Boson-Sampling-Inspired Quantum Metrology

Our group at Louisiana State University has teamed up with researchers at Macquarie University in Sydney and Boise State University in Boise to produce an new publication in Physical Review Letters, entitled, “Linear Optical Quantum Metrology with Single Photons: Exploiting Spontaneously Generated Entanglement to Beat the Shot-Noise Limit.” For regular readers of this blog, you will know that Boson Sampling is a new paradigm in quantum computing whereby single photons, inputted into a linear optical interferometer, can carry out a mathematical sampling problem that would be intractable on classical computer. The buzz surrounding Boson Sampling is that, unlike universal linear optical quantum computing, the experimental implementation requires no special quantum gates, like controlled-NOT gates, nor feed forward nor teleportation or any other fancy stuff. Identical single photons rattle around in the interferometer and they are sampled in the number basis when they come out. Sounds simple, but a classical machine cannot efficiently simulate the sampling output, whereas the linear optical device does this quite easily. For our recent review on Boson Sampling the reader is encouraged to go here.

In spite of all the excitement about Boson Sampling as a new paradigm for quantum information processing, the Boson Sampling problem has no know practical application to any mathematics problem anybody is interested in. In some ways the situation is similar to the late 1980s and early 1990s, before Shor’s invention of his factoring algorithm, when the first quantum algorithm shown to give an exponential speedup was the Deutsch-Jozsa (DJ) algorithm that allowed one to tell if a function was balanced or unbalanced. While a very nice result, nobody really gave a rat’s ass whether a function was balanced or unbalanced. It was however hoped that the DJ algorithm was just the tip of an iceberg and indeed the rest of the iceberg was revealed when Shor’s factoring algorithm was discovered. That was an (apparent) exponential speedup on a problem that people cared deeply about.

So too do we hope that Boson Sampling is just the tip of the iceberg when it comes to the power of linear optical interferometers, with simple single-photon inputs, to carry out tasks that are not only impossible classically but also of practical interest. In that direction our paper makes a frontal attack on the berg with a metrological ice axe. The idea emerged from the understanding that in Boson Sampling, an exponentially large amount of number-path entanglement is generated through the natural evolution of the single photons in the interferometer via repeated implementation of the Hong-Ou-Mandel effect at each beam splitter. It has been known for nearly 30 years the number-path entanglement is a resource for quantum metrology, beating the shot-noise limit, and so it was natural for us to ask if this hidden power in linear optics with single photon inputs might be put to work for a metrological advantage. Our paper shows that this is indeed the case.

To briefly summarize our scheme, we send a sequence of single photons into linear optical interferometer that contains an interferometric implementation of the Quantum Fourier Transform coupled with a bank of phase shifters with an unknown phase that is to be measured. Our signal consists of a sampling of the outputs tuned to the same sequence of single photons emerging from the exit ports. The signal-to-noise analysis was quite challenging as it involves the computation of the permanent of a large square matrix with complex entries. While in general this is classically intractable, to our surprise, something about the structure of the Quantum Fourier Transform seems to allow the permanent to be computed analytically in closed form. As least we conjecture this is so. We were able to eyeball a closed form formula for the permanent of a matrix of any rank and confirm it out to rank 20 or so numerically, but a rigorous mathematical proof of the permanent formula is still wanting.

Once we had the signal and variance analysis carried out, we were able to show (carefully counting resources) that the sensitivity of the device, which we christened the Quantum Fourier Transform Interferometer, is well below the classical shot-noise limit. It has been known for years that exotic number-path entangled states, such as N00N states, can beat the shotnoise limit, but N00N states are resource intensive to create in the first place, requiring either very strong Kerr nonlinearities or non-deterministic heralding. Here in our new paper we get super sensitivity for free from the natural evolution of single photons in a passive optical linear interferometer. This then seems to be the first example of the Boson Sampling paradigm providing a quantum advantage in an arena of importance, which is quantum metrology.

 Who knows what is left on this iceberg still yet unexplored?

UK National Strategy for Quantum Technologies

Just winding up a one-week trip to the UK where I attended the Bristol Quantum Information Technologies (BQIT) Workshop at the kind invitation of the organizers. There was some disagreement how the acronym BQIT should be pronounced but upon my arrival we instantly all agreed it should be B-QuIeT. The workshop was a lively set of short talks interspersed with panel discussions and it was the first time I heard in some detail about the new UK National Strategy for Quantum Technology from non-other than Sir Peter Knight himself, who was a speaker on one of the panels focusing on the UK Quantum Hubs Network. There was quite a bit of excitement in the air as Simon Benjamin (University of Oxford, Quantum Computing Hub) gushed effusively about writing a 12-page proposal that came in at £3 million per page! 

There are four hubs dotting the UK countryside from Scotland to England with a total five-year budget of £120M for all four of the hubs with foci in quantum communications, imaging, sensing, and computing. And to complement these hubs are at least three new quantum technologies doctoral training centers. The budget for the training centers was less clear but I suppose all together this is close to £200M for five years potentially renewable in five years for another five. And that is, folks, as they say, new money.

All this activity seems to be coordinated by the UK Quantum Technologies Strategic Advisory Board, chaired by Prof. David Delpy, which has laid out a vision for a coordinated strategy in quantum technologies development in the UK.

It is somewhat disheartening to see all of this activity in the UK from the perspective of a research in the US, where the congress and the president can’t even seem to pass any new budget at all from year to year. I wish the UK program well and I did hear that each hub has set aside funds for international collaborations and so I hope this will be the first of several trips to visit my quantum friends and colleagues on the far side of the big pond. 

For young researchers interested in doing PhD or postdoctoral work in quantum technologies, you should follow your noses and follow the money. The UK seems to be the place where the quantum of action is at these days. 

Guest Ghost Post: The Future of QIP: To parallelize or not?

This year’s Quantum Information Processing conference (QIP) was held in the beautiful and vibrant city of Sydney, Australia from the 12^th to the 16^th of January. Close to 225 researchers from across the world attended the conference. The talks were hosted at University of Technology Sydney (UTS). Runyao Duan led the local organizing committee, and its members were from UTS, University of Sydney, Macquarie University and University of Queensland. They did a splendid job in ensuring that the conference was a grand success.

The 18^th edition of QIP featured about 40 talks and 150 posters covering various important advances in quantum information processing over the past year. A detailed summary of all the talks presented at QIP can be found on the Quantum Pontiff blog http://dabacon.org/pontiff/?p=10785, where Aram Harrow and Steve Flammia were “live-blogging” the conference. In this report, I shall focus on the things not covered by Aram and Steve, especially on the business meeting.

A lot of buzz and anticipation prevailed around this year’s business meeting at QIP. This was largely due to the pending decision on the question of whether “to parallelize or not parallelize” QIP.  Here is some background on the issue. QIP, as it stands today, is a single session-track conference featuring two kinds of talks: 50-minute plenary talks and 30-minute talks. During a five-day period minus one free afternoon, this allows for about 40 talks during the entirety of the conference. However, the number of submissions to the conference has seen a steep increase over the years due to the explosion of research in quantum information processing. What began as a workshop with a few tens of submissions in the early nineties, QIP today receives several hundred submissions each year. Thus the acceptance rates at QIP are now terrifyingly low; the rate for this year’s QIP for a talk was just about 20%.

Each year the program committee has been faced with the increasingly difficult task of rejecting at least 20 to 30 good submissions which they think are just as good as some of the other talks that make the cut. This has led the steering committee to consider introducing parallel sessions with the view that it would allow for more talks. In order to hear the public opinion on the issue, Stephanie Wehner posted a survey on the Web for the QIP community. Stephanie presented the results of the survey at the business meeting. The public sentiment on the issue seemed largely in favor of parallel sessions. When the result of the survey was shared at the business meeting, however, a major concern was raised about the possible fragmentation of the community into sub-communities. In response to this concern, Peter Shor, spoke about how not parallelizing QIP at this point could have the same fragmenting effect at a much graver level. Peter pointed out the precedent of STOC and FOCS, where the latter remained a single session conference for a long time, while the computer science community had grown many fold in size. Peter noted that in due course of time, when certain factions of the community felt that they weren’t being sufficiently accepted at the conference, they decided to split away with their own conference, the STOC. This is already beginning to happen in the quantum information community with the birth of various conferences such as QCrypt, QEC, and Beyond I.I.D. in Information Theory. These conferences provide venues for topics that are becoming more marginalized and less fashionable at the larger QIP conference.

Nevertheless, it was also pointed out by the steering committee that parallel sessions, even if introduced, would only occur during certain sessions. For instance, the plenary talks would still be held in common, and therefore couldn’t result in a complete splitting of the community. At this point, the question of logistics surfaced regarding a single track for plenary sessions and two parallel sessions for other talks, namely the need to secure one big room and two small rooms at the conference venue, which could be more expensive. Barry Sanders, the lead organizer for QIP 2016, in his presentation about the conference venue at Banff (near Calgary, Canada), however guaranteed that this would not be an issue at next year’s QIP. From the pulse of things at this year’s QIP, it seems rather likely that we will see parallel sessions in next year’s edition. Yet, this is by no means a certainty.

Another development worth mentioning from the business meeting was the proposal for open refereeing of papers at QIP. Aram Harrow and Steve Flammia, who had already implemented such a scheme at TQC (Theory of quantum computation, communication and cryptography) 2014, put forth the proposal. Aram explained why he thought referee reports of QIP submissions should be available on the public domain. The real purpose cited was not the obvious ones---it was neither to make it open the reasons behind why a paper is accepted or rejected, nor to push referees to write reports according to what this year’s program committee chair Ronald de Wolf called the “golden rule” of refereeing, namely to write referee reports the way one would like his/her own paper to be reviewed. The real reason cited was rather simply to make available expert summaries and critiques, which could immensely benefit other researchers, especially the younger researchers, which otherwise go underutilized aiding in the publication decision process alone. Although the general perception about the idea was positive, it seems unlikely that the QIP steering committee would recommend the scheme as a whole to the program committee. Ronald and Andrew Doherty raised concern about how such a scheme could result in a huge extra burden on the already over-burdened program committee. However, it seems likely that, as an intermediate step, the program committee summaries of the accepted talks would be made available to the public at QIP 2016, as was done earlier at TQC 2014.

The business meeting also saw ETH Zurich and Microsoft Research bid for hosting QIP 2017. The public opinion seemed to be in favor of the ETH bid for 2017, while it seemed that Microsoft could potentially host QIP during the subsequent year, i.e., 2018.

Earlier, proceedings at QIP this year kicked off with tutorial sessions during the weekend in the lead-up to the conference. Entry to the tutorials was included as part of the conference registration. Itai Arad of CQT covered the local Hamiltonian problem (I couldn’t make this one due to flight delay.) The second speaker of the day was Roger Colbeck of Univ. of York, who discussed the topic of device independence in quantum information processing. Roger described the goal of the device independence model in the context of cryptography as to provide unconditional security while allowing for device failure or tampering, and discussed the various tools that go into proving security of protocols within the model. He also highlighted one of the main challenges of the approach as the need of protocols that allow for reuse of the devices while guaranteeing unconditional security. On the second morning, Krysta Svore of Microsoft gave a fascinating tutorial on the various components that go into the design and implementation of quantum software architecture for an automated control and programming of tomorrow’s large-scale quantum computers. Later, Alexandre Blais of Univ. of Sherbrooke delivered the final tutorial on superconducting qubits. Addressing a largely theoretical audience, Alexandre did a splendid job of describing the basic physics behind the superconducting transmon qubit. He also discussed the control and readout via strong coupling to a microwave resonator along with results from various recent experiments.

The social aspects of the conference included a banquet and a rump session. The banquet was a fancy affair, being held on a showboat. The Sydney weather, which had been dull and rainy until then, had moved to great, UV-rich sunshine just in time for the banquet. The boat set sail from the Sydney Darling Harbor around half past seven with plenty of food, beer, wine, and the awesome folks from the conference. Some spectacular views of the Sydney skyline in the magical twilight soon followed, which were a real treat. Despite being given numerous warnings from the organizers, many participants unfortunately “missed the boat”.

This year’s rump session was a fun ride with the lighter side of the QIP community. The session was held at the “Manning” bar in the University of Sydney. Steve Flammia introduced himself as the “MR---the Master of Rump” for the night. Among the speakers, John Smolin poked fun at the ensuing trend of adding the “quantum” suffix to literally anything in the world in the name of quantum information research. Later Daniel Gottesman decided to take the new proposal for open refereeing to a whole new level. While we’ve heard of double-blinded refereeing, where the identity of the authors is conceals from the referees, Daniel suggested triple and quadruple blinding, where the text of the paper is encrypted from the referee and where the talk is concealed from the audience, respectively.

From excellent and stimulating talks and posters, through the intriguing business meeting, to the fun-filled banquet and rump session, QIP 2015 had it all. Parallel sessions or not, you can’t help, but be excited about QIP 2016 already.

Kaushik P. Seshadreesan is a doctoral student in physics at Louisiana State University, working under the supervision of Jonathan P. Dowling and Mark M. Wilde. He will graduate with his PhD in quantum information theory and quantum metrology in May of 2015.

Linear optical quantum metrology with single photons --- Exploiting spontaneously generated entanglement to beat the shotnoise limit

Keith R. Motes, Jonathan P. Olson, Evan J. Rabeaux, Jonathan P. Dowling, S. Jay Olson, Peter P. Rohde

http://arxiv.org/abs/1501.01067

(Submitted on 6 Jan 2015)

Quantum number-path entanglement is a resource for super-sensitive quantum metrology and in particular provides for sub-shotnoise or even Heisenberg-limited sensitivity. However, such number-path entanglement has thought to have been resource intensive to create in the first place --- typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feed-forward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multi-photon walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer --- fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection --- is capable of significantly beating the shotnoise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology.