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A quantum register using collective excitations in an atomic ensemble without a Rydberg blockade
by Elisha Haber, Zekai Chen, Nicholas P. Bigelow
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Submission summary
Authors (as registered SciPost users):  Elisha Haber 
Submission information  

Preprint Link:  https://arxiv.org/abs/2211.09252v1 (pdf) 
Code repository:  https://github.com/ehaber64/A_quantum_register_using_collective_excitations_in_an_atomic_ensemble_without_a_Rydberg_blockade.git 
Date submitted:  20221118 14:13 
Submitted by:  Haber, Elisha 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Computational 
Abstract
A qubit made up of an ensemble of atoms is attractive due to its resistance to atom losses, and many proposals to realize such a qubit are based on the Rydberg blockade effect. In this work, we instead consider an experimentally feasible protocol to coherently load a spindependent optical lattice from a spatially overlapping BoseEinstein condensate. Identifying each lattice site as a qubit, with an empty or filled site as the qubit basis, we discuss how highfidelity single qubit operations, twoqubit gates between arbitrary pairs of qubits, and nondestructive measurements could be performed. In this setup, the effect of atom losses has been mitigated, and we never need to remove the atoms from the computational basis in the ground state manifold, both of which can be significant sources of decoherence in other types of atomic qubits.
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Reports on this Submission
Anonymous Report 1 on 2023111 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2211.09252v1, delivered 20230111, doi: 10.21468/SciPost.Report.6503
Report
In their manuscript the authors propose a protocol that utilizes
collective atomic excitations in order to create single qubit and
entangling gates in a cold atom quantum register. An emphasis is
made on the point that no Rydberg blockade is needed.
As far as I understand the idea is to create a statedependent
lattice within a BEC and to encode qubits in the individual lattice
sites. Entangling gates between qubits are then mediated via the
BEC.
I think the idea can be interesting, but in my view the paper is
incomprehensible in its current form and cannot be accepted for
publication. Here are some examples/reasons explaining why I arrive
at this conclusion:
1) The current way in which the paper is written, i.e. the
decomposition into small sections and small appendices, does not
work. I think the appendices have to be combined with the main text
in order to enhance readability.
2) I question the choice of equations that are shown in the
manuscript: What do I need Eq. (1) for? Also, I think it would be
good to see details of the derivation of Eq. (4), which appears to
be the most important one of the paper.
3) I find the notation confusing. In Eq. (5) you define
\Omega_si^rj, but actually you are using \Omega_0, \Omega_1,
\Omega_2 in the text. I think this can be fine, but I think the
more appropriate choice would be to formulate the theory in terms
of a minimal model that only contains the states which are really
necessary? This would make the whole discussion far more
comprehensible and would also avoid rather cumbersome equations
such as Eq. (5).
4) Another example for the lack of detail is a statement in Sec.
IV: "...for the lattice sites farthest from the center of the trap,
is 1/364." As a reader one wonders where this comes from and what
the significance of this statement is.
5) A further example is given by the way the magnetic field is
discussed: it is introduced in Eq. (1), then it is mentioned in the
context of spinchanging collision and later it is mentioned again
in the context of the single qubit rotations. When reading the text
one actually wonders whether this is always the same magnetic field
or not because the story is not told in a coherent way.
I think that this is all fixable. My suggestion is to write the
paper in a way in which one introduces the general system at the
beginning and then develops an effective fewlevel model from which
the theory should be derived in a comprehensible fashion.
I also have a technical question: How come that in the inequality
\Omega_0 << U/hbar (Sec IV) there is no enhancement factor \sqrt{N}
appearing?
A final comment: the authors may want to include the following
reference: Collectively encoded Rydberg qubit, Physical Review
Letters 127, 063604 (2021)