Transcript The Learnability of Quantum States

The Ghost in the Quantum Turing
Machine
Scott Aaronson (MIT)
Aharonov 80th Birthday Conference, Anaheim, CA
Happy 81st-to-Last Antibirthday,
Yakir!
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Stuff I considered talking about:
Postselection in quantum computing
Quantum computing with closed timelike curves
Psi-epistemic theories in quantum mechanics
The information content of quantum states
 80
In addition to Yakir’s 80th birthday, this
year we celebrate Alan Turing’s 100th
Turing is best-known as the “founder of computer science,” but he
also worried about many of the same issues Yakir does (including
the foundations of QM)…
Here’s a postcard Turing sent
Robin Gandy in March 1954,
months before his death:
“The Universe is the interior of the light cone of the Creation.
Science is a differential equation. Religion is a boundary condition”
This Talk
Building on previous ideas, I’ll explore an unusual perspective on
the ancient “physics and free will” debate—one that really would
put “free will” in the universe’s boundary conditions
I’ll place a much higher premium on being interesting than on
being right
Thanks
Determinist? Robot? No problem! Whenever I
say “free will,” you can assume I’m merely
investigating some sort of “effective” free will
My version of free will will be stronger than the usual
“compatibilist” kind, but compatibilists might still find
much of what I have to say “compatible” with their views
What is free will? What’s determinism?
I’ll try to sidestep the moral, legal, and theological issues that have
dominated the free-will debate for ~2500 years…
There’s no free will, says the philosopher / To hang is most unjust.
There’s no free will, assent the officers / We hang because we must.
—Ambrose Bierce
Basic observation: If you stretch the notion of “determination” far
enough, you can make anything trivially “determined”!
(e.g., by God’s Encyclopedia, which only He can read)
So I don’t think determinism even merits scientific interest (or “grows
fangs,” or constitutes a credible threat to anyone), unless it involves
in-principle predictability by devices consistent with physical law
Cf. the debate around Bell inequality and “superdeterminism”
A “Turing Test” for Free Will?
AMT 1950: “I propose to consider
Turing’s revised question:
My position: If the answer to this revised question is no,
the question, ‘Can machines
“Are there imaginable
then there’s not much more science could possibly do
think?’ … The original question … I
digital computers which
toward “showing the universe is hospitable to free will”!
believe to be too meaningless to
would do well in the
there’s not much
deserveConversely,
discussion.”if the answer is yes, then
imitation game?”
more science could possibly do toward showing it isn’t.
Do humans
have free will?
Revised question: Is it physically possible to
build a machine that, given some human’s
environmental stimuli as an input feed,
predicts that human’s future choices to any
desired accuracy and arbitrarily far into the
future—at least in the probabilistic sense that
radioactive decay is predictable, and without
killing or “drastically altering” the human?
Even if this “prediction game” were
winnable, why should we care?
Even if someone could predict which finger I’d flick a few seconds
in advance (cf. Libet et al.), that doesn’t seem very threatening!
More like a conjuring trick.
(Also, they obviously couldn’t tell me their prediction
beforehand, since then I’d just do the opposite!)
The problem arises from what I call the…
“Predictor Principle”: Once a predictor of your
choices becomes reliable enough, we ought to
regard it as simply another copy of you—with all
the sci-fi consequences that would entail
Want to visit Mars? Just fax
yourself!
(And have the “original you”
painlessly euthanized … or not)
Going on a dangerous mountain-climbing trip?
Remember to back up your brain first!
Most scientists: brain = computer program
John Searle: brain  computer program—because brains have
mysterious, unspecified “causal powers” that mere programs lack
My view: If there’s a difference, the best place to look for it is
almost certainly in computer programs’ physical copyability
(a property that isn’t obviously shared by brain states!)
Lots of people have claimed that the randomness of quantum
measurements, as chaotically amplified by brain activity, could
already make humans physically unpredictable in the relevant way.
Alas, those people are wrong!
p  
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 free will
What we’d need instead is
“Knightian Uncertainty”
Economists’ fancy term for uncertainty that can’t even be
objectively quantified using probabilities
(also shows up as nondeterminism in computer science)
But where, in a law-governed universe, could Knightian
uncertainty possibly be hiding? I think there’s exactly one
possibility that physics hasn’t persuasively closed off…
Lack of knowledge of the
initial conditions
+
The No-Cloning Theorem
What was the pure or mixed
state at the Big Bang?
What are the relevant
“indexical” facts? (“Where
are you” in the multiverse?)
Illustrative applications:
Quantum key distribution
Quantum money
Copy-protected quantum
software
To make the issue as concrete as possible:
TIME
Microscopic neural
event (e.g., opening of
a sodium-ion channel)
PMD
PMD
PMD
“Past macroscopic determinants”
(PMDs): observables that could
have been non-invasively
measured long before the event,
and that influence its probability
BIG BANG
Can every event today be “grounded” in PMDs, from which we can use
quantum mechanics to calculate its probability? Or do some causal
chains go all the way back to the Big Bang without terminating at PMDs?
The “Freedom from the Inside Out” (FIO) Perspective
(Hoefer 2002, Stoica 2008)
Look, isn’t it anti-scientific insanity to imagine that our choices
today could “affect” (or even be nontrivially correlated with) the
universe’s microstate at the Big Bang?
The FIO Answer: Recall that the known equations of physics are
all time-reversible, making forward-in-time causation seem just as
incomprehensible as the opposite!
On the modern view, causality is an “emergent phenomenon,”
associated with the Second Law
BLOCK UNIVERSE
But if we’re talking about undecohered
qubits left over the Big Bang, then there’s
no entropy increase anyway—so why not
annotate the static “Block Universe” with
backwards causal arrows in those cases?
?
The “Harmonization Problem”
Hoefer (2002) raised the obvious problem: Once
we let causal arrows point backward in time,
(say) from events today to the microstate at the
Big Bang, how do know a globally-consistent
solution even exists? How do we prevent causal
cycles—i.e., closed timelike curves?
In this account, the answer is simple:
“Macrofact”: Whether a
Stegosaurus kicked a particular
rock 150 million years ago
“Microfact”: The polarization
state of some particular
photon of the CMB radiation
Retrocausal explanations are allowed only for microfacts, not for
macrofacts. Together with No-Cloning, ensures CTCs don’t arise
The Initial-State Objection
Don’t we know that the initial state at the Big Bang was basically
thermal, and hence couldn’t have encoded any interesting info?
3 POSSIBLE RESPONSES:
Famously, the Second Law implies the Big Bang state must have
been maximally far from thermal, for not-yet-understood reasons
Inflation doesn’t solve this problem unless Hilbert space dimension can grow
Quantum field theorists thought they knew black hole event
horizons were thermal, but AdS/CFT suggests otherwise!
More broadly, we’ve learned that many physical theories have
both “bulk” and “boundary” formulations, and that the boundary
picture can not only nontrivially encode “everything that happens
in the bulk,” but even clarify issues that were obscure in the bulk
picture (e.g., why is the entropy upper-bounded by the surface area?)
The Gerbil Objection
Why doesn’t the following system have “Knightian free will” as
discussed in this talk?
USB LINK
SENSORS
AI PROGRAM
ABLE TO PASS
TURING TEST
Gerbil in a box, whose movements
provide Knightian indeterminism
If we say it’s because the gerbil and AI-program are “separable,”
then why aren’t the brain’s “Knightian noise” and its cognitive
information-processing similarly separable?
Well, transferring a brain into silicon certainly seems more
“invasive” than unhooking the gerbil box! But honestly I don’t know
The Many-Worlds Objection
Consider an observer (e.g., Wigner’s friend) being asked lots of
questions in superposition:
q1 O1    qN ON
N
 microdetails
Even if microscopic details of the initial state could somehow
affect one observer’s answer, how could the same details affect
all the Everett branches independently of one another?
Conclusion: If we want to accept this account, then we have to
assume that there exists irreversible decoherence (whatever its
source—gravity?), and that such decoherence is a necessary
condition for ‘free will’
The Advertiser Objection
(Generic objection to any account of free will)
Humans are depressingly predictable in practice—advertisers,
salespeople, seducers, demagogues all take advantage of this
Response: It’s obvious that humans are somewhat predictable;
the only question at issue is whether the prediction accuracy
can approach that of physics
On the other side of the intuitive ledger, we need to put the
conspicuous failure of psychics, stock market analysts, pundits,
etc. to predict what individuals or even entire populations will do
(Of course, forecasters typically excel at explaining why
whatever choices were made were “inevitable”!)
“Penrose Lite”
The view I’m discussing would affirm Roger Penrose’s core
belief in a link between the mysteries of mind and those of
modern physics, while denying almost all of the particulars…
No appeal to Gödel, or to the Platonic perceptual abilities of
human mathematicians
No barrier to a digital computer passing the Turing Test (at
most, a barrier to simulating a particular person)
Nothing exotic supposed about the biology of the brain (e.g.,
no long-range entanglement or gravity-sensitive microtubules)
No uncomputable quantum-gravity dynamics
No attempt to explain consciousness (which incidentally seems
logically impossible to me, regardless of what physics is assumed!)
“Application” to the Boltzmann Brain Problem
I exist
On my account, a necessary condition for “freely-willed
observerhood” would be having the right kind of causal relationship
to the universe’s initial state. Boltzmann brains wouldn’t count as
observers because they wouldn’t have that relationship
Is This Picture Falsifiable?
“Predictions,” if you want to take it seriously:
Psychology will never become physics (the accuracy of brainprediction won’t asymptotically approach that of comet-prediction)
(Ordinary) quantum uncertainty can indeed be chaotically
amplified by brain activity on “reasonable” timescales
Some of the relevant quantum states can’t be “grounded” in
PMDs, but only traced back to the early universe
A quantum-gravitational description of the early universe won’t
reveal it to have a simply-describable pure or mixed state
Irreversible decoherence, whatever its source, will forever
prevent us from doing “Wigner’s friend” experiments on
uncontroversially-conscious subjects
Conclusions
David Deutsch’s “momentous dichotomy”:
Either a given technology is possible, or else there’s
some principled reason why it’s not possible.
When it comes to perfect brain-predictors, I think either horn of
this dichotomy would have “crazy” consequences! In other
words, there’s no “safe, conservative option”
Key question: To what extent can our decisions be
probabilistically grounded in past macroscopic determinants?
Reason for hope: This is an empirical question! Future
discoveries in physics, biology, and other fields could very
plausibly tell us more