Abstract
We generalize solid-state tight-binding techniques for the spectral analysis of large superconducting circuits. We find that tight-binding states can be better suited for approximating the low-energy excitations than charge-basis states, as illustrated for the interesting example of the current-mirror circuit. The use of tight binding can dramatically lower the Hilbert space dimension required for convergence to the true spectrum, and allows for the accurate simulation of larger circuits that are out of reach of charge basis diagonalization.
Highlights
Increasing coherence and noise resilience in superconducting qubits is a key requirement on the roadmap for developing the generation of error-corrected quantum processors surpassing the NISQ era
In order to evaluate the accuracy of the tight-binding method, we first apply it to the familiar case of the threejunction flux qubit
Using the same metric for memory efficiency previously applied to the fluxqubit example, we find that tight binding is advantageous over a wide range of nonzero Hamiltonian matrix elements (nH) values
Summary
Increasing coherence and noise resilience in superconducting qubits is a key requirement on the roadmap for developing the generation of error-corrected quantum processors surpassing the NISQ era. Achieving simultaneous protection from depolarization and dephasing is impossible for small circuits like the transmon, and instead necessitates circuits with two or more degrees of freedom Such larger circuits, especially of the size considered for the current-mirror circuit [3] or rhombi lattice [4,5], pose significant challenges for the quantitative analysis of energy spectra and prediction of coherence times. As long as construction of the tailored basis and decomposition of the Hamiltonian in that basis can be accomplished efficiently, this approach will allow for reduced truncation levels and enable coverage of circuit sizes otherwise inaccessible numerically Our construction of such tailored basis states is based on the observation that low-lying eigenstates of superconducting circuits are often localized in the vicinity of minima of the potential energy, when expressed in terms of appropriate generalized-flux variables.
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