New paper: Energy-participation quantization of Josephson circuits

Energy-participation quantization of Josephson circuits

After years of efforts,

The Energy-Participation Ratio (EPR) for the design and quantization of a #quantumcomputing chip now on the arXiv
arxiv.org/abs/2010.00620

Glad the EPR method seems to already be useful to some 25+ groups
github.com/zlatko-minev/p…

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“Where is the energy?”

is the only question you need to ask & answer to design both the dissipative budget and the quantum #Hamiltonian of any #quantum device

— irrelevant of its topology or the constitution of its nonlinear elements.

The answer to this question is the Energy-Participation Ratio (EPR) p — a number between 0 and 1,

which says how much of the energy of a mode is stored in a nonlinear element (e.g., Josephson junction).

The EPR is the key to the classical-to-quantum bridge for #quantumcircuits

Accuracy:

We designed dozen of quantum device with the #EPR method, including my recent @nature paper work on #quantumjumps.

Results demonstrate percents-level agreement for the Hamiltonian,

over five-orders of magnitude in energy scales,

and across dozens of samples.

Appendices C and D seem to now contain a mini-treatise on our field of #superconducting #quantum #circuits

arxiv.org/abs/2010.00620 #quantumcomputing #pyEPR

Abstract:

Superconducting microwave circuits incorporating nonlinear devices, such as Josephson junctions, are one of the leading platforms for emerging quantum technologies. Increasing circuit complexity further requires efficient methods for the calculation and optimization of the spectrum, nonlinear interactions, and dissipation in multi-mode distributed quantum circuits. Here, we present a method based on the energy-participation ratio (EPR) of a dissipative or nonlinear element in an electromagnetic mode. The EPR, a number between zero and one, quantifies how much of the energy of a mode is stored in each element. It obeys universal constraints---valid regardless of the circuit topology and nature of the nonlinear elements. The EPR of the elements are calculated from a unique, efficient electromagnetic eigenmode simulation of the linearized circuit, including lossy elements. Their set is the key input to the determination of the quantum Hamiltonian of the system. The method provides an intuitive and simple-to-use tool to quantize multi-junction circuits. It is especially well-suited for finding the Hamiltonian and dissipative parameters of weakly anharmonic systems, such as transmon qubits coupled to resonators, or Josephson transmission lines. We experimentally tested this method on a variety of Josephson circuits, and demonstrated agreement within several percents for nonlinear couplings and modal Hamiltonian parameters, spanning five-orders of magnitude in energy, across a dozen samples.