Baths can be beneficial, even for qubits.
One of the most important things to try to understand about real quantum computers is how they behave in the presence of environments. Sometimes these environments are called ‘baths’ by physicists. I like this term because it’s really evocative of what’s physically going on. You can imagine any quantum system you’re building as always being ‘bathed’ in the glow of these environments.
It’s a very interesting fact that you can never get away from these baths, even in principle. No object in our universe — as far as we know — can be completely isolated from the rest of the universe. As Lawrence Krauss so eloquently describes, even ‘nothing’ is something.
Even if we were to build a quantum computer in the depths of interstellar space, and cool it to zero temperature, it would still be bathed in a bath formed of the virtual particles that boil and seethe in the fabric of space-time itself. There is no escape from our connections to the physical universe.
A Lovecraftian aside that has nothing to do with the paper or the NPR interview
By the way you Lovecraft fans out there — here is a famous bit from The Dream-Quest of Unknown Kadath:
[O]utside the ordered universe [is] that amorphous blight of nethermost confusion which blasphemes and bubbles at the center of all infinity—the boundless daemon sultan Azathoth, whose name no lips dare speak aloud, and who gnaws hungrily in inconceivable, unlighted chambers beyond time and space amidst the muffled, maddening beating of vile drums and the thin monotonous whine of accursed flutes.
“Azathoth has existed since the universe began. He dwells outside normal time and space. He is blind, idiotic, and indifferent.” Now go watch Krauss describe “Something from Nothing” and tell me they’re not talking about the same thing!
Lovecraft had an uncanny ability to grok modern concepts from physics and weave them into his stories. His descriptions of Azathoth, and the physics underlying Krauss’ explanations of what seems to be physically occurring deep inside the fabric of spacetime, are just too close to not point out. Of course they use different language. But think carefully about the context in which these ideas are being delivered. (Am I stretching making a connection between Krauss’ something that lives in nothing and Lovecraft’s description of Azathoth? Definitely. But I think it’s an interesting thing to think about how these two descriptions might not be incompatible.)
Back to qubits and baths
Anyway back to qubits and baths. This is not just fascinating science (although it is that). It is also a fundamentally important issue in constructing computing machines that harness quantum mechanics. Because all quantum systems MUST live in baths, it’s extremely important to understand in detail how these baths affect their behavior.
Not so long ago, it was suspected that these baths would always destroy the curious properties of quantum mechanics for large objects. But then this turned out to not be true. The first large objects where quantum behavior remained even in the presence of really big and hot baths were loops of superconducting metal — the great – great – great grandparents of our qubits.
Now the question of what effect these baths really have on large collections of large objects is being debated, and goes to the heart of many of the technical issues in building useful quantum computers.
The paper that just published
The paper that just published is called Thermally assisted quantum annealing of a 16-qubit problem.
It describes what I believe to be a key result in advancing this understanding. It looks very carefully at what happens to a quantum system in the presence of a bath, where both the quantum system and the bath have been exquisitely characterized. As was the case when macroscopic quantum coherence was first observed, the results are counter-intuitive.
Here is the abstract from the paper.
Efforts to develop useful quantum computers have been blocked primarily by environmental noise. Quantum annealing is a scheme of quantum computation that is predicted to be more robust against noise, because despite the thermal environment mixing the system’s state in the energy basis, the system partially retains coherence in the computational basis, and hence is able to establish well-defined eigenstates. Here we examine the environment’s effect on quantum annealing using 16 qubits of a superconducting quantum processor. For a problem instance with an isolated small-gap anticrossing between the lowest two energy levels, we experimentally demonstrate that, even with annealing times eight orders of magnitude longer than the predicted single-qubit decoherence time, the probabilities of performing a successful computation are similar to those expected for a fully coherent system. Moreover, for the problem studied, we show that quantum annealing can take advantage of a thermal environment to achieve a speedup factor of up to 1,000 over a closed system.
The key result is that for the specific type of bath acting on a real processor, the quantum effects required for quantum computation can successfully be tapped by protecting them in a specific way. Specifically — and this is a point that has caused much confusion — the decoherence time of the individual qubits, which is the time to decohere in the energy basis, does not set the timescale for losing quantum coherence in the measurement basis. Quantum coherence in the measurement basis (which is the resource tapped in this approach) is an equilibrium property of the system, as long as the bath is not so big and hot that well defined energy eigenstates disappear.
While the paper is primarily an experimental paper, the theory underlying all of this is very satisfactory in my view. Mohammad and his collaborators have developed a very good theoretical understanding of what really happens in real open quantum systems, and the agreement between these models and what is seen in the lab is striking.
So congratulations to all on this result.
The NPR interview and my proudness at working ‘meatiest’ into a national radio program
On a mostly unrelated note, here is a radio piece that Geoff Brumfiel of NPR did recently. It is of note because I managed to work in the word ‘meatiest’ into the discussion, of which I am understandably quite proud.
. The coupling terms are proportional to the dot product of the dictionary atoms.
has to be zero for all pairs of variables 
and 
that are not connected in hardware? If we can achieve this structure in the dictionary, we get a very interesting result. Instead of being fully connected, the QUBOs with this restriction can be engineered to exactly match the underlying problem the hardware solves. If we can do this, we get closer to using the full power of the hardware.
data objects 
, where each 
components;
real valued matrix 
, where 
is the number of dictionary atoms we choose, and we define its 
column to be the vector 
;
binary valued matrix 
;
, which is called the regularization parameter,
for all pairs 
that are not connected in the quantum chip being used.
converges to a minimum.
vertices. In that graph, each vertex is connected to a bunch of others. Call 
the number corresponding to the connectivity of the least connected variable in the graph. Then this paper proves that you can define a set of real vectors in dimension 
where non-adjacent nodes in the graph can be assigned orthogonal vectors.
not connected in hardware — can be done if the length of the vectors 
is greater than 
. So as long as the dimension of the dictionary atoms is greater than 512 – 5 = 507, we can always perform Step 1.
and 
that are orthogonal (the dot product 
is zero). What’s the minimum dimension these vectors have to live in such that this can be done? Well imagine that they both live in one dimension — they are just numbers on a line. Then clearly you can’t do it. However if you have two dimensions, you can. Here’s an example: 
and 
. If you have more that two dimensions, you can also, and the choices you make in this case are not unique.
), and want to assign vectors to each vertex such that all of these vectors are orthogonal to all the others, that’s equivalent to asking “given a 
. It’s easy but there isn’t a native function in numpy or scipy that does it.
that minimizes![G(\vec{w}; \lambda) = \sum_{j=1}^{K} w_j [ \lambda + \vec{d}_j \cdot (\vec{d}_j -2 \vec{z}) ] + 2 \sum_{j \leq m}^K w_j w_m \vec{d}_j \cdot \vec{d}_m](http://s0.wp.com/latex.php?latex=G%28%5Cvec%7Bw%7D%3B+%5Clambda%29+%3D+%5Csum_%7Bj%3D1%7D%5E%7BK%7D+w_j+%5B+%5Clambda+%2B+%5Cvec%7Bd%7D_j+%5Ccdot+%28%5Cvec%7Bd%7D_j+-2+%5Cvec%7Bz%7D%29+%5D+%2B+2+%5Csum_%7Bj+%5Cleq+m%7D%5EK+w_j+w_m+%5Cvec%7Bd%7D_j+%5Ccdot+%5Cvec%7Bd%7D_m&bg=ffffff&fg=333333&s=0 "G(\vec{w}; \lambda) = \sum_{j=1}^{K} w_j [ \lambda + \vec{d}_j \cdot (\vec{d}_j -2 \vec{z}) ] + 2 \sum_{j \leq m}^K w_j w_m \vec{d}_j \cdot \vec{d}_m")
and 
dictionary atoms 
and 
. Because we haven’t added any restrictions on what these atoms need to look like, these dot products can all be non-zero (the dictionary atoms don’t need to be, and in general won’t be, orthogonal). This means that the problems generated by the procedure are all fully connected — each variable is influenced by every other variable.
physical qubits — Rainier can embed a fully connected 17 variable graph, while Vesuvius can embed a fully connected 33 variable graph. Shown to the right is an 
).
