High precision needed for quantum computing

Craig Feinstein asks:

Leonid Levin said, "Exponential summations used in QC require hundreds if not millions of decimal places accuracy. I wonder who would expect any physical theory to make sense in this realm."

Peter Shor replies:

If you believe the fault-tolerant threshold theorem for quantum computers, you do not require hundreds of digits of accuracy.

Levin does not believe this theorem. More precisely, he believes that the hypotheses required for the theorem to work do not apply to the actual universe.

I believe his mental model of quantum mechanics resembles the idea that the physics of the universe is being simulated on a classical machine which has floating point errors. I don't believe this is true. ...

The real question is whether the rules of the universe are exact unitary evolution or something else. If they're exact unitary evolution and you have locality of action (quantum field theories, including QED, satisfy these) then the fault-tolerant threshold theorem holds. If the universe has extra levels of weirdness under the quantum field theory, then it's not clear the hypotheses are satisfied.

I am not sure who is right here. Quantum mechanics is a linear theory and has been verified to high precision is some contexts. But a linear theory is nearly always an approximation to a nonlinear theory, and I don't think that the quantum computer folks have shown that they are operating within a valid approximation.

Shor assumes "unitary", but there are interpretations of quantum mechanics that are not unitary, and no one has proved them wrong. So how do we know nature is really unitary?

If being unitary is some physically observed law, like conservation of momentum, then we should have error bars that show us just how close to being unitary the world, and what confidence in different situations.

If being unitary is a metaphysical necessary truth, derived from the conservation of probability, then how have so many textbooks managed to get by with the Copenhagen interpretation?

I say that quantum computing is a vast extrapolation of known physics, and extrapolations are unreliable.

In other news:

An international team of researchers has created an entanglement of 103 dimensions with only two photons, beating the previous record of 11 dimensions.

The discovery could represent an advance toward toward better encryption of information and quantum computers with much higher processing speeds, according to a statement by the researchers.

Until now, to increase the “computing” capacity of these particle systems, scientists have mainly turned to increasing the number of qubits (entangled particles), up to 14 particles. ...

“The most immediate practical use is expected to be in secure communication,” Huber explained to KurzweilAI in an email interview.

I haven't read the paper but I am pretty sure than there is no practical application to secure communication. I expected them to claim that all those dimensions could be used for quantum computing.

Lectures on the impossibility of quantum computers

Steve Flammia writes:

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.

... 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. ...

And most importantly, we are open to being wrong.

No, there is no significant progress. No one has made scalable qubits, and no one has demonstrated a quantum speedup.

He sure doesn't sound like someone who is open to being wrong. Papers on this subject by physicists subscribing to this consensus never admit that the whole field is based on speculative premises. I am a skeptic.

Evidence closes in on singularity

Modern physics teaches certain singularities in general relativity (black holes and big bang) and quantum field theory (renormalization). I have expressed skepticism about whether there is truly a singularity in the black hole and at the big bang. Max Tegmark has also expressed skepticism about actual infinities in nature.

Now that the BICEP2 has given us evidence close to the alleged big bang singularity, Matt Strassler and Lubos Motl have reopened the debate about whether there really is a singularity. Those are sensible mainstream views. Others will push back harder, and speculate about before the big bang and into the multiverse.

I have to agree with Strassler that the evidence points to energies high enough that our physical theories break down, so we cannot go further. I also agree with Tegmark that we never observe true singularities in nature. I am a positivist, and I believe in what has been demonstrated. Infinities and singularities are wonderful mathematical tools, but math is not the same as physics.

Depending on how the inflation evidence plays out, I am not sure the big bang has anything to do with general relativity or a spacetime singularity. The physics was not dominated by gravity or the standard model, as we know them. Something mysterious called an inflaton field was releasing huge amounts of energy. I am not even sure about the reports that BICEP2 saw gravity waves. Maybe they saw inflaton waves. Some physicists have said that this proves gravity is quantized. I don't know how they can say that, when no one knows what the inflaton is or how it relates to gravity.

I expect the meaning of BICEP2 to be settled in the next year or so, but unwarranted speculation about time and multiverses to go on for the foreseeable future.

Update: Strassler argues:

Who is still telling the media and the public that the universe really started with a singularity, or that the modern Big Bang Theory says that it does? I’ve never heard an expert physicist say that. And with good reason: when singularities and other infinities have turned up in our equations in the past, those singularities disappeared when our equations, or our understanding of how to use our equations, improved.

Moreover, there’s a point of logic here. How could we possibly know what happened at the very beginning of the universe? No experiment can yet probe such an early time, and none of the available equations are powerful enough or usable enough to allow us to come to clear and unique conclusions.

Lumo responds:

But by endorsing the idea that the Big Bang singularity exists, we don't claim that the classical general relativity is exactly accurate and all of its conclusions about quantities' being infinite at the singularity are strictly right. We never mean such things.

Mermin resolves metaphysical issues in Nature

I posted before on Mermin taking Bohr seriously, SciAm pushes Quantum Bayesianism, and Counterfactuals: Time on the metaphysics of time. Now Cornell Physicist N. David Mermin has an essay in the current Nature journal:

Schrödinger wrote in a little-known 1931 letter2 to German physicist Arnold Sommerfeld that quantum mechanics “deals only with the object–subject relation”. Another founder of quantum mechanics, Danish physicist Niels Bohr, insisted in a 1929 essay3 that the purpose of science was not to reveal “the real essence of the phenomena” but only to find “relations between the manifold aspects of our experience”. ...

People who believe wavefunctions to be as real as stones have invested much effort in searching for objective physical mechanisms responsible for such changes in the wavefunction: ...

Another celebrated part of the muddle produced by the exclusion of the perceiving subject is 'quantum non-locality', the belief of some quantum physicists and many mystics, parapsychologists and journalists that an action in one region of space can instantly alter the real state of affairs in a faraway region. Thousands of papers have been written about this mysterious action at a distance over the past 50 years. A clue that the only change is in the expectations of the perceiving subject7 is that to learn anything about such alterations one must consult somebody in the region where the action took place. ...

The issue for Einstein was not the famous revelation of relativity that whether or not two events in two different places happen at the same time can depend on your frame of reference. It was simply that physics seems to offer no way to identify the Now even at a single event in a single place, although a local present moment — Now — is evident to each and every one of us as undeniably real. How can there be no place in physics for something as obvious as that? ...

When I recently mentioned to an eminent theoretical physicist that I was writing an essay explaining how the QBist view of science solves the strictly classical problem of the Now, he said: “Ah, you're going to explain why we all have that illusion.” And a distinguished philosopher of science recently derided the attitude that there ought to be a Now on my world-line as “chauvinism of the present moment”9.

My only quarrel with Mermin is that he acts as if he is saying something new. He is just reciting the view of Bohr and everyone else not infected with Einstein's disease.

There are physicists and philosophers today who (1) believe wavefunctions to be as real as stones; (2) assert quantum non-locality; and (3) deny Now as just chauvinism of the present moment. They have bizarre and foolish philosophies that lead to unresolvable paradoxes. Mermin's common sense explanations from a century ago are perfectly adequate.

Counterfactuals: Hard Science

Counterfactual reasoning is used all the time in the hard sciences. When you learn the formulas for gravity, the first thing you do is to answer questions like, “If you drop a rock off a 100-foot cliff, how long will it take to hit the ground?”

Dropping a rock from a cliff could also be called hypothetical reasoning, because one can easily imagine conducting the experiment. However physics also has all sorts of thought experiments that have no hope of ever being carried out. For example, explanations of relativity frequently involve spaceships taking people near the speed of light or being swallowed up in a black hole.

Counterfactuals are essential to the scientific method. Science is all about doing experiments that favor some hypothesis over some counterfactual.

The ability to make a precise prediction from a counterfactual is what distinguishes the hard sciences from the soft.

A famous example is Hendrik Lorentz's discovery of space and time transformations (now called Lorentz transformations) to explain the Michelson-Morley experiment. The counterfactual was aether motion, as Lorentz interpreted experiments to show that no such motion was detectable. He then used his formulas to predict relativistic mass, which was then confirmed by experiment. (Einstein later published similar theories, but the consensus of historians is that he paid no attention to the experiments.)

An example that failed to disprove the counterfactual was the 1543 Copernicus heliocentric model of the solar system. The established theory was Ptolemy's, but both theories predicted the sky with about the same accuracy. Experiments and models with much greater accuracy were achieved by Tycho Brahe and Johannes Kepler around 1600. The 20th century theory of relativity taught that motion is relative, and heliocentricity could never be proven.

Kepler's theory was superior not only for its accurate predictions, but for its counterfactual predictions. He had a complete theory of what kinds of orbits were possible in the solar system, so he could have made predictions about any new planet or asteroid that might be discovered. But he did not have a causal mechanism.

Causality is closely connected with counterfactual analysis. If an event A is followed by an event B, we only say that A caused B if counterfactuals for A would have been followed by something other than B. If rain follows my rain dance, I only argue that the dance caused the rain if I have a convincing argument that it would not have rained if I had not danced. A truly causal argument would provide a connected chain of events from the dance to the rain, with every link in the chain causing the next link.

Isaac Newton found a more powerful theory of mechanics by positing a gravitational force between any two massive objects, and saying that the force causes the orbital motion. Laplace argued in 1814 that all of nature is predictable with causal mechanics, given sufficient data.

This Newtonian causality was not true causality, because it required action-at-a-distance. One planet could exert a force on another planet over millions of miles, without any intermediate effects. A truly causal theory required the invention of the concept of field, such as electric or gravitational field, that can propagate thru empty space from one object to another. James Clerk Maxwell worked out such a theory for electric and magnetic fields in 1865, and that was the first relativistic theory.

A field is a physical way of describing certain counterfactuals. Saying that there is an electric field, at a particular point in space and time, is another way of saying what would happen if an electric charge were put at that point. The field is one of the most important concepts in all of physics, because it allows reducing the universe to the mechanics of locally defined objects. Thus physics is rooted in counterfactuals at every level. You could say that reductionism works in physics because of clever schemes for distributing counerfactual info over space and time.

A trendy topic in theoretical astrophysics is the multiverse. This involves a loose collection of unrelated ideas, but they all involve hypothetical universes outside of our observational abilities. It is a giant counterfactual exercise, with no experiment to decide who is right.

A particular fascination is the possibility of intelligent life in other universes. It appears that our universe is finely tuned for life. That is, it is hard to imagine the development of life in most of the counterfactual universes.

The most bizarre approach to counterfactuals is the many-worlds interpretation (MWI) of quantum mechanics. It simply posits that every possible counterfactual has an objective reality in an alternate universe. The extra universes do not really explain anything because they do not communicate with each other. There can be no experimental evidence for the other universes. There is no theoretical reason either, except that some physicists are unhappy with counterfactuals being just countefactuals.

The many-worlds seems like an endorsement of counterfactual thinking, but it corrupts such thinking by declaring the the counterfactuals real. A counterfactualist might argue, "if a new ice age were beginning, then we would probably notice cooler termperatures, but we don't, so we are not in a new ice age." But in many-worlds, all exceptionally improbable events take place in different universes, and we could be in one of them. Thus many-worlds leaves no good rationale for rejecting counterfactuals.

Stapp on quantum consciousness

Henry Stapp has a new edition of his book:

Mindful Universe: Quantum Mechanics and the Participating Observer (The Frontiers Collection)
March 24, 2014

Author: Henry P. Stapp
Publisher: Springer (4/26/2011)

The classical mechanistic idea of nature that prevailed in science during the eighteenth and nineteenth centuries was an essentially mindless conception: the physically described aspects of nature were asserted to be completely determined by prior physically described aspects alone, with our conscious experiences entering only passively. During the twentieth century the classical concepts were found to be inadequate. In the new theory, quantum mechanics, our conscious experiences enter into the dynamics in specified ways not fixed by the physically described aspects alone. Consequences of this radical change in our understanding of the connection between mind and brain are described. This second edition contains two new chapters investigating the role of quantum phenomena in the problem of free will and in the placebo effect.

He is right that quantum mechanics was created as a subjective theory, and that made it different from previous physics theories.

Aaronson says Tegmark devoid of content

Scott Aaronson reviews Max Tegmark's book on the Mathematical Universe Hypothesis (MUH):

Briefly, I think it’s a superb piece of popular science writing — stuffed to the gills with thought-provoking arguments, entertaining anecdotes, and fascinating facts. I think everyone interested in math, science, or philosophy should buy the book and read it. And I still think the MUH is basically devoid of content, as it stands. ...

Putting the two points [about the laws of physics] together, it seems fair to say that the physical world is “isomorphic to” a mathematical structure — and moreover, a structure whose time evolution obeys simple, elegant laws.   All of this I find unobjectionable: if you believe it, it doesn’t make you a Tegmarkian; it makes you ready for freshman science class.

But Tegmark goes further.  He doesn’t say that the universe is “isomorphic” to a mathematical structure; he says that it is that structure, that its physical and mathematical existence are the same thing.

I am glad to see that Aaronson does not believe in any of Tegmark's multiverses, but this review is nonsense.

When Tegmark says that the universe is a mathematical structure, that is just a shorthand for saying that the universe is isomorphic to a mathematical structure. So Aaronson takes two versions of the same statement, accepts one as trivially obvious and rejects the other one.

And why is Aaronson promoting a book whose main point is such a dopey idea?

I think that the MUH does have content, because I believe that it is false.

The public face of physics is largely shaped by popular books written by big-shot MIT professors like Tegmark and Aaronson. I expect more from these guys. Tegmark apparently bet $100 on the success of BICEP2. Maybe he could be explaining that to the public.

Aaronson responds:

As far as falsifiability goes, please help me understand how the string landscape is any more falsifiable than MUH?

Well, the string landscape has well-known falsifiability issues too! But if (hypothetically) you could build a particle accelerator the size of the universe, capable of reaching the Planck scale, then you could at least imagine doing experiments that would definitively confirm or rule out string theory. Whereas even with such resources, it seems to me that the MUH would remain just as empirically inaccessible as before.

This is like talking about the equipment to count how many angels can dance on the head of a pin.

Update: Here is another answer:

Nex Says: English language describes the World so well that it cannot be a coincidence. And it’s not. But the right conclusion is not that the World and the English language are one and the same thing, rather the language was tailored to serve that purpose.

Same thing with mathematics.

Scott Says: Nope, try again! The view that analogizes math to the English language seems totally unable to account for things like complex numbers, linear algebra, Riemannian geometry, or group representations, which were all developed decades or even centuries before anyone thought of any applications to physics, but then turned out to be exactly what physicists needed.

Which English words were coined decades or centuries before anyone needed them?

That is an argument, but thousands of English words were coined before being applied to physics. Those math concepts were all needed when they were developed, just not needed by physicists. So both English words and math concepts were developed long before being applied to physics.