## QIP 2015 Return of the Live-blogging, Day 1

Jan 14 update at the end.

The three Pontiffs are reunited at QIP 2015 and, having forgotten how painful liveblogging was in the past, are doing it again. This time we will aim for some slightly more selective comments.

In an ideal world the QIP PC would have written these sorts of summaries and posted them on scirate, but instead they are posted on easychair where most of you can’t access them. Sorry about this! We will argue at the business meeting for a more open refereeing process.

The first plenary talk was:

### Ran Raz (Weizmann Institute) How to Delegate Computations: The Power of No-Signaling ProofsTR13-183

Why is the set of no-signalling distributions worth looking at? (That is, the set of conditional probability distributions $p(a,b|x,y)$ that have well-defined marginals $p(a|x)$ and $p(b|y)$.) One way to think about it is as a relaxation of the set of “quantum” distributions, meaning the input-output distributions that are compatible with entangled states. The no-signalling polytope is defined by a polynomial number of linear constraints, and so is the sort of relaxation that is amenable to linear programming, whereas we don’t even know whether the quantum value of a game is computable. But is the no-signalling condition ever interesting in itself?

Raz and his coauthors (Yael Kalai and Ron Rothblum) prove a major result (which we’ll get to below) about the computational power of multi-prover proof systems where the provers have access to arbitrary non-signalling distributions. But they began by trying to prove an apparently unrelated classical crypto result. In general, multiple provers are stronger than one prover. Classically we have MIP=NEXP and IP=PSPACE, and in fact that MIP protocol just requires one round, whereas k rounds with a single prover is (roughly) within the k’th level of the polynomial hierarchy (i.e. even below PSPACE). So simulating many provers with one prover seems in general crazy.

But suppose instead the provers are computationally limited. Suppose they are strong enough for the problem to be interesting (i.e. they are much stronger than the verifier, so it is worthwhile for the verifier to delegate some nontrivial computation to them) but to weak to break some FHE (fully homomorphic encryption) scheme. This requires computational assumptions, but nothing too outlandish. Then the situation might be very different. If the verifier sends its queries using FHE, then one prover might simulate many provers without compromising security. This was the intuition of a paper from 2000, which Raz and coauthors finally are able to prove. The catch is that even though the single prover can’t break the FHE, it can let its simulated provers play according to a no-signalling distribution. (Or at least this possibility cannot be ruled out.) So proving the security of 1-prover delegated computation requires not only the computational assumptions used for FHE, but also a multi-prover proof system that is secure against no-signalling distributions.

Via this route, Raz and coauthors found themselves in QIP territory. When they started it was known that

• MIPns[2 provers]=PSPACE [0908.2363]
• PSPACE $\subseteq$ MIPns[poly provers] $\subseteq$ EXP [0810.0693]

This work nails down the complexity of the many-prover setting, showing that EXP is contained in MIPns[poly provers], so that in fact that classes are equal.

It is a nice open question whether the same is true for a constant number of provers, say 3. By comparison, three entangled provers or two classical provers are strong enough to contain NEXP.

One beautiful consequence is that optimizing a linear function over the no-signalling polytope is roughly a P-complete problem. Previously it was known that linear programming was P-complete, meaning that it was unlikely to be solvable in, say, log space. But this work shows that this is true even if the constraints are fixed once and for all, and only the objective function is varied. (And we allow error.) This is established in a recent followup paper [ECCC TR14-170] by two of the same authors.

### Francois Le Gall. Improved Quantum Algorithm for Triangle Finding via Combinatorial ArgumentsabstractarXiv:1407.0085

A technical tour-de-force that we will not do justice to here. One intriguing barrier-breaking aspect of the work is that all previous algorithms for triangle finding worked equally well for the standard unweighted case as well as a weighted variant in which each edge is labeled by a number and the goal is to find a set of edges $(a,b), (b,c), (c,a)$ whose weights add up to a particular target. Indeed this algorithm has a query complexity for the unweighted case that is known to be impossible for the weighted version. A related point is that this shows the limitations of the otherwise versatile non-adaptive learning-graph method.

### Ryan O’Donnell and John Wright Quantum Spectrum TestingabstractarXiv:1501.05028

A classic problem: given $\rho^{\otimes n}$ for $\rho$ an unknown d-dimensional state, estimate some property of $\rho$. One problem where the answer is still shockingly unknown is to estimate $\hat\rho$ in a way that achieves $\mathbb{E} \|\rho-\hat \rho\|_1 \leq\epsilon$.
Results from compressed sensing show that $n = \tilde\Theta(d^2r^2)$ for single-copy two-outcome measurements of rank-$r$ states with constant error, but if we allow block measurements then maybe we can do better. Perhaps $O(d^2/\epsilon)$ is possible using using the Local Asymptotic Normality results of Guta and Kahn [0804.3876], as Hayashi has told me, but the details are – if we are feeling generous – still implicit. I hope that he, or somebody, works them out. (18 Jan update: thanks Ashley for fixing a bug in an earlier version of this.)

The current talk focuses instead on properties of the spectrum, e.g. how many copies are needed to distinguish a maximally mixed state of rank $r$ from one of rank $r+c$? The symmetry of the problem (invariant under both permutations and rotations of the form $U^{\otimes n}$) means that we can WLOG consider “weak Schur sampling” meaning that we measure which $S_n \times U_d$ irrep our state lies in, and output some function of this result. This irrep is described by an integer partition which, when normalized, is a sort of mangled estimate of the spectrum. It remains only to analyze the accuracy of this estimator in various ways. In many of the interesting cases we can say something nontrivial even if $n= o(d^2)$. This involves some delicate calculations using a lot of symmetric polynomials. Some of these first steps (including many of the canonical ones worked out much earlier by people like Werner) are in my paper quant-ph/0609110 with Childs and Wocjan. But the current work goes far far beyond our old paper and introduces many new tools.

### Han-Hsuan Lin and Cedric Yen-Yu Lin. Upper bounds on quantum query complexity inspired by the Elitzur-Vaidman bomb testerabstractarXiv:1410.0932

This talk considers a new model of query complexity inspired by the Elitzur-Vaidman bomb tester. The bomb tester is a classic demonstration of quantum weirdness: You have a collection of bombs that have a detonation device so sensitive that even a single photon impacting it will set it off. Some of these bombs are live and some are duds, and you’d like to know which is which. Classically, you don’t stand a chance, but quantum mechanically, you can put a photon into a beamsplitter and place the bomb in one arm of a Mach-Zender interferometer. A dud will destroy the interference effects, and a homodyne detector will always click the same way. But you have a 50/50 chance of detecting a live bomb if the other detector clicks! There are various tricks that you can play related to the quantum Zeno effect that let you do much better than this 50% success probability.

The authors define a model of query complexity where one risks explosion for some events, and they showed that the quantum query complexity is related to the bomb query complexity by $B(f) = \Theta(Q(f)^2)$. There were several other interesting results in this talk, but we ran out of steam as it was the last talk before lunch.

### Kirsten Eisentraeger, Sean Hallgren, Alexei Kitaev and Fang Song A quantum algorithm for computing the unit group of an arbitrary degree number fieldSTOC 2014

The unit group is a fundamental object in algebraic number theory. It comes up frequently in applications as well, and is used for fully homomorphic encryption, code obfuscation, and many other things.

My [Steve] personal way of understanding the unit group of a number field is that it is a sort of gauge group with respect to the factoring problem. The units in a ring are those numbers with multiplicative inverses. In the ring of integers, where the units are just $\pm1$ , we can factor composite numbers into $6 = 3 \times 2 = (-3)\times (-2)$. Both of these are equally valid factorizations; they are equivalent modulo units. In more complicated settings where unique factorization fails, we have factorization into prime ideals, and the group of units can in general become infinite (though always discrete).

The main result of this talk is a quantum algorithm for finding the unit group of a number field of arbitrary degree. One of the technical problems that they had to solve to get this result was to solve the hidden subgroup problem on a continuous group, namely $\mathbb{R}^n$.

The speaker also announced some work in progress: a quantum algorithm for the principal ideal problem and the class group problem in arbitrary degree number fields [Biasse Song ‘14]. It sounds like not all the details of this are finished yet.

### Dominic Berry, Andrew Childs and Robin Kothari Hamiltonian simulation with nearly optimal dependence on all parametersabstract1501.01715

Hamiltonian simulation is not only the original killer app of quantum computers, but also a key subroutine in a large and growing number of problems. I remember thinking it was pretty slick that higher-order Trotter-Suzuki could achieve a run-time of $\|H\|t\text{poly}(s)(\|H\|t/\epsilon)^{o(1)}$ where $t$ is the time we simulate the Hamiltonian for and $s$ is the sparsity. I also remember believing that the known optimality thoerems for Trotter-Suzuki (sorry I can’t find the reference, but it involves decomposing $e^{t(A+B)}$ for the free Lie algebra generated by $A,B$) meant that this was essentially optimal.

Fortunately, Berry, Childs and Kothari (and in other work, Cleve) weren’t so pessimistic, and have blasted past this implicit barrier. This work synthesizes everything that comes before to achieve a run-time of $\tau \text{poly}\log(\tau/\epsilon)$ where $\tau = \|H\|_{\max}st$ (where $\|H\|_{\max}$ is $\max_{i,j} |H_{i,j}|$ can be related to the earlier bounds via $\|H\| \leq d \|H\|_{\max}$).

One quote I liked: “but this is just a generating function for Bessel functions!” Miraculously, Dominic makes that sound encouraging. The lesson I suppose is to find an important problem (like Hamiltonian simulation) and to approach it with courage.

### Salman Beigi and Amin Gohari Wiring of No-Signaling Boxes Expands the Hypercontractivity RibbonabstractarXiv:1409.3665

If you have some salt water with salt concentration 0.1% and some more with concentration 0.2%, then anything in the range [0.1, 0.2] is possible, but no amount of mixing will give you even a single drop with concentration 0.05% or 0.3%, even if you start with oceans at the initial concentrations. Similarly if Alice and Bob share an unlimited number of locally unbiased random bits with correlation $\eta$ they cannot produce even a single bit with correlation $\eta' > \eta$ if they don’t communicate. This was famously proved by Reingold, Vadhan and Wigderson.

This talk does the same thing for no-signaling boxes. Let’s just think about noisy PR boxes to make this concrete. The exciting thing about this work is that it doesn’t just prove a no-distillation theorem but it defines an innovative new framework for doing so. The desired result feels like something from information theory, in that there is a monotonicity argument, but it needs to use quantities that do not increase with tensor product.

Here is one such quantity. Define the classical correlation measure $\rho(A,B) = \max \text{Cov}(f,g)$ where $f:A\mapsto \mathbb{R}$, $g:B\mapsto \mathbb{R}$ and each have variance 1. Properties:

• $0 \leq \rho(A,B) \leq 1$
• $\rho(A,B) =0$ iff $p_{AB} = p_A \cdot p_B$
• $\rho(A^n, B^n) = \rho(A,B)$
• for any no-signaling box, $\rho(A,B) \leq \max(\rho(A,B|X,Y), \rho(X,Y))$

Together this shows that any wiring of boxes cannot increase this quantity.

The proof of this involves a more sophisticated correlation measure that is not just a single number but is a region called the hypercontractivity ribbon (originally due to [Ahlswede, Gacs ‘76]). This is defined to be the set of $(\lambda_1, \lambda_2)$ such that for any $f,g$ we have
$\mathbb{E}[f_A g_B] \leq \|f_A\|_{\frac{1}{\lambda_1}} \|g_B\|_{\frac{1}{\lambda_2}}$
A remarkable result of [Nair ‘14] is that this is equivalent to the condition that
$I(U;AB) \geq \lambda_1 I(U:A) + \lambda_2 I(U:B)$
for any extension of the distribution on AB to one on ABU.

Some properties.

• The ribbon is $[0,1]\times [0,1]$ iff A,B are independent.
• It is stable under tensor power.
• monotonicity: local operations on A,B enlarge $R$

For boxes define $R(A,B|X,Y) = \cap_{x,y} R(A,B|x,y)$. The main theorem is then that rewiring never shrinks hypercontractivity ribbon. And as a result, PR box noise cannot be reduced.

These techniques are beautiful and seem as though they should have further application.

### Masahito Hayashi Estimation of group action with energy constraintabstractarXiv:1209.3463

Your humble bloggers were at this point also facing an energy constraint which limited our ability to estimate what happened. The setting is that you pick a state, nature applies a unitary (specifically from a group representation) and then you pick a measurement and try to minimize the expected error in estimating the group element corresponding to what nature did. The upshot is that entanglement seems to give a quadratic improvement in metrology. Noise (generally) destroys this. This talk showed that a natural energy constraint on the input also destroys this. One interesting question from Andreas Winter was about what happens when energy constraints are applied also to the measurement, along the lines of 1211.2101 by Navascues and Popescu.

Jan 14 update: forgot one! Sorry Ashley.

### Ashley Montanaro Quantum pattern matching fast on averageabstractarXiv:1408.1816

Continuing the theme of producing shocking and sometimes superpolynomial speedups to average-case problems, Ashley shows that finding a random pattern of length $m$ in a random text of length $n$ can be done in quantum time $\tilde O(\sqrt{n/m}\exp(\sqrt{\log m}))$. Here “random” means something subtle. The text is uniformly random and the pattern is either uniformly random (in the “no” case) or is a random substring of the text (in the “yes” case). There is also a higher-dimensional generalization of the result.

One exciting thing about this is that it is a fairly natural application of Kuperberg’s algorithm for the dihedral-group HSP; in fact the first such application, although Kuperberg’s original paper does mention a much less natural such variant. (correction: not really the first – see Andrew’s comment below.)

It is interesting to think about this result in the context of the general question about quantum speedups for promise problems. It has long been known that query complexity cannot be improved by more than a polynomial (perhaps quadratic) factor for total functions. The dramatic speedups for things like the HSP, welded trees and even more contrived problems must then use the fact that they work for partial functions, and indeed even “structured” functions. Pattern matching is of course a total function, but not one that will ever be hard on average over a distribution with, say, i.i.d. inputs. Unless the pattern is somehow planted in the text, most distributions simply fail to match with overwhelming probability. It is funny that for i.i.d. bit strings this stops being true when $m = O(\log n)$, which is almost exactly when Ashley’s speedup becomes merely quadratic. So pattern matching is a total function whose hard distributions all look “partial” in some way, at least when quantum speedups are possible. This is somewhat vague, and it may be that some paper out there expresses the idea more clearly.

Part of the strength of this paper is then finding a problem where the promise is so natural. It gives me new hope for the future relevance of things like the HSP.

Posted in Conferences, Liveblogging | 6 Comments

## Your Guide to Australian Slang for QIP Sydney

To everyone that’s attending QIP, welcome to Sydney!

Since I’ve already had to clarify a number of the finer points of Australian slang to my fellow attendees, I thought I would solve the general problem and simply post a helpful dictionary that translates some uniquely Australian words and usages into standard American English.

Also, this thing on the right is called an ibis. It’s not venomous.

## Coffee

Flat white – Try this at least once while you’re here, preferably prepared by a highly skilled barista at one of the better cafes. It’s similar to a latte or to a cappuccino without the foam, but there are important differences.

Long black – Australian version of the Americano, a bit stronger and with crema. It’s the closest you’ll get to a cup of filtered drip coffee, if that’s your thing.

Short black – If you want a standard espresso, order a short black.

## The Beach

Thongs – Sandals, or flip-flops. The highest level of dress code in Australia is “no thongs”.

Togs – Swimwear.

Esky – A cooler; the place where you store your beer to keep it cold while you’re getting pissed at the beach.

Pissed – Drunk; the state that a nontrivial fraction of people are in because it’s legal to drink at the beach.

Sunnies – Sunglasses.

Mozzy – Mosquito. Usually not a problem at the beach because there is almost always a breeze.

## The Pub

Schooner – (SKOO-ner) A medium-sized glass of beer.

Jug – A pitcher of beer.

Shout – To buy a beer for someone, or a round of beers for your table.

Skol – To chug a beer. Usage: “Hey Robbo, if you skol that schooner I’ll shout you a jug.”

Hotel – In addition to the standard meaning, a hotel is a particular style of pub. It usually has high occupancy and a limited beer selection (though this is starting to improve as craft beer is finally catching on here).

## Sports

Football – see “Footy”.

Footy – Rugby. It comes in several varieties, with League and Union being the two most popular varieties.

Gridiron – American football. Not generally watched much down under.

Cricket – An inscrutable game that takes 5 days to play. I think the only way you could like this game is to have the British invade, conquer your land, and occupy your territory under their colonial yoke for at least a few generations. That seems to be how everyone else got into it.

Rooting – Do not make the mistake of saying that you are “rooting for team X”; in Australia, rooting is slang for having sex.

## Miscellaneous

Arvo – Afternoon.

Bickie – A cookie or biscuit.

Brekkie – Breakfast.

Fair dinkum – The closest translation is probably “for real”. It’s used to express the sentiment that you’re not deceiving the listener or exaggerating your claims.

## Should Papers Have Unit Tests?

Perhaps the greatest shock I’ve had in moving from the hallowed halls of academia to the workman depths of everyday software development is the amount of testing that is done when writing code. Likely I’ve written more test code than non-test code over the last three plus years at Google. The most common type of test I write is a “unit test”, in which a small portion of code is tested for correctness (hey Class, do you do what you say?). The second most common type is an “integration test”, which attempts to test that the units working together are functioning properly (hey Server, do you really do what you say?). Testing has many benefits: correctness of code, of course, but it is also important for ease of changing code (refactoring), supporting decoupled and simplified design (untestable code is often a sign that your units are too complicated, or that your units are too tightly coupled), and more.

Over the holiday break, I’ve been working on a paper (old habit, I know) with lots of details that I’d like to make sure I get correct. Throughout the entire paper writing process, one spends a lot of time checking and rechecking the correctness of the arguments. And so the thought came to my mind while writing this paper, “boy it sure would be easier to write this paper if I could write tests to verify my arguments.”

In a larger sense, all papers are a series of tests, small arguments convincing the reader of the veracity or likelihood of the given argument. And testing in a programming environment has a vital distinction that the tests are automated, with the added benefit that you can run them often as you change code and gain confidence that the contracts enforced by the tests have not been broken. But perhaps there would be a benefit to writing a separate argument section with “unit tests” for different portions of a main argument in a paper. Such unit test sections could be small, self-contained, and serve as supplemental reading that could be done to help a reader gain confidence in the claims of the main text.

I think some of the benefits for having a section of “unit tests” in a paper would be

• Documenting limit tests A common trick of the trade in physics papers is to take a parameter to a limiting value to see how the equations behave. Often one can recover known results in such limits, or show that certain relations hold after you scale these. These types of arguments give you confidence in a result, but are often left out of papers. This is sort of kin to edge case testing by programmers.
• Small examples When a paper gets abstract, one often spends a lot of time trying to ground oneself by working with small examples (unless you are Grothendieck, of course.) Often one writes a paper by interjecting these examples in the main flow of the paper, but these sort of more naturally fit in a unit testing section.
• Alternative explanation testing When you read an experimental physics paper, you often wonder, am I really supposed to believe the effect that they are talking about. Often large portions of the paper are devoted to trying to settle such arguments, but when you listen to experimentalists grill each other you find that there is an even further depth to these arguments. “Did you consider that your laser is actually exciting X, and all you’re seeing is Y?” The amount of this that goes on is huge, and sadly, not documented for the greater community.
• Combinatorial or property checks Often one finds oneself checking that a result works by doing something like counting instances to check that they sum to a total, or that a property holds before and after a transformation (an invariant). While these are useful for providing evidence that an argument is correct, they can often feel a bit out of place in a main argument.

Of course it would be wonderful if there we a way that these little “units” could be automatically executed. But the best path I can think of right now towards getting to that starts with the construction of an artificial mind. (Yeah, I think perhaps I’ve been at Google too long.)

Posted in Off The Deep End, Programming | 5 Comments

## Self-correcting Fractals

A really exciting paper appeared on the arxiv today: A proposal for self-correcting stabilizer quantum memories in 3 dimensions (or slightly less), by Courtney Brell. It gives the strongest evidence yet that self-correcting quantum memories are possible in “physically realistic” three-dimensional lattice models. In particular, Courtney has constructed families of local Hamiltonians in 3D whose terms consist of X- and Z-type stabilizer generators and that show phase-transition behavior akin to the 2D Ising model for both the X- and Z-type error sectors. This result doesn’t achieve a complete theoretical solution to the question of whether self-correcting quantum memories can exist in principle, as I’ll explain below, but it makes impressive progress using a mix of rigorous analysis and physical argument.

First, what do I mean by “physically realistic”? Well, obviously I don’t mean physically realistic (without quotes)—that’s a much greater challenge. Rather, we want to abstractly characterize some features that should be shared by a physically realistic implementation, but with enough leeway that a theorist can get creative. To capture this, Courtney introduces the so-called Caltech Rules for a self-correcting quantum memory.

The phrase “the Caltech Rules” is (I believe) attributable to David Poulin. Quantum memory aficionados have been debating these rules in emails and private discussions for the last few years, but I think this is the first time someone has put them in print. As rules, they aren’t really set in stone. They consist of a list of criteria that are either necessary or seemingly necessary to avoid models that are self-correcting for trivial and unphysical reasons (e.g., scaling the coupling strengths as a function of $n$). In Courtney’s version of the rules, we require a model with finite-dimensional spins (so no bosonic or fermionic models allowed… this might be objectionable to some people), bounded-strength short-range interactions between the spins, a constant density of spins, a perturbatively stable degenerate ground space for the encoded states, an efficient decoding algorithm, and an exponential memory lifetime against low-temperature thermal noise. One might wish to add even more desiderata like translation-invariant couplings or a spectral gap (which is closely related to stability), but finding a self-correcting memory subject to these constraints is already a tall order. For some more discussion on these points, check out another awesome paper that came on the arxiv yesterday, an excellent review article on quantum memories at finite temperature by Ben Brown et al..

To motivate the construction, it helps to remember everyone’s favorite models, the Ising model and the Toric code. When the temperature $T$ is zero, it’s easy to store a classical bit using the 1D Ising model; this is just a repetition code. Similarly, the 2D toric code can store quantum information at $T=0$. Both of these codes become unstable as memories at $T\textgreater 0$ because of the presence of string-like logical operators. The physical process by which these strings are created costs some energy, but then the strings can stretch and grow without any energy cost, and thermal fluctuations alone will create enough strings in a short time to cause a decoding failure. By contrast, the 2D Ising model can store a classical bit reliably for an exponential amount of time if you encode in the total magnetization and you are below the Curie temperature. The logical operators are now membranes that cost energy to grow. Similarly, the 4D toric code has such a phase transition, and this is because the X- and Z-type errors both act analogously to 2D Ising models with membranous logical operators.

Sierpinski carpet, with edges placed to form a “Sierpinski graph”.

The codes that Courtney defines are called embeddable fractal product codes (EFPC). The idea is that, if a product of two 1D Ising models isn’t a 2D self-correcting model, but a product of two 2D Ising models is a self-correcting memory, then what happens if we take two 1.5D Ising models and try to make a 3D self-correcting memory? The backbone of the construction consists of fractals such as the Sierpinski carpet that have infinite ramification order, meaning that an infinite number of edges on an associated graph must be cut to split it into two infinite components. Defining an Ising model on the Sierpinski graph yields a finite-temperature phase transition for the same reason as the 2D Ising model, the Peierls argument, which is essentially a counting argument about the density of domain walls in equilibrium with fixed boundary conditions. This is exactly the kind of behavior needed for self-correction.

Splitting the Sierpinski graph into two infinite components necessarily cuts an infinite number of edges.

Using the adjacency of the Sierpinski graph, the next step is to use a toric code-like set of generators on this graph, paying careful attention to the boundary conditions (in particular, plaquette terms are placed in such a way that the stabilizer group contains all the cycles that bound areas of the fractal, at any length scale). Then using homological product codes gives a natural way to combine X-like and Z-like copies of this code into a new code that naturally lives in four dimensions. Although the natural way to embed this code requires all four spatial dimensions, it turns out that a low-distortion embedding is possible with distortion bounded by a small constant, so these codes can be compressed into three dimensions while retaining the crucial locality properties.

Remarkably, this construction gives a finite-temperature phase transition for both the X- and Z-type errors. It essentially inherits this from the fact that the Ising models on the Sierpinski graph have phase transitions, and it is a very strong indication of self-correcting behavior.

However, there are some caveats. There are many logical qubits in this code (in fact, the code has constant rate), and only the qubits associated to the coarsest features of the fractal have large distance. There are many logical qubits associated to small-scale features that have small distance and create an exponential degeneracy of the ground space. With such a large degeneracy, one worries about perturbative stability in the presence of a generic local perturbation. There are a few other caveats, for example the question of efficient decoding, but to me the issue of the degeneracy is the most interesting.

Overall, this is the most exciting progress since Haah’s cubic code. I think I’m actually becoming optimistic about the possibility of self-correction. It looks like Courtney will be speaking about his paper at QIP this year, so this is yet another reason to make it to Sydney this coming January.

Posted in Quantum | 1 Comment

## A Breakthrough Donation for Computer Science

Lance Fortnow has a post summarizing some of the news affecting the CS community over the past month, including updates on various prizes as well as the significant media attention focusing on physics- and math-related topics such as movies about Turing and Hawking as well as Terrence Tao on the Colbert Report.

From his post, I just learned that former Microsoft chief executive Steven Ballmer is making a donation to Harvard that will endow twelve—that’s right, 12—new tenured and tenure-track faculty positions in computer science. This is fantastic news and will have a huge positive impact on Harvard CS.

One thing missing from Lance’s list was news about the Breakthrough Prizes in mathematics and fundamental physics. In case you’ve been living under a rock, these prizes give a very hefty US $3 million purse to the chosen recipients. The winners are all luminaries in their field, and it’s great to see them get recognition for their outstanding work. On the other hand, juxtaposing Ballmer’s donation and the Breakthrough Prizes couldn’t offer a starker contrast. It costs the same amount—$3 million—to endow a university full professor with appointments in more than one discipline at Duke University. My initial googling would suggest that this is a pretty typical figure at top-tier institutions.

## Quantum computers can work in principle

Gil Kalai has just posted on his blog a series of videos of his lectures entitled “why quantum computers cannot work.”  For those of us that have followed Gil’s position on this issue over the years, the content of the videos is not surprising. The surprising part is the superior production value relative to your typical videotaped lecture (at least for the first overview video).

I think the high gloss on these videos has the potential to sway low-information bystanders into thinking that there really is a debate about whether quantum computing is possible in principle. So let me be clear.

There is no debate! The expert consensus on the evidence is that large-scale quantum computation is possible in principle.

Quoting “expert consensus” like this is an appeal to authority, and my esteemed colleagues will rebuke me for not presenting the evidence. Aram has done an admirable job of presenting the evidence, but the unfortunate debate format distorts perception of the issue by creating the classic “two sides to a story” illusion. I think it’s best to be unequivocal to avoid misunderstanding.

The program that Gil lays forth is a speculative research agenda, devoid of any concrete microscopic physical predictions, and no physicist has investigated any of it because it is currently neither clear enough nor convincing enough. At the same time, it would be extremely interesting if it one day leads to a concrete conjectured model of physics in which quantum computers do not work. To make the ideas more credible, it would help to have a few-qubit model that is at least internally consistent, and even better, one that doesn’t contradict the dozens of on-going experiments. I genuinely hope that Gil or someone else can realize this thrilling possibility someday.

For now, though, the reality is that quantum computation continues to make exciting progress every year, both on theoretical and experimental levels, and we have every reason to believe that this steady progress will continue. Quantum theory firmly predicts (via the fault-tolerance threshold theorem) that large-scale quantum computation should be achievable if noise rates and correlations are low enough, and we are fast approaching the era where the experimentally achievable noise rates begin to touch the most optimistic threshold estimates. In parallel, the field continues to make contributions to other lines of research in high-energy physics, condensed matter, complexity theory, cryptography, signal processing, and many others. It’s an exciting time to be doing quantum physics.

And most importantly, we are open to being wrong. We all know what happens if you try to update your prior by conditioning on an outcome that had zero support. Gil and other quantum computing skeptics like Alicki play a vital role in helping us sharpen our arguments and remove any blind spots in our reasoning. But for now, the arguments against large-scale quantum computation are simply not convincing enough to draw more than an infinitesimal sliver of expert attention, and it’s likely to remain this way unless experimental progress starts to systematically falter or a concrete and consistent competing model of quantum noise is developed.