Pith. sign in

REVIEW 2 major objections 6 minor 1 cited by

Quantum computing with superconductors I: Architectures

T0 review · 2 major / 6 minor · reviewed 2026-08-28 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A phase qubit coupled to a nanomechanical resonator can store and retrieve quantum states with better than 90% fidelity, according to the paper's simulations.

desk verdict A competent 2006 review of superconducting qubit architectures, with a useful beyond-RWA section but a forward-looking memory-fidelity claim that rests on a unitary simulation. read the letter →

arxiv quant-ph/0603224 v1 pith:7G6WRYZT submitted 2006-03-24 quant-ph

Michael R. Geller , Emily J. Pritchett , Andrew T. Sornborger , F. K. Wilhelm This is my paper · ORCID
classification quant-ph
keywords superconductingqubitsJosephsonjunctionsphasequbitchargefluxnanomechanicalresonatorquantummemoryrotating-waveapproximation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This review of superconducting qubit architectures sets out the circuit models for the three basic Josephson-junction qubits—phase, charge, and flux—and organizes the routes to multi-qubit logic into fixed linear couplings, tunable couplings, and resonator-mediated dynamic couplings. Its most concrete forward claim is numerical: a phase qubit coupled to a nanomechanical resonator can act as a fast quantum memory, with storage-and-retrieval fidelity above 90% provided the qubit and resonator coherence times exceed a few tens of nanoseconds. The authors reach this by going beyond the rotating-wave approximation with a perturbative dressed-state method and then optimizing the resonant interaction times and detunings used in the memory protocol. The claim matters because it says a working quantum memory—an essential primitive for solid-state quantum computation—should be buildable from superconducting circuits that already exist.

What carries the argument

The load-bearing object is the coupled phase-qubit–resonator model of Eq. (75), $H = \sum_m \epsilon_m c_m^\dagger c_m + \hbar\omega_0 a^\dagger a - i g \sum_{m m'} x_{m m'} c_m^\dagger c_{m'}(a - a^\dagger)$, which describes a current-biased Josephson junction, kept here to two levels when computing with it, linearly coupled to a single harmonic phonon mode of a nanomechanical resonator. The analytical machinery around it is the Jaynes–Cummings dressed-state basis, with the counter-rotating and diagonal terms gathered into a perturbation $V$ that is included systematically rather than dropped. Evaluating the dressed-state propagator in that basis turns a time-evolution problem into sums over stationary states, which the authors compute perturbatively and then use to simulate and optimize the memory gate; the optimization of resonant interaction times and off-resonant detunings is what buys the high fidelity at strong coupling.

What would settle it

A direct experimental test would be to build the described circuit—a current-biased phase qubit coupled to a piezoelectric disc resonator—extract the coupling $g$ from the vacuum Rabi splitting, run the optimized store-and-retrieve sequence, and compare the measured fidelity at gate times around 10–50 ns against the above-90% prediction; a device with coherence times above a few tens of nanoseconds that falls clearly below that fidelity would contradict the paper's central claim. A cheaper check is numerical: add relaxation and dephasing terms to the same Hamiltonian and see whether the optimized fidelities still exceed 90%.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the rotating-wave approximation is not the right starting point for fast resonator-coupled phase-qubit gates, and that a perturbative treatment of the terms the RWA drops makes strong-coupling operation accurate. For the model Hamiltonian of a current-biased Josephson junction coupled to a piezoelectric nanomechanical resonator, the authors show that at a coupling ratio $g/\Delta\epsilon = 0.30$ the RWA badly misses the exact dynamics, while their dressed-state perturbation theory reproduces the transfer probabilities. They then simulate a complete memory operation—transfer the qubit state into the resonator, hold it, and transfer it back—and, after numerically optimizing interaction times and off-resonant detunings, report memory fidelities squared above 90% for coupling strengths that allow gate times short enough to fit inside the available coherence window. This is presented as a prediction for existing superconducting circuits, not a measured result.

Load-bearing premise

The prediction rests on the assumption that Eq. (75), with the qubit treated as two levels, the resonator as one harmonic mode, and no dissipation or higher energy levels, accurately describes a real phase-qubit-plus-resonator device, and that the actual qubit and resonator coherence times exceed a few tens of nanoseconds.

Editorial extensions

If this is right

  • A fast quantum memory for phase qubits does not require new materials: the building blocks are a current-biased Josephson junction and a piezoelectric disc resonator, both already demonstrated separately.
  • Because the optimized pulse sequences allow stronger qubit-resonator coupling, memory gates can be made fast enough to fit many operations within the expected coherence window.
  • The dressed-state perturbation theory supplies a way to design resonator-coupled gates outside the rotating-wave approximation, which is necessary once the coupling ratio approaches tens of percent and the RWA demonstrably fails.
  • The same resonator-mediated interaction that stores a qubit in the memory protocol can, in principle, be used to transfer quantum information between qubits on a shared bus, extending the architecture from storage to multi-qubit logic.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same dressed-state optimization strategy should transfer to other resonator-coupled qubit platforms, such as charge or flux qubits coupled to microwave cavities, because the counter-rotating corrections it targets are generic to linear qubit-oscillator couplings, not specific to phase qubits.
  • A natural next step is to add dissipation to the model: the paper's fidelity numbers come from a closed system, and how much relaxation and dephasing of the qubit and resonator degrade them is a quantitative question the paper leaves open.
  • If the predicted fidelities survive at stronger coupling, the architecture becomes a route to entangling two phase qubits through a shared resonator by storing one qubit, swapping it out into a second qubit, and reading out the joint state—a two-qubit gate the authors do not simulate here but the model directly supports.
  • The 90% memory-fidelity threshold with coherence times of a few tens of nanoseconds sets a concrete engineering benchmark that later superconducting-qubit experiments could have looked for, making the 2006 prediction a falsifiable historical milestone.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Request a human review

A listed scientist reviews the paper for a fee and the review publishes here regardless of verdict. See the reviewers or get listed.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. This paper is a review chapter on superconducting qubit architectures. It derives circuit Hamiltonians for phase, charge, and flux qubits; discusses fixed linear couplings (capacitively coupled phase and charge qubits), tunable couplings (tunable EJ, Makhlin-Schön-Shnirman register, Averin-Bruder electrostatic transformer, rf coupling), and dynamic couplings via resonators. The final section contains original material: a dressed-state perturbative treatment of a phase qubit coupled to a nanomechanical resonator beyond the rotating-wave approximation (Sec. 5.3), and a numerical study of a quantum memory operation with optimized interaction times and detunings (Sec. 5.4). The paper's forward-looking claim is that memory fidelities better than 90% can be achieved with phase qubits and resonators whose coherence times exceed a few tens of nanoseconds.

Significance. If the claimed results hold, the paper provides a useful pedagogical review of superconducting qubit architectures and a concrete numerical proposal for a fast quantum memory. The perturbative dressed-state method in Sec. 5.3 is benchmarked against exact diagonalization for a finite-dimensional model, which is a genuine internal consistency check. The circuit derivations in Secs. 2–4 are clearly presented and will be helpful to researchers entering the field. The main forward-looking quantitative claim in Sec. 5.4, however, is based on a unitary simulation and therefore needs careful qualification before it can be taken as a prediction for realistic devices.

major comments (2)
  1. [Sec. 5.4, Eq. (86) and Fig. 15] The memory fidelity F^2 = |α* c00(tf) + β* c10(tf)|^2 is computed from the unitary Hamiltonian of Eq. (75), with no dissipation, qubit leakage, or higher phonon states beyond the truncation. The subsequent statement that 'memory fidelities better than 90% can be achieved using phase qubits and resonators with coherence times longer than a few tens of ns' is therefore not directly supported by the simulation: the coherence-time threshold is an external assumption, not a parameter of the model. The lower panel of Fig. 15 shows optimized gate times that are themselves tens of nanoseconds over much of the plotted range, so the assumed coherence time is not clearly much longer than the total store-and-retrieve time. Please either include a dissipative (e.g., master-equation) estimate of the memory fidelity, or explicitly state that the quoted fidelities are coherent state-transfer fidelities and that the coherence-time condition is an additional constraint that the model does not quantify.
  2. [Sec. 5.2–5.3, Eq. (75) and gates] The simulations in Secs. 5.3 and 5.4 treat the phase qubit as a two-level system and the resonator as a single harmonic mode, truncating the phonon Hilbert space (to five states) and neglecting higher Josephson-junction levels. The coupling constant g is stated to depend on material properties and size of the resonator, but no numerical estimate is provided for the range of g/Δε actually realizable in existing circuits. Since the paper concludes that a fast quantum memory 'should be possible' with existing circuits, the validity of the two-level approximation and the achievable coupling range are load-bearing for that conclusion. Please add a short discussion justifying the truncation and give an estimate (or literature values) for g/Δε in concrete device parameters.
minor comments (6)
  1. [Sec. 3.0.1, Eq. (34)] The second equation of motion contains a typo: it reads EJ2(sinφ1 − s1) but should read EJ2(sinφ2 − s2).
  2. [Sec. 3.0.1, Eq. (46)] The interaction term δH ≡ g σ_y^i σ_y^i has the same index on both Pauli operators; it should be σ_y^1 σ_y^2 (or σ_y^i σ_y^j with i ≠ j). The matrix representation in Eq. (47) shows the intended form.
  3. [Sec. 3.0.1, text after Eq. (42)] There is a duplicated word: 'defined in in (42)' should read 'defined in (42)'.
  4. [Sec. 5.3.2] The phrase 'and, for mn /nequal00' is a typo and should read 'and, for mn not equal to 00'.
  5. [References] The reference to Rouse et al. contains 'discinct quantum levels' which should be 'distinct quantum levels'.
  6. [General] The paper is a review chapter and would benefit from a short 'scope and limitations' statement near the beginning, indicating which sections are review material and which contain original numerical results.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the numerical predictions are model-based computations benchmarked by exact diagonalization, and the coherence-time clause is an external condition rather than a fitted input.

full rationale

The paper is a review chapter whose central forward-looking claim, the Sec. 5.4 memory-fidelity projection, is a computation within an explicitly stated model. The fidelity F^2 in Eq. (86) is defined directly from the state-transfer amplitudes c_00(t_f) and c_10(t_f) obtained from the Hamiltonian in Eq. (75); it is not obtained by fitting a parameter to the quantity it predicts. The model Hamiltonian is cited to the authors' prior work, but it is a standard circuit-QED form, and the perturbative dressed-state results are tested against exact numerical diagonalization of the same finite-dimensional model, as stated in Sec. 5.3. This is internal validation rather than circular reduction. The clause 'coherence times longer than a few tens of ns' is not derived from the simulation and is not a fitted parameter; it is an external assumption about hardware. That is a correctness or completeness risk, not a circularity. Self-citations appear throughout, but they do not function as unverified premises that force the conclusion: the memory-fidelity numbers are presented as the outcome of solving the stated unitary model, with the coherence-time requirement stated separately as a condition for physical relevance. No equation is equivalent to its own input by construction, and no fitted quantity is relabeled as a prediction. The review also covers standard material on phase, flux, and charge qubits and on coupling schemes without invoking a contested uniqueness theorem. Accordingly, no circular step meeting the evidentiary bar is present, and the appropriate finding is no significant circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper relies on standard circuit QED assumptions, such as the Josephson relations and two-level qubit truncation, and does not introduce new physical entities. The free parameters are the resonator coupling strength, the control parameters optimized in the memory simulation, and the phonon truncation size. These are modeling choices, not fitted to experimental data.

free parameters (3)
  • Resonator coupling strength g = not specified, designed via material and size
    The value of g is stated to depend on material properties of the resonator but is not derived from first principles in this chapter (Sec. 5.1).
  • Optimized interaction times and detunings = numerically optimized to maximize fidelity
    In Sec. 5.4, the resonant interaction times and off-resonant detunings are varied numerically to maximize the memory gate fidelity; these are control parameters, not measured data, but the optimization is a form of fitting to a target.
  • Truncation at five phonon states = 5
    The test simulation in Sec. 5.3 uses a finite-dimensional single-qubit, five-phonon system; this truncation is a modeling choice and may affect the accuracy of the perturbative comparison.
assumptions (4)
  • domain assumption Josephson equations I = I0 sin(phi) and V = alpha phi_dot with alpha = hbar/2e
    Used throughout Secs. 2-5 as the basis for circuit quantization.
  • domain assumption The phase difference phi and Cooper-pair number N are canonically conjugate with [phi,N] = i.
    Invoked in Sec. 2 to derive the single-qubit Hamiltonians.
  • domain assumption The resonator is treated as a single harmonic mode of frequency omega0.
    Used in the resonator-coupled phase qubit model of Sec. 5.1; higher modes and anharmonicity are neglected.
  • domain assumption Decoherence and dissipation are neglected in the memory fidelity calculations.
    The simulations in Secs. 5.3 and 5.4 use unitary evolution; the fidelity results depend on this idealization.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Quantum computing with superconductors I: Architectures." pith.science (2026). https://pith.science/paper/7G6WRYZT

@misc{pith2026quant-ph0603224,
  author       = {Pith},
  title        = {Pith review of: Quantum computing with superconductors I: Architectures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7G6WRYZT}},
  note         = {Machine review of arXiv:quant-ph/0603224}
}
read the original abstract

Josephson junctions have demonstrated enormous potential as qubits for scalable quantum computing architectures. Here we discuss the current approaches for making multi-qubit circuits and performing quantum information processing with them.

Figures

Figures reproduced from arXiv: quant-ph/0603224 by the authors.

Figure 1
Figure 1. Circuit model for a current-biased JJ, neglecting dissipation. Here α ≡ ~/2e. 2. The basic qubits: phase, flux, and charge The primitive building block for all the qubits is the JJ shown in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Basic phase qubit circuit. where e is the magnitude of the electron charge, and the Cooper-pair charging energy Ec ≡ (2e) 2 2C , (4) with C the junction capacitance. For example, EJ = 2.05 meV×I0[µA] and Ec = 320 neV C[pF] , (5) where I0[µA] and C[pF] are the critical current and junction capacitance in mi￾croamperes and picofarads, respectively. In the regimes of interest to quantum computation, EJ and Ec are assum… view at source ↗
Figure 3
Figure 3. Effective potential for a current-biased JJ. The slope of the cosine potential is s. The potential is harmonic for the qubit states unless s is very close to 1. According to the Josephson equations, the classical canonical momentum P = ∂L ∂ϕ˙ is proportional to the charge Q or to the number of Cooper pairs Q/2e on the capacitor according to P = ~Q/2e. The quantum Hamiltonian can then be written as HJJ = EcN 2 + U, (… view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Effective potential in the anharmonic regime, with s very close to 1. State preparation and readout are carried out in this regime. The second spin form uses a basis of eigenstates with a fixed value of bias, s0. In this case H = − ~ωp(s0) 2 σ z − EJℓ √ 2 (s − s0)σ x ,…
Figure 5
Figure 5. Figure 5: Basic charge qubit circuit. The upper wire constitutes the superconducting box or island. and H = Ec(N − Ng) 2 − EJ cos ϕ, with Ec = (2e) 2 2(C+Cg) . (15) Here Ng ≡ − CgVg 2e (16) is the gate charge, the charge qubit’s control variable. It is most convenient to use the…
Figure 6
Figure 6. Figure 6: Basic rf-SQUID flux qubit and circuit model. Φ is the total flux threading the ring. The dashed curve in the upper figure indicates the integration contour Γ used to derive condition (26). The coil in the lower figure has self-inductance L. as H = Ec(Ng − 1 2 )σ x − EJ…
Figure 7
Figure 7. Figure 7: Double-well potential of the flux qubit. The dashed curve is the cosine potential of the JJ alone; the solid curve shows the modification caused by the self-inductance of the ring. The states |0i and |1i are that of circulating and counter-circulating supercurrent, whi…
Figure 8
Figure 8. Figure 8: Capacitively coupled phase qubit circuit Referring to [PITH_FULL_IMAGE:figures/full_fig_p011_8.png]
Figure 9
Figure 9. Figure 9: This architecture [PITH_FULL_IMAGE:figures/full_fig_p012_9.png]
Figure 9
Figure 9. Figure 9: Capacitively coupled charge qubit circuit. most advanced in the field of solid-state quantum information processing. The equations of motion for the two phases are7 α 2 (C1 + Cg1 + Cint) ¨ϕ1 + EJ1 sin ϕ1 − αCg1V˙ g1 − α 2Cintϕ¨ 2 = 0 (48) α 2 (C2 + Cg1 + Cint) ¨ϕ2 + EJ…
Figure 10
Figure 10. Figure 10: Tuning EJ with a dc SQUID. The spin form in the charge basis is H = X i [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]
Figure 11
Figure 11. Figure 11: Circuit of Makhlin, Sch¨on, and Shnirman. Cm Cg V1 Vg V2 Cg Cm j1 j j2 [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: Electrostatic transformer. The significant feature of the interaction in (66), compared to (58), is that the EJ’s here can be tuned by using dc SQUIDs. This gives, in principle, a fully tunable interaction between any pair of qubits attached to the same inductor. 4.0.…
Figure 13
Figure 13. Figure 13: Two current-biased Josephson junctions (crossed boxes) coupled to a piezoelectric disc resonator. oscillators are ineffective as computational qubits, because the lowest pair of levels cannot be frequency selected by an external driving field, they are quite desirable…
Figure 14
Figure 14. Figure 14: Probabilities |c10| 2 and |c01| 2 for the intermediate case of g/∆ǫ = 0.30. Here there are large deviations from the RWA behavior, which are correctly accounted for by the dressed-state perturbative method. exactly in resonance. The Hamiltonian for this system is diag…
Figure 15
Figure 15. Figure 15: (upper panel) Memory fidelity for equator state 2− 1 2 (|0i + |1i) as a function of g/∆ǫ, using both the RWA (unfilled circles) and optimized (solid circles) pulse times. (lower panel) Time needed to store and retrieve state, using both the RWA (dashed curve) and opti…

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Quantum Circuit Simplification and Level Compaction

    quant-ph 2006-04 conditional novelty 6.0 of 10

    Template rules for NOT, CNOT, and controlled-sqrt-of-NOT gates automatically simplify quantum circuits and reduce their depth.

Reference graph

Works this paper leans on

43 extracted references · 43 canonical work pages · cited by 1 Pith paper

  1. [1]

    Averin, D. V. and C. Bruder: 2003, `Variable electrostatic transformer: C ontrollable coupling of two charge qubits'. Phys. Rev. Lett. 91 , 57003

    work page 2003

  2. [2]

    Berkley, A. J., H. Xu, R. C. Ramos, M. A. Gubrud, F. W. Strauch, P. R. Johnson, J. R. Anderson, A. J. Dragt, C. J. Lobb, and F. C. Wellstood: 2003, `Entangled macroscopic quantum states in two superconducting qubits'. Science 300 , 1548--50

    work page 2003

  3. [3]

    Huang, A

    Blais, A., R.-S. Huang, A. Wallraff, S. M. Girvin, and R. J. Schoelkopf: 2004, `Cavity quantum electrodynamics for superconducting electrical circuits: A n architecture for quantum computation'. Phys. Rev. A 69 , 62320

    work page 2004

  4. [4]

    Massen van den Brink, and A

    Blais, A., A. Massen van den Brink, and A. M. Zagoskin: 2003, `Tunable coupling of superconducting qubits'. Phys. Rev. Lett. 90 , 127901

    work page 2003

  5. [5]

    Caldeira, A. O. and A. J. Leggett: 1981, `Influence of dissipation on quantum tunneling in macroscopic systems'. Phys. Rev. Lett. 46 , 211--4

    work page 1981

  6. [6]

    Caldeira, A. O. and A. J. Leggett: 1983, `Quantum tunneling in a dissipative system'. Ann. Phys. (N.Y.) 149 , 374--456

    work page 1983

  7. [7]

    Clarke, J., A. N. Cleland, M. H. Devoret, D. Esteve, and J. M. Martinis: 1988, `Quantum mechanics of a macroscopic variable: The phase difference of a J osephson junction'. Science 239 , 992--7

    work page 1988

  8. [8]

    Cleland, A. N. and M. R. Geller: 2004, `Superconducting qubit storage and entanglement with nanomechanical resonators'. Phys. Rev. Lett. 93 , 70501

    work page 2004

Show all 43 references
  1. [9]

    Devoret, M. H., J. M. Martinis, and J. Clarke: 1985, `Measurements of macroscopic quantum tunneling out of the zero-voltage state of a current-biased J osephson junction'. Phys. Rev. Lett. 55 , 1908--11

    1985

  2. [10]

    Friedman, J. R., V. Patel, W. Chen, S. K. Tolpygo, and J. E. Lukens: 2000, `Quantum superpositions of distinct macroscopic states'. Nature (London) 406 , 43--6

    2000

  3. [11]

    Geller, M. R. and A. N. Cleland: 2005, `Superconducting qubits coupled to nanoelectromechanical resonators: A n architecture for solid-state quantum information processing'. Phys. Rev. A 71 , 32311

    2005

  4. [12]

    Geller, M. R., E. J. Pritchett, A. T. Sornborger, M. Steffen, and J. M. Martinis: 2006, `Controlled-NOT logic for J osephson phase qubits'. e-print cond-mat/0000000

    2006

  5. [13]

    Johnson, P. R., F. W. Strauch, A. J. Dragt, R. C. Ramos, C. J. Lobb, J. R. Anderson, and F. C. Wellstood: 2003, `Spectroscopy of capacitively coupled J osephson-junction qubits'. Phys. Rev. B 67 , 20509

    2003

  6. [14]

    Sch\"on, and A

    Makhlin, Y., G. Sch\"on, and A. Shnirman: 1999, `Josephson-junction qubits with controlled couplings'. Nature (London) 398 , 305--7

    1999

  7. [15]

    Sch\"on, and A

    Makhlin, Y., G. Sch\"on, and A. Shnirman: 2001, `Quantum-state engineering with J osephson-junction devices'. Rev. Mod. Phys. 73 , 357--400

    2001

  8. [16]

    Marquardt, F. and C. Bruder: 2001, `Superposition of two mesoscopically distinct quantum states: C oupling a C ooper-pair box to a large superconducting island'. Phys. Rev. B 63 , 54514

    2001

  9. [17]

    Martinis, J. M., M. H. Devoret, and J. Clarke: 1985, `Energy-level quantization in the zero-voltage state of a current-biased J osephson junction'. Phys. Rev. Lett. 55 , 1543--6

    1985

  10. [18]

    Martinis, J. M., M. H. Devoret, and J. Clarke: 1987, `Experimental tests for the quantum behavior of a macroscopic degree of freedom: The phase difference across a J osephson junction'. Phys. Rev. B 35 , 4682--98

    1987

  11. [19]

    Martinis, J. M., S. Nam, J. Aumentado, and C. Urbina: 2002, `Rabi oscillations in a large J osephson-junction qubit'. Phys. Rev. Lett. 89 , 117901

    2002

  12. [20]

    Massen van den Brink, A.: 2005, `Hamiltonian for coupled flux qubits'. Phys. Rev. B 71 , 64503

    2005

  13. [21]

    McDermott, R., R. W. Simmonds, M. Steffen, K. B. Cooper, K. Cicak, K. D. Osborn, D. P. Oh, S. Pappas, and J. M. Martinis: 2005, `Simultaneous state measurement of coupled J osephson phase qubits'. Science 307 , 1299--302

    2005

  14. [22]

    Mooij, J. E., T. P. Orlando, L. S. Levitov, L. Tian, C. H. van der Wal, and S. Lloyd: 1999, `Joesphson persistent-current qubit'. Science 285 , 1036--9

    1999

  15. [23]

    Nakamura, Y., C. D. Chen, and J. S. Tsai: 1997, `Spectroscopy of energy-level splitting between two macroscopic quantum states of charge coherently superposed by J osephson coupling'. Phys. Rev. Lett. 79 , 2328--31

    1997

  16. [24]

    Nakamura, Y., Y. A. Pashkin, and J. S. Tsai: 1999, `Coherent control of macroscopic quantum states in a single- C ooper-pair box'. Nature (London) 398 , 786--8

    1999

  17. [25]

    Orlando, T. P., J. E. Mooij, L. Tian, C. H. van der Wal, L. S. Levitov, S. Lloyd, and J. J. Mazo: 1999, `Superconducting persistent-current qubit'. Phys. Rev. B 60 , 15398--413

    1999

  18. [26]

    Pashkin, Y. A., T. Yamamoto, O. Astafiev, Y. Nakamura, D. V. Averin, and J. S. Tsai: 2003, `Quantum oscillations in two coupled charge qubits'. Nature (London) 421 , 823--6

    2003

  19. [27]

    Plastina, F. and G. Falci: 2003, `Communicating J osephson qubits'. Phys. Rev. B 67 , 224514

    2003

  20. [28]

    Pritchett, E. J. and M. R. Geller: 2005, `Quantum memory for superconducting qubits'. Phys. Rev. A 72 , 10301

    2005

  21. [29]

    Blais, and M

    Rigetti, C., A. Blais, and M. H. Devoret: 2005, `Protocol for universal gates in optimally biased superconducting qubits'. Phys. Rev. Lett. 94 , 240502

    2005

  22. [30]

    Han, and J

    Rouse, R., S. Han, and J. E. Lukens: 1995, `Observation of resonant tunneling between macroscopically discinct quantum levels'. Phys. Rev. Lett. 75 , 1614--7

    1995

  23. [31]

    Sch\"on, and Z

    Shnirman, A., G. Sch\"on, and Z. Hermon: 1997, `Quantum manipulations of small J osephson junctions'. Phys. Rev. Lett. 79 , 2371--4

    1997

  24. [32]

    Sornborger, A. T., A. N. Cleland, and M. R. Geller: 2004, `Superconducting phase qubit coupled to a nanomechanical resonator: B eyond the rotating-wave approximation'. Phys. Rev. A 70 , 52315

    2004

  25. [33]

    Strauch, F. W., P. R. Johnson, A. J. Dragt, C. J. Lobb, J. R. Anderson, and F. C. Wellstood: 2003, `Quantum logic gates for coupled superconducting phase qubits'. Phys. Rev. Lett. 91 , 167005

    2003

  26. [34]

    van der Wal, C. H., A. C. J. ter Haar, F. K. Wilhelm, R. N. Schouten, C. J. P. M. Harmans, T. P. Orlando, S. Lloyd, and J. E. Mooij: 2000, `Quantum superpositions of macroscopic persistent current'. Science 290 , 773--7

    2000

  27. [35]

    Aassime, A

    Vion, V., A. Aassime, A. Cottet, P. Joyez, H. Pothier, C. Urbina, D. Esteve, and M. H. Devoret: 2002, `Manipulating the quantum state of an electrical circuit'. Science 296 , 886--9

    2002

  28. [36]

    Wallraff, A., D. I. Schuster, A. Blais, L. Frunzio, R.-S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf: 2004, `Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics'. Nature (London) 431 , 162--7

    2004

  29. [37]

    Yamamoto, T., Y. A. Pashkin, O. Astafiev, Y. Nakamura, and J. S. Tsai: 2003, `Demonstration of conditional gate operations using superconducting charge qubits'. Nature (London) 425 , 941--4

    2003

  30. [38]

    You, J. Q. and F. Nori: 2005, `Superconducting circuits and quantum information'. Physics Today, November 2005. p. 42

    2005

  31. [39]

    You, J. Q., J. S. Tsai, and F. Nori: 2002, `Scalable quantum computing with J osephson charge qubits'. Phys. Rev. Lett. 89 , 197902

    2002

  32. [40]

    Yu, Y., S. Han, X. Chu, S.-I. Chu, and Z. Wang: 2002, `Coherent temporal oscillations of macroscopic quantum states in a J osephson junction'. Science 296 , 889--92

    2002

  33. [41]

    P.: 2002, `A multi- J osephson junction qubit'

    Yukon, S. P.: 2002, `A multi- J osephson junction qubit'. Physica C 368 , 320--3

    2002

  34. [42]

    Zhou, X., M. Wulf, Z. Zhou, G. Guo, and M. J. Feldman: 2004, `Dispersive manipulation of paired superconducting qubits'. Phys. Rev. A 69 , 30301

    2004

  35. [43]

    Zhu, S.-L., Z. D. Wang, and K. Yang: 2003, `Quantum-information processing using J osephson junctions coupled through cavities'. Phys. Rev. A 68 , 34303

    2003

Pith tools

Reviewed August 28, 2026 · model on record in the stance chip above.