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I am new here in StackExchange and this will be my first question to ask. I have a background in Computer Science and I am interested in looking into Distributed Quantum Computing (DQC). I have read some papers in DQC and one of the mentioned motivations in doing research in this field is the issue of quantum decoherence with respect to the size of superposition in the quantum system being used for computation. One might opt to resort to DQC by letting quantum computers using small quantum superpositions perform distributed computation than use a monolithic quantum computer using large quantum superposition (resulting to higher decoherence rate). The papers which I have read so far do not provide references to researches working on the relationship of size of quantum superposition to the rate of quantum decoherence though.

I am interested to know whether an upper bound on the size of superposition of a quantum system can be defined as a factor for considering DQC with respect to decoherence rate in place of the monolithic design of a quantum computer using a large quantum superposition.

There are also works on coping up with decoherence like manipulation of the environment to improve the rate. I just think that DQC is still an interesting field for research though.

I would appreciate any references to works on relationship of size of superposition to rate of decoherence anyone could provide.

Best Regards.

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  • $\begingroup$ this might be more a physics question. one area to look into, there are some relatively recent physics experiments that show "large" size superpositions eg with superconductors. this was surprising at the time where it was thought "quantum weirdness" aka decoherence might intrinsically have something to do with scale. $\endgroup$ – vzn Jul 4 '13 at 14:36
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    $\begingroup$ The answer to this question is quite complicated. In general, one would expect the rate of decoherence to grow linearly in the number of qubits in superposition. But it depends on quite a few other factors, including on whether you're using quantum error correcting codes to provide quantum fault tolerance or not. $\endgroup$ – Peter Shor Jul 4 '13 at 14:53
  • $\begingroup$ Yes @vzn. I recently came across a paper "Decoherence of quantum superpositions through coupling to engineered reservoirs" by Myatt et al. In their paper they were able to show empirically via experiments that "decoherence rate scales with the square of a quantity describing the amplitude of the superposition state". With this result and assuming that the needed quantum error correction for coping up with decoherence is costly, would it already be a strong justification for looking into DQC (using smaller superpositions) as an option in contrast to the monolithic design of a quantum computer? $\endgroup$ – Jeff Aborot Jul 5 '13 at 6:20
  • $\begingroup$ Oh wow Prof. @PeterShor! I have just read your paper back a few sem Sir. In the paper of Myatt et al. on decoherence it was shown that "the rate of decoherence scales as the square of the separation of the wave packets". Also, in the paper of Giovannetti et al. on quantum RAM architecture, it was mentioned that large superpositions would require expensive and difficult quantum error correction techniques. I am thinking that maybe if I would like to keep error correction to a minimum, then maybe I could bound the size of superposition up to some number k...[continued] $\endgroup$ – Jeff Aborot Jul 5 '13 at 7:17
  • $\begingroup$ and could opt to perform the computation distributedly using several quantum computers with k-bounded superposition size. If the execution time of the algorithm being executed will be greater than the coherence time of its required superposition, then maybe one might opt for DQC using smaller superposition size, therefore longer coherence time. I would greatly appreciate your insights on my thoughts Prof. @PeterShor. $\endgroup$ – Jeff Aborot Jul 5 '13 at 7:20

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