REVIEW
Controllable Coupling in Phase-Coupled Flux Qubits
Mesoscale and Nanoscale Physics · Submitted 26 Feb 2006 · 28 references
Pith's verdict: A clean analytical tunable-coupling proposal for phase-coupled flux qubits; the unshown numerics are a real gap, but the core cancellation argument holds.
T0 · AI review
Why Pith says this
Highlight any text to comment on it.
Referee report
The paper
The paper claims
Two dc-SQUIDs threaded by opposite control fluxes make the coupling between phase-coupled flux qubits continuously tunable from a strong value of order the junction Josephson energy down to exactly zero.
The reading
What carries the argument
The argument is carried by the effective potential $U_{\rm eff}$ built from the inductive, qubit, and connecting-loop Josephson energies, reduced by the boundary conditions to the phase coordinates $\varphi_m,\varphi_p$ and $\varphi'_m,\varphi'_p$. The connecting loop feels an effective flux $f'_{\rm eff}=(\varphi_{L1}-\varphi_{R1})/2\pi$ set by the phase difference between the two qubits; this is large for opposite current states and zero for same current states. The two dc-SQUIDs behave as a single tunable Josephson element with effective energy $\tilde E'_J = 2E'_J\cos\pi f'$. Minimizing $U_{\rm eff}$ gives the local-minimum energies $E_{ss}$ and $E_{s,-s}$ whose difference is the coupling $J$, so turning $f'$ from $0$ to $1/2$ shrinks $\tilde E'_J$ to zero and switches the coupling off.
Extended reading notes
Core claim
On its own terms, the paper establishes that two phase-coupled three-junction flux qubits coupled by a connecting loop with two dc-SQUIDs are described by an effective Hamiltonian $H_{\rm coup} = h_L\sigma_z^L + h_R\sigma_z^R - J\sigma_z^L\sigma_z^R + t_L\sigma_x^L + t_R\sigma_x^R + E_0$ whenever the control fluxes satisfy $f'_L=f'_R=f'$. The coupling constant follows from the difference between same-current and opposite-current state energies, $2J = E_{s,-s}-E_{ss}$, and evaluates to Eq. (41). This means the device can be tuned continuously from a strong coupling of order $E'_J$ at $f'=0$ to a switched-off state at $f'=0.5$, without changing the qubit energy levels. If the control fluxes instead have the same direction, or if only one dc-SQUID is used, the energies of $|\downarrow\uparrow\rangle$ and $|\uparrow\downarrow\rangle$ split, producing unwanted effective fluxes on the qubits, and the system no longer fits the simple coupling Hamiltonian.
Load-bearing premise
The tuning works only when the two SQUID control fluxes are exactly equal and opposite, the qubits sit exactly at the co-resonance point $f_L=f_R=0.5$, and induced flux and kinetic inductance are negligible; any real-world deviation shifts qubit levels and spoils the clean cancellation.
Editorial extensions
If this is right
- At $f'=0.5$ the two qubits are completely decoupled, so the same circuit can perform single-qubit operations without crosstalk and then be switched back to strong coupling for two-qubit gates.
- With three-junction qubits where $E_J/E_{J1}$ is not small, the on-state coupling reaches the $E'_J$ scale, far above the roughly 0.5 GHz typical of inductively coupled flux qubits.
- The same control line that switches the coupling also sets its magnitude continuously, because $J(f')$ is monotone between $f'=0$ and $f'=0.5$.
- The two-SQUID arrangement preserves the equalities $E_{\downarrow\downarrow}=E_{\uparrow\uparrow}$ and $E_{\downarrow\uparrow}=E_{\uparrow\downarrow}$ needed for the two-qubit Hamiltonian, whereas a single SQUID or same-direction fluxes break this symmetry.
Reading between the lines
- A direct spectroscopic test of Eq. (41) would measure the four-state energies as $f'$ is swept; deviations from the predicted $J(f')$ would indicate that the effective Josephson energy $\tilde E'_J=2E'_J\cos\pi f'$ is not the whole story at larger coupling.
- The same opposite-flux cancellation should apply to other phase-coupling geometries, including the four-junction qubits used in the cited experiment, where the effective $\tilde E'_J$ renormalization would enter the coupling formula in the same way.
- Because kinetic inductance and induced flux are neglected in the analytic derivation, a real device's 'off' point will have a residual coupling that grows with loop inductance; measuring this residual would quantify how close to ideal decoupling the scheme can get.
- If the twisted scalable layout is used so that one global field direction acts as opposite fluxes on the two SQUIDs, the practical difficulty of applying two opposing fields disappears, but then any global field noise couples symmetrically and may set a new decoherence floor.
Original abstract
We propose a scheme for tunable coupling of phase-coupled flux qubits. The phase-coupling scheme can provide a strong coupling strength of the order of Josephson coupling energy of Josephson junctions in the connecting loop, while the previously studied inductive coupling scheme cannot provide due to small mutual inductance and induced currents. We show that, in order to control the coupling, we need {\it two} dc-SQUID's in the connecting loop and the control fluxes threading the dc-SQUID's must be in {\it opposite} directions. The coupling strength is analytically calculated as a function of the control flux at the co-resonance point.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We propose a scheme for tunable coupling of phase-coupled flux qubits. The phase-coupling scheme can provide a strong coupling strength of the order of Josephson coupling energy of Josephson junctions in the connecting loop, while the previously studied inductive coupling scheme cannot provide due to small mutual inductance and induced currents. We show that, in order to control the coupling, we need {\it two} dc-SQUID's in the connecting loop and the control fluxes threading the dc-SQUID's must be in {\it opposite} directions. The coupling strength is analytically calculated as a function of the control flux at the co-resonance point.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We propose a scheme for tunable coupling of phase-coupled flux qubits. | contribution 1.00 | 0.59 | 0.18 | asserted 0.62 |
| s1 | The phase-coupling scheme can provide a strong coupling strength of the order of Josephson coupling energy of Josephson junctions in the connecting loop, while the previously studied inductive coupling scheme cannot provide due to small mutual inductance and induced currents. | result 0.48 | 0.29 | 0.30 | asserted 0.86 |
| s2 | We show that, in order to control the coupling, we need {\it two} dc-SQUID's in the connecting loop and the control fluxes threading the dc-SQUID's must be in {\it opposite} directions. | result 0.52 | 0.86 | 0.44 | asserted 1.00 |
| s3 | The coupling strength is analytically calculated as a function of the control flux at the co-resonance point. | result 0.46 | 0.93 | 0.11 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v3
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:cond-mat/0602604 by the authors.
References
Discussion
Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.