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Quantum Computation is an active area of research that aims to take advantage of quantum physics (e.g. quantum entanglement) to advance the efficiency capabilities of computers (does not alter the Church-Turing thesis).

What are the most significant experiments that have been conducted to demonstrate quantum-computing theory (such as qubits and teleportation)?

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    $\begingroup$ I read the question title and thought it was very vague. But the question itself is quite specific. Maybe you could edit the title to something like 'Are there known actual implementations for basic quantum computing constructs' ? $\endgroup$ – Suresh Venkat Aug 16 '10 at 21:09
  • $\begingroup$ @Suresh: I made the change. $\endgroup$ – Shane Aug 16 '10 at 21:22
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At this stage progress on experimental quantum computing is relatively slow, but there are now a wide variety of systems that can be used to implement one or more qubits.

At the moment the most developed systems as

  1. Ion traps
  2. Liquid state NMR
  3. Linear optics quantum computing
  4. Superconducting qubits

There has also been a lot of recent work with defects in solid state, solid state NMR, endohedral fullerenes, neutral atom traps, atom chips, etc.

The highest numbers of qubits tend to be in ion traps and NMR, though linear optics is doing well too.

As regards significant experiments, that really depends what constitutes progress to you. There was a very nice experiment back in 2007 where two separate ion traps were coupled optically, and some nice recent work on segmented ion traps, which demonstrate ways of scaling ion trap computation beyond 10 or so qubits. There has also been some very nice implementations of measurement based computation using optics, which is also important for scalability. If you have a better idea of the type of experiments you have in mind it would make the task of answering much easier.

The US quantum computing roadmap, available here, provides an excellent, though slightly dated overview of the state of the art circa 2004.

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    $\begingroup$ "At this stage progress on experimental quantum computing is relatively slow". Really? Apparently there is even a Quantum Moore's Law at work! ;-) quantenblog.net/physics/moores-law-quantum-computer $\endgroup$ – Martin Schwarz Oct 15 '12 at 17:02
  • $\begingroup$ @MartinSchwarz: I think it is basically the fact that exponential growth looks linear starting off. But, I wrote that answer over two years ago, and I think it is really speeding up. I'm particularly excited about IBM's recent results. $\endgroup$ – Joe Fitzsimons Oct 16 '12 at 13:43
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This is a nice survey. It is one of the most up to date papers that you'll find about building quantum computers.

Quantum Computers. Nature 464

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For actual physical implementation of conceptual quantum computing devices and what methods may be best suited for these practices, Nielsen and Chuang's book has an entire chapter which is very well written and easy to understand on this.

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    $\begingroup$ Unfortunately that chapter is now somewhat out of date, as there have been significant developments since the book was written. $\endgroup$ – Joe Fitzsimons Sep 6 '10 at 9:21
  • $\begingroup$ The first author is Nielsen. $\endgroup$ – Tsuyoshi Ito Oct 20 '10 at 1:14
  • $\begingroup$ spelling is still wrong :) $\endgroup$ – Alessandro Cosentino Oct 15 '12 at 4:01
  • $\begingroup$ Haha, ah the side effects of too little caffeine. Fixed both problems. Sorry about that! $\endgroup$ – Vincent Russo Oct 15 '12 at 4:11

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