# Quantum Bayesian Networks

## June 17, 2012

### Dissing the Prima Donna

Filed under: Uncategorized — rrtucci @ 7:35 pm

According to Wikipedia, John R. Pierce “…wrote on electronics and information theory, and developed jointly the concept of Pulse code modulation (PCM) with his Bell Labs colleagues Barney Oliver and Claude Shannon. He supervised the Bell Labs team which built the first transistor, and at the request of one of them, Walter Brattain, coined the term transistor.”

From Mark Wilde’s book, I learned that “John R. Pierce issued the following quip at the end of his 1973 retrospective article on the history of information theory [193]:”

“I think that I have never met a physicist who understood information theory. I wish that physicists would stop talking about reformulating information theory and would give us a general expression for the capacity of a channel with quantum effects taken into account rather than a number of special cases.”

John Pierce, John Pierce, your words cut us to the quick. They are still approximately true in 2012.

[193] John R. Pierce. The early days of information theory. IEEE Transactions on Information Theory, IT-19(1):3-8, January 1973.

## June 15, 2012

### A New Standard of Beauty for String Theory

Filed under: Uncategorized — rrtucci @ 7:12 pm

For a decade or two, Caltech professor of physics John Preskill has given many excellent talks and lectures about quantum computing (and also about high energy physics, his original specialty). Much of this material can be found at his Caltech webpage, which is a pleasure dome for physics nerds.

Ten years ago, Preskill gave a wonderful talk, one with very little math, understandable by most physics undergrads, entitled

Quantum Computation and the Future of Physics (delivered at the Berkeley Workshop on Theory of Computation and the Sciences. – 10 May 2002)

The title alone invites endless speculation. Quantum computing is likely to change considerably the technology landscape, but what about “fundamental” physics? Will it change that too very much or not much at all?

All of the talk is interesting, but there is one transparency that I find particularly intriguing (transparency number 48 out of 49). Here it is:

So he thinks Matrix M-theory cannot be simulated efficiency by a quantum computer, although quantum field theory can be. Or at least he thought this 10 years ago. I wonder if he has changed his mind since then. I hope Preskill will be proven wrong (or right) in the near future by someone. String Theorists, get to work.

Should physical theories be required to satisfy certain complexity constraints, and can such requirements serve to winnow out a lot of bad theories? Maybe if the time evolution of a version of string theory cannot be simulated with polynomial efficiently, on a quantum computer, then that version of string theory should be considered kaput and verboten?

## June 12, 2012

### The Importance of Being Consistent

Filed under: Uncategorized — rrtucci @ 4:40 pm

Full Title: The Importance of Being Earnest, A Trivial Comedy For Serious People

Ralph Waldo Emerson said “A foolish consistency is the hobgoblin of little minds” in his essay “Self-Reliance”. I think I know what he meant. Being stuck in the same classical rut all the time is no fun.

Recently I came across the following paper

• Decoherent histories of quantum searching, by Wim van Dam, Hieu D. Nguyen, arXiv:1206.1946

I didn’t look at the paper too closely, but it made me learn a bit about a subject I had never studied before: the decoherent histories (or consistent histories) approach to (or interpretation of) quantum mechanics. This approach is due to Griffiths, Gell-Mann, Hartle, Omnes, and others. Here is a review:

• J.J.Halliwell, A Review of the Decoherent Histories Approach to Quantum Mechanics, arXiv:gr-qc/9407040
• The Net Advance of Physics: DECOHERENT HISTORIES (Interpretation of Quantum Mechanics) here

It occurred to me that quantum Bayesian nets (QB nets) can be used to study consistent histories. Here is how. The following are not very deep observations. What did you expect?! this is a trivial blog for serious people.

Let $Z_{1,N} = \{1,2,\cdots, N\}$. Consider a QB net with $N$ nodes $\underline{x}_1,\underline{x}_2, \cdots, \underline{x}_N$, where for each $j\in Z_{1,N}$, the random variable $\underline{x}_j$ takes on values $x_j\in S_{\underline{x}_j}$.

Let $J\subset Z_{1,N}$ and let $J^c= Z_{1,N}-J$ be its complement. Let $x_J = (x)_{j\in J}$.

Suppose $\rho_{meta}$ is the meta density matrix of the QB net. (See my mixology paper for a definition of meta density matrices.)

Suppose $x_J$ and $y_J$ are both elements of $S_{\underline{x}_J}$. Note that

$[\langle x_J| + \langle y_J|\;]\rho_{meta}[{\rm h.c.}] =$

$= \langle x_J|\rho_{meta}| x_J \rangle + \langle y_J|\rho_{meta}| y_J\rangle + 2 {\rm Re} \langle x_J|\rho_{meta}| y_J\rangle$

Define $x_J$ and $y_J$ to be consistent histories if

${\rm tr}_{\underline{x}_{J^c}}\;\;{\rm Re}\langle x_J|\rho_{meta}| y_J\rangle= 0$

We could define it differently. For example, we could ask instead that

$Av\;\;{\rm Re}\langle x_J|\rho_{meta} | y_J\rangle = 0$

where $Av(\cdot) = \langle f_{J^c}|\cdot|f_{J^c}\rangle$ for a particular, fiducial state $f_{J^c}\in S_{\underline{x}_{J^c}}$.

## June 5, 2012

### Yao Assembling QC Dream Team For China

Filed under: Uncategorized — rrtucci @ 8:14 pm

Andrew Chi-Chih Yao was born in Shanghai 65 years ago. He did his undergraduate studies at the National Taiwan University. He got a PhD in physics from Harvard Univ. in 1972. Then he got a second PhD in computer science from the Univ. of Illinois at Urbana-Champaign in 1975.

He is the recipient of many prestigious computer science awards, including the Polya, Knuth and Turing awards. He has taught at many famous American Universities (MIT, Stanford, Berkeley, Princeton). He now works at Tsinghua Univ in Beijing.

Recently, Yao has become a serious advocate for quantum computing in China.

In Jan 2011, he inaugurated the Center for Quantum Information (CQI) (cookie?) at Tsinghua University. CQI is currently very busy recruiting a quantum computing dream team. They seem to have a bottomless money purse, courtesy of the Chinese government.

In the past year, Yao has given at many venues a talk entitled

Quantum Computing: A Great Science in the Making.

Here is a video of the talk when he gave it at Brown Univ.. Very instructive and revealing. Well worth viewing if you are a QC aficionado.

Yao’s history clearly shows that he is a very ambitious and competitive person. Like any ambitious coach, he will want his QC team to win big.

footnote: Yao’s middle name is chichi. According to Webster,