Laboratory and the Quantum Computing Department at the University of Waterloo revisit the problem with a highly critical and pedantic eye. Their new analysis shows that "CTCs do not improve state discrimination," contradicting what was previously reported. The problem now becomes how to reconcile these results. The answer lies in the fact that 2 + 2 doesn't always add up to 4.

In a linear system, the properties of a mixture are simply equal to the (weighted) sum of the properties of the individual components. In fact, quantum mechanics is mathematically founded on the idea of a linear set of equations and linear independence of solutions. It turns out that a CTC does not represent a linear operation, rather a nonlinear one where the outcome is not merely the sum of the components. Computationally, this means that a quantum computer traveling through a loop in time would only see a computational benefit with a specific subset of inputs, not the more general case of every possible input as has been previous postulated. For that general case to be possible, the operation of the computer looping in time would need to be linear.

The fact that quantum mechanics could have some nonlinearities has been soundly rebutted in past literature, but this is a new proposal which may shed new light onto the subject. It would also change the way we need to think about quantum problems: not only would the particles in a given system need to be considered, but every particle in the universe, even those that do not participate, would need to be taken into account. It would also mean that a complex problem of two or more systems would need to take into account the entire history of the universe that each subsystem exists in from the begining of time to the present to accurately calculate a result.

While this paper has, in my opinion, an excellently mind-bending postulate, it is not something that one needs to lose sleep over. It does highlight (again, in my opinion) why theory is so much more elegant than experimental work. Where else can entire papers and fields of study be carried out where no realistic quantum computer has ever been developed, and no method of time travel has ever been shown to be physically possible (note that is also has not been shown to be physically impossible), yet can work out what would happen if they had a time traveling quantum computer? Awesome.

Physical Review Letters, 2009. DOI: 10.1103/PhysRevLett.103.170502