Design Constraints for Unruh-DeWitt Quantum Computers

1. new proposal for quantum computer architecture.
2. includes discussion of implementation in real-life settings.

1. presentation in the first sections somewhat unclear.
2. discussions in later sections not sufficiently concrete.

In this article, the authors propose a design for quantum computers based on Unruh-DeWitt detectors linking qubits through Luttinger Liquid quantum channels.

I find the core idea of the proposal interesting and worthy of publication.
However, I also feel that the current manuscript is unclear in its introduction of the results, and lacks concreteness in later sections.

My main reasons for saying that are:

1) The central idea is coupling a qubit to a (helical) 1D bosonic field acting as a quantum channel. This is done by a Hamiltonian such as the one in Eq 2 or 5. These Hamitlonians are completely standard descriptions of spin-boson coupling. It is unclear why the authors insist on calling them "Unruh-DeWitt detectors" when they are not used as detectors in any way; when there is no Unruh physics involved; and when there are many other, more appropriate (standard) ways of describing the same types of spin-boson coupling.

2) The proposal to use the bosonic degrees of freedom in Luttinger Liquids to couple qubits to, is a good idea. But the degrees of freedom you couple to are then really bosons, and the proposal is not very different from earlier proposals for coupling qubits through bosonic channels. The proposed channel certainly does not use a "strongly coupled fermionic system" to act as a channel, as claimed in the introduction. In fact, it uses precisely the bosonic (LL) channel that is left over after all strongly correlated elecectron physics at high energies has been integrated out.
Moreover, the fact that a bosonic field can yield non-zero channel capacity and even perfect communication is a previously known result, cited by the authors. It is therefore unclear which part of the current proposal really represents a new ingredient in the search for efficient quantum channels.

3) Although the authors define gate operations in section 3C, they omit a discussion of how these would be implemented in any concrete setting. Especially gates of the form of eq 20 do not seem to conserve the total charge in the LL, and seem at first sight hard to implement in any concrete way. Additional discussion on this point would be welcome.

4) The whole proposal heavily depends on the availability of an actual Luttinger Liquid in real systems. Although the three experimental settings mentioned by the authors are good candidate systems for Luttinger Liquid physics, and a Luttinger Liquid is expected to be present in them at very low temperatures, real unambiguous experimental demonstrations of Luttinger Liquid physics in these (and other) systems are rare. Finite-size corrections to Luttinger Liquid physics are crucial in most practical setups, and are likely to also strongly influence the proposed quantum channels.
If the authors could provide a quantitative analysis of how robust their proposal is to such effects, and what the expected influence of finite size effects would be in their proposed setups, this would make their proposal much more concrete.

5) The discussion of how to implement the proposal in three possible experimental settings is a welcome part of the manuscript. However, in this discussion the authors selectively combine several different techniques at the cutting edge of current developments in their respective fields. I expect that using femto-second voltage pulses, which can controllably select and target just one of several nm-sized qubit seperated by microns, inside a cryogenic environment, and with the possibility of simultaneously applying a 9T magnetic field, will be technically challenging. This makes the presentation of the experimental implementations less concrete than the estimates of engineering constraints presented by the authors seem to suggest.
A more realistic discussion on this point would certainly improve the presentation of the current proposal.

6) The simulation presented in section V is not actually a simulation of the proposed quantum gates, nor of the proposed communication through the quantum channel, nor even of a Luttinger liquid. The simulation only shows topological edge states present in a prototype model for a topological insulator, under various boundary condition. The outcomes are not unexpected and reproduce well known results from the literature. It is thus unclear what these simulations add to the proposal.
I would recommend that the authors simulate the quantum gates and quantum communication protocols they propose. Showing that numerically they can achieve efficient coupling between qubits and channel, lossless communication for quantum information between qubits, and programmable all-to-all connectivity would strengthen the manuscript.

Because of these points above, I cannot recommend publication of the present manuscript.
Rather than rewriting or revising the current results, I would personally suggest to the authors that doing simulations of their proposed gates and protocols and making more concrete predictions for realistic implementations might be a better way to connect their idea of Luttinger Liquid quantum channels to the existing state of the field.

see report.