Download Current State of Quantum Computing

Reykjavik University
New Technology
Spring 2006
Students
Guðmundur Már Einarsson
Hlynur Tryggvason
March 19th 2006
Current State of Quantum Computing
Table of Contents
Introduction.......................................................................................................... 3
Basics of quantum computing ................................................................................. 3
Origins of quantum computing ................................................................................ 5
Recent advancements in quantum computing ........................................................... 5
Current problems in quantum computing .................................................................. 6
How does this technology relate to Moore’s Law?....................................................... 7
Potential impact on software design and programming ............................................... 9
Potential impact on daily life ................................................................................... 9
Security issues..................................................................................................10
Searching.........................................................................................................11
Business ..........................................................................................................11
Accessibility......................................................................................................11
Disruptive technology ........................................................................................12
Conclusion ...........................................................................................................12
References ..........................................................................................................13
Appendicies .........................................................................................................15
Appendix A: Email to/from Charles Ross - former Secretary of the Quantum Computers
in Europe Pathfinder Project. ..............................................................................15
Appendix B: Email to/from George I. Bourianoff – senior program manager in the
Strategic Research group at Intel ........................................................................16
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Current State of Quantum Computing
Introduction
Moore’s Law states that the power of microprocessors will double every 18 months. This
has been valid for at least last 40 years and if it continues to hold, then today’s chip
manufacturing techniques will exhaust their capabilities by the year 2020, when a
transistor would become no larger than the size of an atom. So the need for a new
technology in building computers is clear if we are going to keep up with Moore’s Law
after 10 to 15 years.
Enter quantum computing, potentially the next step of computer evolution. Functional
quantum computer is a realistic option that could be available after 10 years or so.
Quantum computers have the potential to become so powerful that problems which take
today’s computers years to solve would take minutes for a quantum computer. In this
paper we look at the origins of quantum computing, see how they differ from todays
computers and look at current problems in the field. Then we look at how quantum
computers could extend Moore’s Law and finally at the huge impact quantum computers
could have if they would exist. For example, if one quantum computer would be
available today, no information on the internet would be safe.
Basics of quantum computing
Almost every computer today is based on the Turing machine, developed by Alan Turing
in the 1930s. The Turing machine consists of a tape of unlimited length that is divided
into little squares where each square can hold one bit (0 or 1) or be left blank. A readwrite device reads these symbols and blanks which gives the machine its instructions.
In a quantum turing machine the difference is that the tape and the read-write head
exist in a quantum state, which means that each square can now hold one qubit which is
either 0 or 1 or a superposition of 0 and 1 (being in a superposition basically means that
the qubit can hold multiple values at the same time).
Figure 1: Classical and Quantum Registers:
(a) A comparison of a classical bit and a quantum bit.
(b) Superposition states allow quantum registers to store all possible values simultaneously. [12]
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Current State of Quantum Computing
Roughly speaking, a computer with N
qubits
1
1
equivalent to a classical computer with
2
4
2
the
processing
Equivalent Classic bits ( 2Qubits )
power
N
has
Qubits
classic bits. The table on the right
3
8
the
4
16
computing power a quantum computer
5
32
might provide.
6
64
7
128
Just to put things in perspective, if we
8
256
would have a quantum computer with
16
65536 = 8 KB
32
4294967296 = 512 MB
might
give
some
sense
of
300
300 qubits, then we would have 2
states, approx. the same number of
atoms in the known universe. [12]
Since each qubit can hold multiple values, it follows that a quantum computer can work
on multiple computations at the same time, which gives us native parallelism. But now
you must be thinking: “I can listen to music, download movie trailers and work on my
thesis at the same time on my computer, is this not parallelism?”. It is a form of
parallelism, but it is not native. Classic computers have gotten very powerful and are
able to effectively simulate parallelism. But the fact remains that each processor (or each
processor core if the processor has multiple cores) can only work on one computation at
the same time. With quantum computers, it would essentially be possible to create a new
processor for each application, process or thread that would require it.
Although quantum computers have the potential of becoming a lot faster than Turingbased computers, they can be simulated using a Turing machine (given an unpractical
amount of time and memory). This means that quantum computers cannot solve any
problem that a Turing machine can’t,
such as the infamous halting problem
[2].
Figure 2: Hypothetical high-level view of
a quantum processor. [16]
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Current State of Quantum Computing
Origins of quantum computing
We don’t have to go far back to find the origins of quantum computing. While computers
have been around for the majority of the 20th century, quantum computing was first
theorized just 20 years ago, by a physicist at the Argonne National Laboratory. [1]
The idea of quantum computing came to be when scientist predicted the future of
classical computation. If it would follow Moore’s Law, then silicon chips would eventually
be no larger than a few atoms. But that introduces a problem, because the classic laws of
physics (those that silicon chips are based on) do not apply on an atomic scale.
Fortunately, quantum mechanics apply on an atomic scale and because of that, scientist
began to speculate on a new breed of computers based on quantum physics. [3]
The first quantum algorithm was devised by Peter Shor, a research and computer
scientist at AT&T’s Bell Laboratories in New Jersey. The algorithm solves an important
number theory problem, factorization, that many encription methods (such as RSA) are
based on. In fact, if a working quantum computer would be devised that could run this
algorithm, no information anywhere in the world would be safe! Fortunately, methods do
exist that use quantum properties to encrypt data as well. [3]
Recent advancements in quantum computing
The most advanced quantum computers today have 7 qubits [1], meaning that they are
still at the “1 + 1” state.
Government organisations such as USA’s DARPA, the UK’s Defence Evaluation and
Research Agency, the Deutsche Forschungsgemeinschaft, and The European Union are
spending a lot of money in research as well as the leading players in the information
technology and networking industries in order to get closer to a real machine. [10]
Physicists in academic labs and at firms such as IBM, HP and NEC have tried a variety of
quantum computing approaches but none seems likely to deliver a working machine in
less than 10 years. IBM currently owns the most advanced quantum computer, which can
manipulate 7 qubits, meaning that they are still at the “1 + 1” state [1]. Despite the
difficulties that are currently associated with quantum computing, a company called DWave Systems plans to have a working quantum computer in three years [15]. The
computer will not be fully functional quantum compuer but will be able to solve problems
like the traveling-salesman problem in reasonable time. D-Wave Systems have already
applied for some patents [14] in the field.
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Current State of Quantum Computing
By the end of 2005, researchers at the University of Michigan pushed quantum
computing closer to the real world with the fabrication of a key component, an “ion trap”.
This ion trap is important because it can host a quantum bit (qubit), the fundamental
element in quantum computing. This could be one way to mass-produce hardware for
quantum computers. [4]
So, every day we are getting closer and closer, although it is a fact that we are still many
years off from functional quantum computer.
Current problems in quantum computing
Although a lot of progress have been made over the past few years, quantum computers
are still in their infancy. For them to be practical in solving real-world problems, they
would need have several dozens of qubits. [1]
We contacted (by email) one of Intel’s quantum researchers, George I. Bourianoff11,
titled as senior program manager in the Strategic Research Group at Intel Corporation.
One of the questions we asked him was “Is quantum computing the future?”
His answer was:
“Quantum computing requires ultra low temperatures and is out of
equilibrium with the room temperature background and can therefore be
very low power. However, I personally feel that it is too difficult to
maintain quantum state and quantum computing is many years off if
ever.”
As seen by his answer, quantum computing can become very efficient in terms of power
consumption and cooling, allowing for a lot higher clock speed in quantum processors
than in current processors. Despite this fact, we are still facing a very difficult problem,
error correction. Quantum computers have the tendancy to enter an inconsistent state
just by being exposed to the environment. This is unavoidable since just by reading the
state of a qubit will force it to decend from the superposition to become either 0 or 1,
effectively destroying the data held in the superposition. In 1998, researches at Los
Alamos National Laboratory and MIT managed to read the state of a single qubit without
actually looking at it. [3] This is a significant milestone in quantum error correction and
has given a lot of hope to researchers in the field.
1
George Bourianoff – Bio: http://www.intel.com/technology/techresearch/people/bios/bourianoff_g.htm
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Current State of Quantum Computing
Quantum hardware is also just in its infancy but is becoming more important to test the
theories that have been introduced. Seth Lloyd, Professor of Mechanical Engineering at
MIT is currently a prominent researcher in quantum hardware. [3] We sent him a query
about his work by e-mail but unfortunately did not receive a response in time.
How does this technology relate to Moore’s Law?
In 1965, Gordon Moore, co-founder of Intel, wrote an article on the future development
of semiconductor industry for the 35th anniversary issue of Electronics magazine. In the
article, Moore noted that the complexity of minimum cost semiconductor components
had doubled per year since the first prototype microship was produced in 1959. This
exponential increase in the number of components on a chip became later known as
Moore’s Law. [7]
In 1980, Moore’s Law started to be described as the doubling of number of transistors on
a chip every 18 months. At the beginning of the 1990s, Moore’s Law became commonly
interpreted as the doubling of microprocessor power every 18 months.[8] And today,
Moore’s Law is so general that it basically says that the rate of technological development
will double every 18 months.
The demise of Moore’s Law has been predicted repeatedly over the last few decades and
now more and more papers and articles are written about “the end of Moore’s Law”.
Although Moore’s Law has been valid for all this time, like everything else it must come
to an end. If we assume that Moore’s Law will continue to hold in the next few years,
today's chip manufacturing techniques will exhaust their capabilities by the year 2020,
when a transistor would become no larger than the size of an atom. [11]
In 2003, four members of the Institute of Electrical and Electronics Engineers, Zhirnov,
Cavin, Hutchby, and Bourianoff submitted a paper that proposed that we may be about
to hit a wall when it comes to scaling electronics.
Their paper, Limits to Binary Logic Switch Scaling - A Gedanken Model [9] describes that
eventually the tunnelling of electrons and holes will become too great for the transistor to
perform
reliable
operations
so
the
two
state
of
the
switch
would
become
indistinguishable. This cannot be allowed in a binary system, but it would happen if its
size gets as small as 4 nm. Indeed, this would be the size of a transistor produced in 13
years, keeping strict adherence to Moore's Law.
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Current State of Quantum Computing
As mentioned before we contacted George I. Bourianoff, which is one of the writers of
this paper, now working as senior program manager in the Strategic Research Group at
Intel Corporation and has special research interest in quantum computing.
One of the questions we asked him was how Intel is going to respond to these facts he
concludes in his paper. His answer was:
“Intel can project scaling along more or less conventional lines (some
variant of the field effect transistor) for the next 15 years or so. Beyond
that, we are looking for alternative technologies that can be integrated
on to CMOS to extend Moore's Law which we are confident we will be
able to do.”
This might answer why Intel and others have not been pushing so much on this new
technology. The need is maybe not as urgent as some might think, they have all those
years to go. This does not only apply to Intel, other chip manufacturers are confident
that they will be able keep up with Moore’s Law for at least the next ten years with
current technology.
In the paper mentioned above they add that the heat from these transistors will be very
difficult to moderate, because to do so would require somehow diverting the heat
produced by this device away from the processor. The entire processor could also be
cooled but that would produce more heat than it takes away.
The heat problem has not even been solved by other technologies. In the email we got
from Bouriannoff he adds:
“The exact nature of those technologies is not clear. However, we
believe that we must look to alternative technologies which are out of
equilibrium with the room temperature thermal environment. In the
case of the binary switch, maintaining state against room temperature
fluctuations requires an energy barrier of ~.02 ev and is responsible for
the energy dissipation in switching.”
On the web we found frequent quotes from scientists saying that “Quantum computing
begins when Moore’s Law ends” and others saying “quantum computing will extend
Moore’s Law.”
It doesn’t matter how they formulate it, we can be pretty sure that Moore’s Law will be
valid for the next 10 years at least, but if we think any further than 10-15 years it is
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Current State of Quantum Computing
almost impossible to predict about the state of processing power. It’s an obvious fact that
we must find some new technology if we are going to keep up with Moore’s Law after 15
years or so but if quantum computers become real we might see growth in processing
power that goes way beyond Moore’s Law.
Potential impact on software design and programming
With the increase of multi core processors, software designers and programmers are
increasingly feeling the pressure of using design patterns that enforce consistency,
especially when the software is doing a lot of things at the same time. The parallel nature
of quantum computing also requires new design patterns that enforce consistency, which
could result in a major rethinking in software design.
On a lighter note, a classic procedural style programming language for quantum
computers has already been designed and implemented [6]. This is very important in
making the transisiton from classic to quantum computers for programmers because it
allows for the implementation and simulation of quantum algorithms. It also shows that
classic methods of programming apply also to quantum computers.
In general though, quantum software will not be extensively studied until quantum
hardware becomes a reality and thus, at this point, we can only speculate how software
design would change with quantum computing.
Potential impact on daily life
Everybody agrees that the impact quantum computer would have is huge. Many
specialists even conclude that the impact on technology would likely be as large as the
impact of the transistor.
In our investigation of the potential impact quantum computers could have we found
multiple speculations of the technological impact, some of them even far, far from reality
(at least to us). But what we found interesting is that not much seems to be written
about the financial/economical impact quantum computers could or would have.
We found one very interesting article called "The Potential Impact of Quantum
Computing" [10] originally published in the Croner Business Networks Briefing in 1998.
What made this different from other articles about this topic is the education of the
authors. Charles Ross2, co-author of this article, studied accounting, law and economics
2
Quantum Information Partners LLP - Charles Ross - http://www.qipartners.com/partners.html
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Current State of Quantum Computing
but has spent his career since 1958 in computing. So we decided to contact Charles in
case he might have spent more time than others in investigating the possible
financial/economical impacts of quantum computers.
Charles replied quickly, telling us that recently he had moved more into Quantum
Cryptography. He is currently writing a paper about Quantum Computing and sent us the
first thoughts for the paper. In his paper there is a chapter called “Immediate Threat”
where he says “CTOs, CIOs and CSOs need to review their current strategies as stored
archives of today’s transmissions will be susceptible to decryption in the future.”
He also told us that together with some colleagues he set up Quantum Information
Partner LLP and they have done some work for the Department of Trade and Industry.
Last May they set up a presentation at the Bank of England of all the Quantum
Cryptography systems now available.
So it is obvious that the threat is real and organizations that rely on cryptography are
watching out.
Security issues
If quantum computers would become true we would face a lot of security issues, for
example many security codes, like passwords can be broken just by guessing, check the
answer and then guess again until you got the right code (today in most cases you won’t
actually get infinitely many guesses, but let’s assume so). Let’s say there are n possible
answers to check, then it would take an average of (n+1)/2 guesses to find the answer
using today's computers. The only reason why this is okay is that it would in most cases
take years to do. But the
time for quantum computer
to solve this problem would
probably
be
counted
in
minutes if not seconds. [2]
Today's
cryptography
algorithms
are
based
on
mathematical problems that
are hard to solve with the
existing
algorithm
technologies and computing
power.
factoring
The
a
problem
of
large number
Figure 3: Potential quantum computing impact. [10]
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Current State of Quantum Computing
that has been made from the multiplication of two large prime numbers is the most
widely used of those mathematical problems.
Quantum computer could easily factor large numbers, and would therefore be extremely
useful for decoding and encoding secret information. Our current methods of encryption
are simple compared to the complicated methods possible in quantum computers. [1] For
example, one method of secure quantum communication is based on the measurement
property of quantum state (recall that just by reading data in a quantum state forces it
do decend from the superpostition). If A would send a secret quantum key to B, then B
could easily detect that the key was intercepted, because if someone had intercepted it,
read it, and forwarded it again, then it would no longer be in a quantum state. Similarly,
if that same someone would not be capture the photon carrying the key, copy it, and
send the original to B, since copying of quantum state is prohibited in quantum
mechanics. [12]
Searching
Algorithms [13] have been written that would allow a quantum computer to almost
instantaneously search massive databases and return very precise results. If this would
come true, things like web search would take much less time and return more precise
results.
Business
Like we said earlier, not much seems to be written about the financial impact quantum
computers would have. That is not really surprising as the quantum technology is still
just in its infancy and has a really long way to go until it will, if ever, come true.
Specialist do although suggest to businessmen that have companies which rely on secure
transmission or cryptography to watch out for quantum computing.
Accessibility
Quantum computing could become so powerful that speech recognition could become
much more reliable than it is today and effectively eliminate keyboards. Furthermore if
quantum teleportation becomes a reality then the need for classic wired or even wireless
networks would be eliminated.
11
Current State of Quantum Computing
Disruptive technology
People seem to be careful before speculating about the possibility of quantum computing
being a disruptive technology, maybe because everybody is in its own corner trying to be
the first instead of telling others about their plans.
But the potential for disruptive technologies in the quantum field is huge and can be seen
just be measuring the number of companies that are currently investing in all kinds of
patents [14] in this field. Among those companies there are many small venture
companies but also the big ones like HP, IBM, Microsoft and more.
Conclusion
Although the principles behind quantum computers have been established and small
model systems constructed, we are still a long way from practical working computers.
Our research shows that quantum computing has immense potential and that engineers
are confident that the remaining hurdles will be surpassed. Optimists believe that
quantum computers will eventually become mainstream and significantly change the
information and computing industry in terms of speed, security and even accessibility.
This new theory brings up a huge challenge for physicists in building working quantum
computers and for computer scientists to develop new algorithms and methods to use
such devices.
There seem to be at least 10 years until we will see quantum computers that can be
compared to today's computers, but if the quantum computing dream will become true it
will probably have huge impact on our lives.
If we live long enough, we just might get to experience it.
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Current State of Quantum Computing
References
[1] How Quantum Computers Will Work. Howstuffworks. Retrieved February 10th 2006,
from Howstuffworks. http://computer.howstuffworks.com/quantum-computer.htm
[2] Quantum computer. (March 2006). Wikipedia. Retrieved February 10th 2006, from
Wikipedia, the free encyclopaedia. http://en.wikipedia.org/wiki/Quantum_computer
[3] The Quantum Computer. (April, 2000). Jacob West. Retrieved February 10th 2006,
from Computer Science at Caltech. http://www.cs.caltech.edu/~westside/quantumintro.html
[4] Quantum Hardware. (December 2005). Kate Greene. Retrieved March 19th 2006,
from Technology Review.
http://www.technologyreview.com/InfoTech/wtr_16063,294,p1.html
[5] Bibliography on Quantum Programming Languages. (June 2005). Simon Gay.
Retrieved February 10th 2006, from Simon Gay's Bibliography on Quantum Programming
Languages. http://www.dcs.gla.ac.uk/~simon/quantum/
[6] QCL - A programming Language for Quantum Computers. (March 2004). Bernhard
Oemer. Retrieved February 10th 2006, from QCL - A Programming language for Quantum
Computers. http://tph.tuwien.ac.at/~oemer/qcl.html
[7] The Lives and Death of Moore's Law. (October 2002). First Monday. Retrieved March
13th 2006, from First Monday. http://www.firstmonday.org/issues/issue7_11/tuomi/
[8] Moore's Law. (March 2006). Wikipedia. Retrieved March 13th 2006, from Wikipedia,
the free encyclopaedia. http://en.wikipedia.org/wiki/Moore%27s_law
[9] Limits to Binary Logic Switch Scaling—A Gedanken Model. (May 2003). Victor V.
Zhirnov, Ralph K. Cavin, James A. Hutchby and George I. Bourianoff. Retrieved March
13th 2006, from Intel Exploratory Research.
http://www.intel.com/research/documents/Bourianoff-Proc-IEEE-Limits.pdf
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Current State of Quantum Computing
[10] Impact of Quantum Computing. (November 1998). Z/Yen Limited. Retrieved March
14th 2006, from Zyen.
http://www.zyen.com/Knowledge/Articles/impact_of_quantum_computing.htm
[11] Life after Moore's Law: Quantum computing. (October 2000). InfoWorld Test Centre.
Retrieved March 13th 2006, from InfoWorld.
http://www.infoworld.com/articles/tc/xml/00/10/16/001016tcquantum.html
[12] The Development of Quantum Hardware for Quantum Computing. (July 2005). A. J.
Daley, J. I. Cirac and P. Zoller. Retrieved March 19th 2006, from Center for Quantum
Optics and Quantum Information.
http://th-physik.uibk.ac.at/qo/news_items/200507_Quantum_DCZ/Quantum_DCZ.html
[13] Rapid sampling through quantum computing. (Feb 2000). Lov K. Grover. Retrieved
March 13th 2006, from lanl.arXiv.org e-Print archive mirror.
http://xxx.lanl.gov/PS_cache/quant-ph/pdf/9912/9912001.pdf
[14] Patents in Quantum Computing. Quantum Fog. Retrieved March 14th 2006, from
Quantum Fog. http://www.ar-tiste.com/qc-patents.html
[15] Quantum Calculation. (July 2005). Erika Jonietz. Retrieved March 14th 2006, from
Technology Review.
http://www.technologyreview.com/articles/05/07/issue/forward_quantum.asp
[16] Quantum Computing Architecture Overview. Tzvetan S. Metodi. Retrieved March
19th 2006, from Tzvetan S. Metodi’s website.
http://wwwcsif.cs.ucdavis.edu/~metodiev/qcarch.html
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Current State of Quantum Computing
Appendicies
Appendix A: Email to/from Charles Ross - former Secretary of the Quantum
Computers in Europe Pathfinder Project.
----- Original Message ----From: "Guðmundur Már Einarsson"
<gudmundurme03@ru.is>
To: <charles.ross@qipartners.com>
Sent: Tuesday, March 14, 2006 6:06 PM
Subject: Quantum computing, paper.
Thank you for your e-mail.
The Oxford Business School recently
circulated a report on the commercial
prospects for QIP. You can find it at
http://www.qipirc.org/documents.php .
Recently I have been more involved with
Quantum Cryptography.
Hello Mr. Charles,
We are two students at our last year for
BSc in computer science doing a
research paper in a course called "New
technology" at Reykjavik University,
Iceland.
Together with some colleagues I set up
Quantum Information Partners LLP and
we have done some work for the
Department of Trade and Industry. Last
May we
set up a presentation at the Bank of
England of all the Quantum
Cryptography
systems now available.
The subject of our paper is "Quantum
computing".
We were reading an article about the
impact of quantum computing where you
seem to be the writer. It was published
in 1998 so much can have changed
since then but we decided to send you
email as we found out that you are
also interested in economics and
financials.
We have just signed a Letter of
Understanding with Oxford University to
set
up a commercial test bed to enable
various organisations to design and
engineer commercial applications as part
of a prototype ultra high volume,
ultra high security comms backbone.
What we are thinking is what financial or
economic impact you think quantum
computers would have if they would
become real?
Try www.qipartners.com. We have not
updated our site with the above news.
We
only signed the LOU yesterday!
It would be a huge honour if you could
send us few lines.
Also attached is the first thoughts for a
paper I have to give in the Autumn
about QC. There is a bit more about
Quantum Computing generally.
Best regards,
Gudmundur Mar Einarsson
Hlynur Tryggvason
I hope this is a help.
Good luck with your BSc's. Let me know
how you get on. What are you plans
when you graduate?
Charles Ross
15
Current State of Quantum Computing
Appendix B: Email to/from George I. Bourianoff – senior program manager in
the Strategic Research group at Intel
-----Original Message----From: Guðmundur Már Einarsson
[mailto:gudmundurme03@ru.is]
Sent: Monday, March 13, 2006 10:43 AM
To: Bourianoff, George I
Subject: Quantum computing, paper.
Dear Gudmundur,
The questions you ask are good
questions. Intel can project scaling
along more or less conventional lines
(some variant of the field effect
transistor) for the next 15 years or so.
Beyond that, we are looking for
alternative technologies that can be
integrated on to CMOS to extend Moore's
aw which we are confident we will be
able to do.
Hello Mr. Bourianoff,
We are two students at our last year for
BSc in computer science doing research
paper in a course called "New
technology" at Reykjavik University,
Iceland.
The exact nature of those technologies is
not clear. However, we believe that we
must look to alternative technologies
which are out of equilibrium with the
room temperature thermal environment.
In the case of the binary switch,
maintaining state against room
temperature fluctuations requires an
energy barrier of ~.02 ev and is
responsible for the energy dissipation in
switching.
The subject of our paper is "Quantum
computing". We found very interesting
paper called "Limits to Binary Logic
Switch Scaling-A
Gedanken Model" where you are one of
the writers. We decided to write you as
we saw that your current research
interest is in quantum computing.
We would be really honour if you could
spend a little time answering this email
:)
Quantum computing requires ultra low
temperatures and is out of equilibrium
with the room temperature background
and can therefore be very low power.
However, I personally feel that is too
difficult to maintain quantum state and
quantum computing is many years off if
ever. What I feel may be possible is to
use spin based systems which are
naturally isolated from the thermal
background (e.g. nuclear spin systems)
or else use magnetic cooling on more
conventional spin devices. There are
many problems but I think the answer
lies in this direction.
In the paper you find out that eventually
the tunnelling of electrons and holes will
become too great for the transistor to
perform reliable operations so the two
states of the switch would become
indistinguishable. (plus the heat
problems)
If we expect that Moore's Law will hold
this would probably happen in the next
10-15 years if our calculations are right.
So our questions are these:
What do you think will happen then? Is
this the end of Moore's Law?
Is it something that Intel is worried
about? Is quantum computing the
future?
I hope this helps,
George
Hope you have time to send us few lines,
Best regards,
Gudmundur Mar Einarsson
Hlynur Tryggvason
16