The authors present an introduction to the theory of graphs states, some examples of physical implementations, and an outlook as to the scalability of such systems for distributed quantum computation with graph states. The material is presented in a straight-forward manner that could be a valuable reference for researchers; the introductory material on the theory of graph states and its relation to teleportation protocols is particularly well-done. After addressing the points below, I believe the manuscript should be published in the IJQI special issue on distributed quantum computation.

(1) pg. 2, line 15: (grammar) “Each node is quantum computer…” should be “Each node is a quantum computer…”

(2) pg. 2, line 30: (refs) This is an extensive list of proposals for generating these protocols – would it be useful to reference some of the experimental demonstrations at this point as well? (It may help to make the reader aware early-on of the progress towards the physical implementation of these proposals.)

(3) pg. 2, line 31: “post-selecting” is probably the wrong terminology here, as many of the schemes cited in references 14-24 are actually “heralded” protocols.

(4) pg. 3, lines 21 and 32: S is defined twice, once as an operator and then again as a set.

(5) pg. 3, line 34: Pauli operators defined as \sigma_x,y,z here, but used as X, Y, Z throughout the remainder of the paper.

(6) pg. 10, table 3 caption: “above” should be “below” or “in the table”.

(7) pg. 10, table 3, last row: I am confused by this operation. It appears as though the result of a single-qubit operation (X) on “a” is dependent upon a specific neighboring qubit, “b”. Thus, it appears as though this is a two-qubit operation. Is it actually the case that ALL qubits in the neighborhood of “a” undergo complementation, and that because only an array of 12 qubits is shown that it then appears as though a second qubit has been singled out? If this is case, some comment towards this end should be made.

(8) pg. 11, line 13: “minimal graph state” definition in bold here, where other definitions have been made using italics.

(9) pg. 12, fig. 2 caption: “without using any quantum gates” is confusing here. Both CZ and H gates are indicated in the figure. Please revise this caption.

(10) pg. 12, fig. 2 caption: (grammar) the last word should be singular (“state”), not plural.

(11) pg. 12, 3 lines from bottom: (grammar) repetitive clause, “…the state to be transferred the state to be teleported…”

(12) pg. 13, line 16-17: Stating “…gives an overall measurement in the X-Y plane” sounds like you are getting more information than a single measurement can provide. Perhaps “…enables qubit measurement along any axis in the X-Y plane.”

(13) pg. 13-14, fig. 4 and Eq. 19: Part (d) of Fig. 4 and Eq. 19 are confusing because \alpha and \beta were just used as state amplitudes previously… perhaps choose different notation for the Euler angle decomposition.

(14) pg. 15, sec 3, line 1: (grammar) “systems and form” should be “systems form”.

(15) pg. 15, sec 3, lines 7-9: Just a comment of the robustness of photons to decoherence while traversing materials – it might be worth mentioning that certain photonic qubit encoding is much more susceptible to errors during transmission than others; e.g. frequency or time-bin (double-heralding) is much more robust than polarization encoding.

(16) pg. 16, lines 25 and 30: While describing “Linear optical effects” (line 25) you refer to “spontaneous down-conversion” (line 30), which is a nonlinear effect.

(17) pg. 17, fig. 7 caption: Please describe physically what \phi and \theta refer to for the different optical components.

(18) pg. 17, eq. 24: Please delete the left-hand side of line 2 in this equation – as is, it looks like two separate equations, rather than a reduction of the first.

(19) pg. 18, line 16: (grammar) “…difference in the \omega energy…” should be “…difference in energy \omega…”

(20) pg. 18, line 21: (grammar) “…arises from the electric dipole moment…” should be “…arises from the interaction of the electric dipole moment…”

(21) pg. 19, lines 4, 18, 19, 20, and 22: Formatting errors in polarization vectors.

(22) pg. 20, line 1: Please clarify the statement “…and individually violate energy conservation”.

(23) pg. 20, last paragraph: This paragraph seems disconnected from the discussion, though I assume it is here to contrast it with the next page discussing cavities… please make the transition here better for the reader.

(24) pg. 20, footnote g, line 3: (grammar) “For a eigenstate…” should be “For an eigenstate…”

(25) pg. 21, line 5-6: Perhaps cite some of the bulk cavity work as well, such as the work by H. J. Kimble and G. Rempe.

(26) pg. 21, line 36: Is “tunneling” necessary for the description here? I believe this aspect can be described classically.

(27) pg. 22, sec. 3.3: The tone here appears to dismiss local quantum computing schemes. Since distributed schemes have as of yet not been experimentally demonstrated as more viable than local computing schemes, the way this is addressed in this section should be changed. In particular, there are many viable local quantum computing schemes with atoms, ions, etc. However, I believe there are other reasons to promote distributed quantum computation schemes, such as speed-ups gained by the enabled architecture of the system (see, e.g. http://arxiv.org/abs/quant-ph/0507023 and Quant. Inf. Comput. Vol 9, No 2. (2009)).

(28) pg. 23, lines 4-5: Here the claim is made that an impediment to local quantum computing schemes is addressability, but just a few lines earlier it was stated arbitrary control over small registers of qubits can be readily achieved. Please clarify both of these statements.

(29) pg. 26, sec. 3.5.1, line 5 (also Fig. 9 caption): I believe “post-select” needs to be clarified here. While the light-matter entanglement is post-selected, the matter-matter entanglement is heralded. Given that the matter-matter entanglement is the focus of the following discussion, “herald” is probably better terminology at this point (following the terminology of PRA 75, 052318 (2007)).

(30) pg. 26, sec. 3.5.1, line 9: (grammar) “erasure” should be “erase”.

(31) pg. 26, footnote o: Is the statement here made on the assumption that the two qubits that were being acted upon were previously entangled with other qubits not involved in the operation? If so, please clarify this point.

(32) pg. 27, eq. 47: Given the definition provided on page 17, I believe that after the 1/2 waveplate the horizontal polarization term should pick up a minus sign (and this should be propagated through the following equations).

(33) pg. 27, line 25: Could you please clarify why this final state is referred to as a “singlet state”, when the state produced is symmetric?

(34) pg. 30, line 16: The reference to growing graph states “even if this buffering is not possible” is a bit ambiguous, given the discussion prior to it (double heralded scheme versus lambda). Please clarify the schemes you are referring to that enable only entanglement generation between two nodes (with only one qubit per node) versus those that allow for a probabilistic quantum gate.

(35) pg. 30, sec. 4.1, line 5: Does “post-select” here include “heralded” schemes?

(36) pg. 30, footnote s: This is a very strong statement, and should either be moved into the text and explained, or should be removed from the manuscript.

(37) pg. 33, line 8: (grammar) “…two strategies for that we call…” should be “…two strategies that we call…”

(38) pg. 34, fig. 13 caption: Please clarify “reasonable” graph growth for a success probability of p = 1/3.

(39) pg. 35, line 7: (grammar) “…4 qubits other qubits.”

(40) pg. 36, line 9: Please clarify the “rapid” overhead increase with decreasing success probability (by, for example, a reference to the derivations, such as L.-M. Duan and C. Monroe, Adv. At. Mol. Opt. Phys., vol. 55, E. Arimondo, P.R. Berman and C.C. Lin, eds. (Elsevier, 2008), pp. 419-464).

(41) pg. 38, line 27: (grammar) “…route scalable devices” should be “…route to scalable devices.”

(42) pg. 39, refs: It would help clarity to make groups of citations in the text chronological, for instance, references 14-24 (first cited on page 2).

There is a lot of work that could be cited here. Since some of the references currently cited at this point detail the construction and operation of cavities in solid-state, you could consider citing some of the early optical cavity work with atoms (e.g. Phys. Rev. Lett. 68, 1132 - 1135 (1992)). However, given the topic of discussion (and the significant advances that continue to be made in this field), it may be more appropriate to cite more recent work and review articles, such as:

--Nature 453, 1023-1030 (2008)

--Science 317, 488-490 (2007)

--Appl. Phys. B 76, 125–128 (2003)

There is also a Review of Modern Physics article discussing cavity QED experiments with atoms and microwave radiation:

--RMP 73, 565 (2001)

Given the large body of work that has been done with cavity QED and atomic systems over the last 10-20 years, there may also be other (possibly more well-suited) publications that could be cited here as well.

I have made a change to the article this thread is about. The reason for the change was:

Revised in light of review comments on quantalk

This paper is now accepted for publication in the IJQI Special Issue on Distributed QIP.

The thread will remain open for any interested researcher to post questions, observations etc.