<p>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. </p>

<p>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.</p>

<p>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.</p>

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

<p><em>Best Regards.</em></p>

CC BY-SA 3.0
2013-07-04T14:36:22.040Z
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.
vzn
CC BY-SA 3.0
2013-07-04T14:53:00.957Z
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.
Peter Shor 
CC BY-SA 3.0
2013-07-05T06:20:08.330Z
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?
Jeff Aborot
CC BY-SA 3.0
2013-07-05T07:17:09.117Z
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]
Jeff Aborot
CC BY-SA 3.0
2013-07-05T07:20:55.103Z
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.
Jeff Aborot
CC BY-SA 3.0
2013-07-05T17:51:18.020Z
@jeff, my understanding, DQC is basically a very new area of study and its motivation is partly as you indicate, to deal with difficulty of maintaining large-scale superposition which experimentally is tough. yes in a future architecture DQC would probably play a key role along with error correction mechanisms, there appears to be an interplay as you indicate. you ask questions that are on the edge of knowledge, basically open questions. nobody knows right now what a good workable/working quantum architecture would entail, the literature is full of many ideas & DQC is a plausible contribution.
vzn
CC BY-SA 3.0
2013-07-06T02:54:34.320Z
thank you @vzn. somehow that confirms that I am looking into a still largely unchartered area worth discovering. Van Meter et al. in Japan are already working on a quantum multicomputer, a lab-sized distributed quantum computer. Grover also once touched DQC in one of his early papers. I am really interested in answering my current question. I think I can start on Myatt et al.'s paper on decoherence and superposition. I am thinking that it might be what Prof. Shor has said, we might expect a linear growth in the rate of decoherence in the number of qubits in the superposition.
Jeff Aborot
CC BY-SA 3.0
2013-07-06T03:03:11.090Z
@vzn, I just though that my question can be broken into several questions instead, "Is there a hard upper bound _k_ on the size of the (Schrodinger's) _cat_ for it to be still usable for computation? If so, what is it? Such that when the size of the cat exceeds _k_, then we might opt to shift into DQC and use _kittens_ (smaller cats with size not exceeding k) instead."
Jeff Aborot
<quantum-computing>
Relationship between size of quantum superposition and rate of decoherence
Jeff Aborot
# Relationship between size of quantum superposition and rate of decoherence

(Asked by: username_0 on 2013-07-03)

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.*

**Tags:** quantum-computing
> **Comments:**
> **username_1**: 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.  
> **username_2**: 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.  
> **username_0**: 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?  
> **username_0**: 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]  
> **username_0**: 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.  
> **username_1**: @jeff, my understanding, DQC is basically a very new area of study and its motivation is partly as you indicate, to deal with difficulty of maintaining large-scale superposition which experimentally is tough. yes in a future architecture DQC would probably play a key role along with error correction mechanisms, there appears to be an interplay as you indicate. you ask questions that are on the edge of knowledge, basically open questions. nobody knows right now what a good workable/working quantum architecture would entail, the literature is full of many ideas & DQC is a plausible contribution.  
> **username_0**: thank you @vzn. somehow that confirms that I am looking into a still largely unchartered area worth discovering. Van Meter et al. in Japan are already working on a quantum multicomputer, a lab-sized distributed quantum computer. Grover also once touched DQC in one of his early papers. I am really interested in answering my current question. I think I can start on Myatt et al.'s paper on decoherence and superposition. I am thinking that it might be what Prof. Shor has said, we might expect a linear growth in the rate of decoherence in the number of qubits in the superposition.  
> **username_0**: @vzn, I just though that my question can be broken into several questions instead, "Is there a hard upper bound _k_ on the size of the (Schrodinger's) _cat_ for it to be still usable for computation? If so, what is it? Such that when the size of the cat exceeds _k_, then we might opt to shift into DQC and use _kittens_ (smaller cats with size not exceeding k) instead."  

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## 0 answers

