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A quantum register using collective excitations in a BoseEinstein condensate
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/2211.09252v3 (pdf) 
Code repository:  https://github.com/ehaber64/A_quantum_register_using_collective_excitations_in_an_atomic_ensemble_without_a_Rydberg_blockade.git 
Date submitted:  20230712 00:48 
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 singlequbit 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, the atoms never need to be removed from the ground state manifold, and separate storage and computational bases for the qubits are not required, all of which can be significant sources of decoherence in many other types of atomic qubits.
Author comments upon resubmission
Thank you for soliciting reports from referees, and for recommending that we revise our manuscript. We are also grateful to the referees for providing constructive comments on our submission, we have revised our manuscript accordingly, and believe that it has been significantly improved.
We have provided a short summary of the changes we made below, and a more detailed list in our replies to the referee reports.
Gratefully,
Elisha Haber, Zekai Chen, and Nicholas P. Bigelow
List of changes
We thank referee 1 for their recommended changes, and have revised our manuscript in the following ways:
(1) Section 3.2 on the CNOT gate has been heavily modified to be more clear.
(2) Section 5.3 has been expanded to include quantitative error estimates that arise from the sqrt(N) uncertainty in N.
(3) Sections 3.3 and 4.2 have been modified to take into account the interactions between the BEC in state 0> and atoms in states 1> and 2> during the sqrt{SWAP} gate.
(4) The end of section 3.3 was changed to make it more clear what hat{Sigma} is and how atoms may be transferred between lattice sites so quickly during the sqrt{SWAP} gate.
(5) The last sentence of the abstract has been changed.
(6) The word 'spin' in the third paragraph of the introduction has been changed to 'internal.'
(7) The papers the reviewer suggested have been cited.
(8) We have removed the reference to Eq. (1) as a second quantized Hamiltonian right before Eq. (1).
(9) We have changed the description of the internal energy level spacing of the atoms to 'anharmonic' in section 2.
(10) The l variable after Eq. (3) is now defined to be an axis.
(11) N is now defined in the same sentence that the sqrt{N} Bosonic enhancement factor is mentioned in section 2.
(12) The confusing indices in Eq. (4) have been changed to be consistent with what came before.
(13) Additional discussion on single site addressing and gate fidelities has been added to the last paragraph of section 5.4.
We thank referee 2 for their suggested changes, and have revised our manuscript in the following ways:
(1) Additional details about how the qubit states are defined are given in section 3.1, following Eq. (7).
(2) & (3) In the first paragraph of section 3.2 we added a sentence clarifying that the control and target qubits of the CNOT gate correspond to two different lattice sites. Additional details about addressing schemes during each of the different qubit gates considered in this paper were added to section 4.2.
(4) We have added discussion on gate fidelities in the last paragraph of section 5.4.
(5) We justified initializing specific fractions of the BEC population in states 0> and 2> during the CNOT gate by including additional discussion at the end of section 3.2. We also simulated this process in the meanfield limit and gave the estimated error in the initialization fraction in section 5.3.
(6) We removed the reference to the Rydberg blockade from the title of the new manuscript.
Current status:
Reports on this Submission
Anonymous Report 1 on 202387 (Invited Report)
 Cite as: Anonymous, Report on arXiv:2211.09252v3, delivered 20230807, doi: 10.21468/SciPost.Report.7620
Strengths
This is a novel and interesting scheme for quantum computation with cold trapped atoms.
Weaknesses
The manuscript should be further improved to become more clear and convincing.
Report
The authors have addressed much of the criticism in my previous report and the revised manuscript is much more clear. Yet, some issues still remain and the paper should be further improved to be acceptable for publication, as detailed below.
In the first sentence of the abstract, ensemble qubits based on Rydberg blockade are mentioned, but it is not so relevant to the present study to mention it in the most prominent place.
The HO potential for atoms in the lattice will induce energy shift which should be taken into account. The parameter ε in Eq. (4) is in fact that energy which is neglected in the rest of the paper.
Equation (4) (and (11)) is not exactly BoseHubbard Hamiltonian (the hopping term between the lattice sites is missing, while the driving field Ω acts locally on the atoms and does not induce intersite tuneling). But it is secondquantized Hamiltonian.
For the number of atoms in states 1,2,3 the authors sometimes use lowercase n, sometimes uppercase N, which is confusing. Then, in section 5, lowercase n is used for qubit number.
The explanation of the CNOT gate is more clear now but still confusing. In the text the authors explain that for the qubit state spindown>, after the transfer, the BEC in state 0 will have population N/5 and the BEC is state 2 population 4N/5. Now the control qubit is driven from the BEC 0 or BEC 2? I assume 2, as shown in Fig. 4 third column, but the text in the last paragraph of this section says the opposite. The authors should correct that and also correct the qubit states in that paragraph.
I am still not convinced that the SWAP gate will function as argued by the authors. First, using largely detuned laser coupling to the dense spectrum of many HO levels does not work, because these levels have alternating parity and the sum in the first line of Eq. (12) becomes very small due to the partial cancellation of the different transition paths, as the authors also mention. On the other hand, the brief description of how one can make it work in the last paragraph of section 3.3 is not clear and probably not correct. Even if the laser detuning becomes smaller than the level separation to break the destructive interference of the many paths, the retardation for the atom travelling between the two distant lattice sites will be much longer than the 82.7μs. A simple physics tells me that for the atom to travel between two sites separated by some distance d in time t, it should have the large velocity v=d/t or kinetic energy mv^2/2 = recoil energy h^k^/2m that it can only obtain by absorbing a photon with wavevector k from the laser or MW field Ω, which is small.
I suggest the authors remove this section and all the discussion of the SWAP gate from the paper.
The detunings Δ_1,2 in Eq. (13) and in Eqs. (1415) are not the same as they correspond to different lasers creating the harmonic trap and lattice potential. This should be clarified.
In Sec. 4.2, the authors discuss the implementation of single qubit gates with global RF+MW fields (making only one selected site resonant using focused laser beams). But they also mention Raman transition with two laser beams, for which the described formalism involving (N)^0.5 Ω enhancement of the Rabi frequency does not apply, since the laser does not irradiate the whole BEC of N atoms. I assume the Raman transition is mentioned only to contrast with the RF+MF approach and the authors do not mean to use it.
Requested changes
Make corrections and clarifications requested in the report.
Remove sec. 3.3 and all the discussion of the SWAP gate from the paper.