Superconducting quantum interference device pdf

The measurement of the magnetic field dependence of the critical current has revealed disagreement with the theoretical predictions, which requires further investigation. We hope that a jump in the critical current associated with a change in the quantum number n will be discovered in the investigations of other structures with asymmetric contacts probably made of other superconductors.

If you find a rendering bug, file an issue on GitHub. Or, have a go at fixing it yourself — the renderer is open source! For everything else, email us at [email protected]. Superconducting quantum interference device without Josephson junctions A.

Burlakov, V. Gurtovoi, A. Il in, A. Nikulov, and V. Abstract A new type of a superconducting quantum interference device SQUID based on a single superconducting loop without Josephson junctions and with asymmetric link-up of current leads is proposed. Want to hear about new tools we're making?

For the purpose of demonstrating the model, we will use parameter set 1 in the following, unless otherwise stated. Insets show zooms around the gate time. The parameters used in a are set 1 from Table 1 , and in b they are set 2. As is evident from Fig. The gate fidelities for the individually controlled gates and the total diamond gate are shown in Fig. While one parameter is varied, the remaining two are fixed at the values marked by the gray vertical lines parameter set 1 of Table 1.

With a superconducting circuit implementation in mind, we consider a variety of system infidelites and their impact on the gate fidelities see Fig. Most harmful is a direct capacitive coupling between the target qubits Fig.

The gate fidelities roughly decrease with the square of the cross-coupling strength J T , leading to noticable gate infidelities even for a relatively weak coupling.

Figure 5 b shows simulation results with random noise on the couplings between the target and control qubits emulating asymmetries present in an actual circuit due to fabrication limits. The gate performance is very robust towards this type of noise. The gate fidelity is computed under the following system infidelities: a Crosstalk coupling between the target qubits.

We introduce control state infidelity in the following way. For each data point in Fig. In the simulations, we apply V to the initial state of the control qubits in order to model imperfect state preparation.

The resulting gate fidelity is shown as a function of the maximum infidelity among the four control states. The diamond gate suffers a linear decrease in gate fidelity, but remains high-performing for realistic control state infidelity. Qubit decoherence in the form of relaxation and dephasing is included in the master Eq.

In Fig. We attribute this robustness to the relatively short gate time of In the previous section, we treated a model for four coupled qubits. In the superconducting circuit implementation of Fig. However, in an actual superconducting circuit, the qubits may couple to higher-energy states in the transmon spectrum, which is the spectrum of a slightly anharmonic oscillator The full analysis of the circuit of Fig. The resulting four-qutrit Hamiltonian is a sum of the non-interacting part. The operator is given as.

Hence, the coupling between the first and second excited state is as strong as the coupling between the two lowest qubit levels. Due to the small anharmonicity in transmons, i. In fact, this transition is sometimes used for the CZ gate Notice that this lack of suppression holds for transmons in general, and is not a consequence of the specific model considered here.

This has two undesired consequences. This can be resolved by redefining the control state as. Details are found in the Supplementary Information. Secondly, excitations to the second excited states allow unwanted processes which bypass the control. For instance, when the diamond gate is desired to be idle, leakage across the control can occur via:. Since this is a second-order process in the qutrit model Hamiltonian, it would not pose a threat to the functionality of the diamond gate if it only relied on generally faster first-order processes.

However, the swap operations of Eqs. However, these undesired processes can be mitigated by taking advantage of the effects of crosstalk. The circuit analysis in the Supplementary Information reveals a weak unavoidable crosstalk coupling of strength J T in the interaction Hamiltonian 13 , which by itself has a significant negative impact on the gate fidelities cf.

This leads directly to leakage across the control through processes of the type. This process has the same unwanted outcome as the one of Eq. As we show below, we can therefore restore the gate functionality by tuning the value of J T such that these two unwanted leakage processes cancel each other. Analyzing the problem with second-order perturbation theory in order to calculate the amplitude of the leaked state see the Supplementary Information , we find destructive interference between these processes when the crosstalk strength takes the optimal value.

Figure 6 shows the swap rate for varying J T , with control qubits in each of the four control states. At each zero-point, the gate time inverse swap rate for the swapping gate s is prolonged compared to the results in the previous section. To reduce the gate time, one should pick parameters such that the zero-points are further apart, or such that the inclination of the graphs are steeper. Figure 7 illustrates in more detail the cancellation of unwanted transfer by crosstalk engineering.

Each subfigure shows the swap fidelity for different initial target qubit states. The control is initialized in the state indicated above each column.

As expected from Fig. The optimal value of Eq. Engineering crosstalk to mitigate unwanted leakage through higher-excited states is killing two birds with one stone: Each process is harmful to the functionality of the diamond gate, but letting them cancel each other preserves the ability to control the swap operation. Generally, the phases applied to each target state will be modified for all four controlled gates, but we do not pursue an analysis here, as other factors specific to the implementation will contribute to this as well.

Rather, our main goal was to demonstrate a passive method for dealing with undesired leakage processes. We have proposed a quantum interference device by coupling four qubits with exchange interactions. By analyzing the unitary dynamics of the system, we have shown that it realizes the diamond gate: a four-way controlled two-qubit gate, with the ability to run two different entangling swap and phase operations, a parity phase operation, an idling gate with no dynamics, or an arbitrary superposition of these.

We considered an implementation in superconducting qubits using transmon qubits, and found that it generally operated fast and with high fidelity using state-of-the-art model and noise parameters. When taking second excited states into account, we had to prevent leakage across the control by engineering crosstalk, demonstrating a general method to avoid leakage in superconducting qubit systems. The cost of this was a single redefined control state, one swap gate turning into a phase gate, altered phases on the gates, and a slower gate for the considered parameters.

However, we only consider this analysis a starting point for an actual implementation, which might also include active microwave driving to optimize the operations or to prevent certain transitions. It might also be worthwhile to consider other types of superconducting qubits with larger anharmonicity, or entirely different platforms such as lattices of ultracold atoms or ions, where qubit encoded in hyperfine states or vibrational modes are far detuned from the rest of the spectrum.

We illustrated how the four-qubit diamond gate device can constitute an essential building block in an extensible quantum computer, and proposed a simple scheme where quantum algorithms are run on the computer by parallel processing on each four-qubit module interspersed with two-qubit operations spreading entanglement in the system, and single-qubit operations.

Evidently, this scheme is adaptable to many different algorithms, and future work will investigate which algorithms are suitable to be implemented in the diamond-plaquette device. In this section, we show that the Hamiltonian of Eq. Typically, one thinks of control qubits, or their state, as a catalyzer for a given gate operation performed on the target qubits. The control qubits are allowed to partake in the gate operation, for instance by facilitating state transfer between target qubits not directly coupled, as long as the control qubits return to their initial state after the completion of the gate operation.

A priori we cannot guarantee that this is the case. In this case, each control state is perfectly preserved under the time-evolution, and we can simply determine the gate operation on the target qubits associated with each control state. Ideally, the control—control coupling would be tunable and only on during control state preparation.

On the other hand, since it does not couple to any of the target qubits, we do not expect the value of J C to be of fundamental importance to the nature of the gate operations, which is our main focus here. This has the consequence that the operator exponential can be written as a sum:. The above decomposition of the time-evolution can used whenever one or more control qubits subsystem A catalyze a unitary gate operation on a set of target qubits subsystem B in the sense that the Hamiltonian does not mix the chosen control states.

In our case, we can easily express the Hamiltonians 26 — 29 as matrices and find the unitary matrix exponentials. In the computational basis of the target qubits, they are as follows:. The time-evolution operator for the four-qubit system is then. Thus, each of the four unitaries 34 — 37 above is a gate operation performed on the target qubits, controlled entirely by the four control states, which are unaltered by the operation.

The gate is fully quantum mechanical, as superpositions of control states will run the corresponding computations on the target qubits in parallel. The system comprise a true four-qubit quantum interference device in the form of a four-way controlled two-qubit gate the diamond gate. The case of a non-zero J C is treated in the Supplementary Information. The data that support the findings in this study are available from the corresponding author upon reasonable request.

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Mechanics of individual isolated vortices in a cuprate superconductor. Schwarz, A. Real space visualization of thermal fluctuations in a triangular flux-line lattice. New J. Download references. Rappaport, Martin E. You can also search for this author in PubMed Google Scholar. All authors contributed to the manuscript. Correspondence to Denis Vasyukov or Eli Zeldov.

Reprints and Permissions. Vasyukov, D. A scanning superconducting quantum interference device with single electron spin sensitivity. Nature Nanotech 8, — Download citation. Received : 04 July Accepted : 23 July Published : 01 September Issue Date : September Anyone you share the following link with will be able to read this content:. Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative. Advanced search. Skip to main content Thank you for visiting nature. Subjects Applied physics Scanning probe microscopy Superconducting devices Superconducting properties and materials. Abstract Superconducting quantum interference devices SQUIDs can be used to detect weak magnetic fields and have traditionally been the most sensitive magnetometers available.

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Figure 5: Scanning SOT microscopy images of vortex matter and of magnetic field distribution generated by a. References 1 Cleuziou, J-P.