Numerical analysis of effective models for flux-tunable transmon systems

Abstract

Simulations and analytical calculations that aim to describe flux-tunable transmons are usually based on effective models of the corresponding lumped-element model. However, when a control pulse is applied, in most cases it is not known how much the predictions made with the effective models deviate from the predictions made with the original lumped-element model. In this work we compare the numerical solutions of the time-dependent Schrödinger equation for both the effective and the lumped-element models, for microwave and unimodal control pulses (external fluxes). These control pulses are used to model single-qubit (X) and two-qubit gate (Iswap and Cz) transitions. First, we derive a non-adiabatic effective Hamiltonian for a single flux-tunable transmon and compare the pulse response of this model to the one of the corresponding circuit Hamiltonian. Here we find that both models predict similar outcomes for similar control pulses. Then, we study how different approximations affect single-qubit (X) and two-qubit gate (Iswap and Cz) transitions in two different two-qubit systems. For this purpose we consider three different systems in total: a single flux-tunable transmon and two two-qubit systems. In summary, we find that a series of commonly applied approximations (individually and/or in combination) can change the response of a system substantially, when a control pulse is applied.

References in corpus (10)

• Charge insensitive qubit design derived from the Cooper pair box
• Demonstration of Two-Qubit Algorithms with a Superconducting Quantum Processor
• Circuit quantization in the presence of time-dependent external flux
• Analysis of parametrically driven exchange-type (iSWAP) and two-photon (bSWAP) interactions between superconducting qubits
• Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform
• Benchmarking Coherent Errors in Controlled-Phase Gates due to Spectator Qubits
• Gate-error analysis in simulations of quantum computers with transmon qubits
• Fast multi-qubit gates through simultaneous two-qubit gates
• One bound to rule them all: from Adiabatic to Zeno
• Single Shot i-Toffoli Gate in Dispersively Coupled Superconducting Qubits

Cited by in corpus (3)

• Benchmarking Advantage and D-Wave 2000Q quantum annealers with exact cover problems
• Spectral features of polaronic excitations in a superconducting analog simulator
• On the fragility of gate-error metrics in simulation models of flux-tunable transmon quantum computers