The authors thank the reviewers for their valuable comments on the paper, and the editor for his patience during the revision process.
Our revised paper is available as arXiv:0906.2686v2 [quant-ph]
The principal concern of the reviewers was to make the explanation of the rather complex operation of the architecture clearer; we have addressed this concern primarily by revising the figures to build an understanding of the operation from the bottom up. We have added a new, basic Fig. 2 showing the smallest operational element. We split the former Fig. 4 (circuit diagrams) into the new Figs. 3 & 4, and added architectural building blocks to each figure to show the elements involved and the paths of pulses in the system. The former Fig. 4, the micrographs of the test device, has been deleted and similar micrographs incorporated into the new figures. The text of Secs. 4.1 & 4.2 has been slightly revised to refer to the figures, though the bulk of the description is in their long captions.
We have also added some meat to the end of Section 1 and beginning of Section 2, which will hopefully ease the reader into our system more gradually. In a few additional places, sentences have been revised to be clearer.
Three paragraphs have been added: at the end of Sec. 3 we discuss our assumptions about optical loss in more detail; in Sec. 5.1 we note that the Markov analysis may pessimistically over-estimate required resources; and in Sec. 6, we summarize more concisely the experimental values that must be achieved for this system to work.
The new text and figures are more explicit that the quantum dots are in cavities. We now refer to the larger disks and racetracks as waveguides rather than cavities.
A number of typos and typesetting errors in the bibliography were corrected.
As the paper is long, we are willing to make a revision available with markup indicating changes to the text.
Detailed responses to the reviewers' comments are below.
From Jason Smith:
The paper describes an architecture for a scaled up quantum computer based on 'quantum dots' and micro-optics, that is a hybrid of circuit-based and measurement-based schemes (only to generate entanglement between spatially remote regions). Fabrication errors are handled using topographic methods. The authors suggest that a wide range of candidate materials could be used in this architecture, but do not go into much detail as to the relative merits of each.
It is difficult for me to comment on the information science aspects of the proposal, which are mostly beyond my expertise. The authors' approach certainly seems reasonable and they have provided some good ideas as to how the different quantum device units could co-operate and communicate. By comparison with Steane's work on ion trap computing fewer references are made to experimentally achieved parameter values (there is some discussion of the cavity cooperativity of disk resonators and losses in waveguides). This is understandable given the state of the art in solid state qubits, but in the absence of these, as an experimentalist with interest in the area, I would find it helpful if they could suggest some parameter requirements so that the reader can form his own assessment of which material and processing methods to use.
Section 3.3 has been expanded to include more discussion of the physical characteristics of the loss and cooperativity parameters required of the system.
In summary the contribution of this particular paper is to take a number of existing ideas and combined them in an intelligent and believable way. In general I think that this kind of proposal paper can be useful as a framework for discussion and to foreground schemes that are in principle realisable. The paper appears to achieve that, and if the ideas contained therein are adopted by the community as an attractive route then the paper will likely be cited quite heavily in introduction sections of journal articles on experimental efforts. To increase the chances of this, a little more interrogation of the required parameters for the atom-cavity systems would be helpful.
From Reviewer #2:
In this paper, the authors start with the acute observation that there is a classical communication problem in large-scale quantum computers, and particularly in distributed architectures. The main part of the paper is a proposal for implementing a distributed quantum computer that explicitly solves this problem. The system consists of microcavities coupled by waveguides and quantum busses. There is a built-in balance between deterministic nearest-neighbour two-qubit gates and probabilistic gates between two distant qubits. The error correction is provided by surface codes. I believe that this paper makes a valuable contribution to our knowledge of how to implement (distributed) quantum computing. However, before I can recommend publication, the authors should address the following three points.
First, I found this paper very difficult to read. The reader is overwhelmed with detail from the start, without the benefit of a general overview. The paper would be easier to read if first the general structure of the quantum computer is sketched, and then the key components treated in detail. Figure 2 illustrates this general problem: while aesthetically pleasing, it actually hinders the efficient communication of the basic principles. I can clearly see the mediating quantum bus, but it is not at all obvious to me how teleportation or purification works in this setup. For that matter, I cannot tell whether there is supposed to be a directionality in the figure with respect to the quantum information, or whether that is entirely "virtual". The paper must be rewritten to give a gentler introduction to the architecture. The steps of increasing detail and complexity could be something like this:
1. In the introduction, give a general sketch of the architecture;
2. give brief description of the relevant physics of the key components;
3. indicate how these components work together in the architecture;
4. give overall performance estimates.
With the additions to the text of Sec. 1 and the change in the flow of the figures, we believe that the paper now follows this outline and should be much easier to grasp.
Second, it seems to me that the detailed topological aspect of this architecture is relatively unimportant for this paper. In particular, if we know the required classical communication, and we can create general graph states, then the details of the topological CNOT are not needed to understand this paper. Moreover, the description of the topological CNOT on pages 4 and 5 makes sense only when you already know how it works, in which case it is redundant. I think it is best to drop section 2 altogether: it is not needed to understand the remainder of the paper, and it is not sufficiently detailed to learn about topological codes from it.
After a good deal of thought and debate among the authors, we politely disagree, and ask to keep this section as-is. The reviewer is correct that Sec. 2 alone is insufficient to understand tQEC; indeed, tQEC is an extremely difficult topic and even full-length tutorials require diligence to grasp.
Our purpose in the section is not to detail tQEC, but to (a) establish a vocabulary for use later in the paper, (b) describe broadly how we expect tQEC to be implemented on our architecture (including introducing the issues of hard fault tolerance and the singular factory resource requirements), and (c) help the reader understand which of the numerous references are most relevant to our system. We believe that if we deleted Sec. 2, that in fact most of the text would ultimately have to be sprinkled throughout other sections in the paper, disrupting their flow and making the paper harder to read, rather than easier.
Finally, there are a number of serious omissions in the references. The recent paper by Stace, Barrett, and Doherty (http://link.aps.org/doi/10.1103/PhysRevLett.102.200501
) should be cited in the context of qubit loss in surface codes. This is an extremely relevant result for this work, since it shows how to deal with (among other things) fabrication errors in the chip. Other papers that must be cited are references for distributed quantum computing, in particular the paper by Barrett and Kok (http://link.aps.org/doi/10.1103/PhysRevA.71.060310
), and the paper by Lim, Beige, and Kwek (http://link.aps.org/doi/10.1103/PhysRevLett.95.030505
). These show how to create arbitrary graph states based on probabilistic parity gates. Finally, the original paper demonstrating the idea of the parity gate based on a quantum bus is Barrett et al (http://link.aps.org/doi/10.1103/PhysRevA.71.060302
We expanded the discussion of physical gates in Sec. 3.3 to include most of these references. The paper on dynamic loss of lattice qubits is cited in the new introduction to Sec. 2.