Physics and computation: two papers

Mitchell Porter (
Wed, 18 Dec 1996 16:23:01 +1000

I've just been catching up on physics via the preprint archive at, and found two papers that might be of interest.
(How to interpret the preprint numbers: a paper like trans-tech/991201
would be found at

(i) "Topics in quantum computers" by D.P. DiVincenzio (cond-mat/9612126)
This paper proposes a list of minimal requirements for creating a quantum
computer, which might be summarized as

1) States in a Hilbert space used to encode information (in "qubits")
2) The computer can be placed in some desired starting state
(e.g. a ground state, reached by cooling)
3) Isolation - the computer must not become quantum-entangled
with its environment to any great degree
4) Specified pairs of qubits can be entangled as required
(quantum-computer algorithms are sequences of such operations)
5) The computer can be subjected to a "strong" measurement
(the "textbook" kind, which projects the computer's wavefunction
into an eigenstate of some observable)

The operations in 4) are the computations, the measurement in 5)
I think is the read-out.

DiVincenzio mentions the "linear ion trap" of Cirac and Zoller
(Phys Rev Lett 74 (1995), pp4091-4094; described in quant-ph/9608011)
as an existing system which satisfies all his criteria to some degree.

(ii) "M Theory As A Matrix Model: A Conjecture" by T. Banks, W. Fischler,
S.H. Shenker, L. Susskind (hep-th/9610043).

M theory is the theory believed to underlie all the string theories.
Prior to this paper, so far as I know, noone had a concrete proposal
for the exact equations of M theory, just circumstantial evidence
regarding its general form. So if this conjecture is correct it's
a major advance.

The conjecture is that M theory "in the infinite momentum frame" is
equivalent to "the N=infinity limit of the supersymmetric matrix quantum
mechanics describing D0 branes." I have yet to get a grip on what the
latter refers to, although my impression is that matrix models are
a class of field theories in which the fields are matrix-valued.

In any case, BFSS write that the theory features "the emergence of field
theory as an approximation to an elegant finite structure". So this may
finally be a TOE which deals in bits rather than continua. They also write:

"If the conjecture is correct, [...] in principle, with a sufficiently big
and fast computer any scattering amplitude could be computed in the finite
N matrix model with arbitrary precision. Numerical extrapolation to
infinite N is in principle, if not in practice, possible."

So the theory is computable, but the computations would be practically
impossible using existing methods. Perhaps we'll end up using quantum
computers to extract predictions from M theory!

(iii) While I'm talking about computers, a comment on Intel's
announcement that it's built a teraflop (trillion operations per second)
computer (
wasn't this achieved by a computer in Japan earlier in 1996?