Pulse-level simulators are the lowest-level, most widely used abstraction layer for studying how quantum hardware responds to control signals, but they can be built on Hamiltonian models with very different fidelity and cost. This raises the question: which level of physical abstraction is sufficient for a given simulation objective? We study this question for a flux-tunable two-qubit superconducting device with a fixed bus coupler by comparing three Hamiltonian descriptions of the same hardware: an effective two-level model, a three-mode Duffing model, and a circuit-based transmon model in the charge basis. Using a realistic parameter set, we evaluate these models on a common benchmark suite spanning flux-dependent spectra, extracted two-qubit interaction terms, driven single-qubit dynamics, CZ gate dynamics, leakage outside the computational subspace, and runtime. Across the tested flux range, the Duffing model follows the circuit-based reference more closely than the effective model for static spectra and reduced two-qubit quantities, while in driven benchmarks, the multilevel models reveal effects absent in the effective description. Overall, the results support a layered use of abstraction in pulse-level simulation: effective models for reduced analyses, Duffing models as a practical multilevel default, and circuit-based models for high-fidelity reference simulation or detailed leakage analysis.Pulse-level simulators are the lowest-level, most widely used abstraction layer for studying how quantum hardware responds to control signals, but they can be built on Hamiltonian models with very different fidelity and cost. This raises the question: which level of physical abstraction is sufficient for a given simulation objective? We study this question for a flux-tunable two-qubit superconducting device with a fixed bus coupler by comparing three Hamiltonian descriptions of the same hardware: an effective two-level model, a three-mode Duffing model, and a circuit-based transmon model in the charge basis. Using a realistic parameter set, we evaluate these models on a common benchmark suite spanning flux-dependent spectra, extracted two-qubit interaction terms, driven single-qubit dynamics, CZ gate dynamics, leakage outside the computational subspace, and runtime. Across the tested flux range, the Duffing model follows the circuit-based reference more closely than the effective model for static spectra and reduced two-qubit quantities, while in driven benchmarks, the multilevel models reveal effects absent in the effective description. Overall, the results support a layered use of abstraction in pulse-level simulation: effective models for reduced analyses, Duffing models as a practical multilevel default, and circuit-based models for high-fidelity reference simulation or detailed leakage analysis.

International Conference on SupercomputingJun 30, 20260 citations

Effective Hamiltonians for Predictive Quantum Control

Razvan Stanescu, Hugo Ribeiro

High-fidelity quantum control relies on accurate models of driven dynamics. We examine this re- quirement for single-qubit gates in superconducting transmons by comparing control pulses derived from the standard Duffing approximation and from a Hamiltonian constructed by diagonalizing the transmon eigenbasis. Using the same correction-pulse construction for both models, we show that correction fields derived from the Duffing approximation can substantially reduce the gate error pre- dicted by that model while remaining less effective when combined with an independently calibrated baseline pulse in the diagonalized-transmon model. In the fast-gate regime, such transferred correc- tions can even fail to improve over the uncorrected diagonalized-transmon baseline. We show that small model-dependent differences in both the energy spectrum and the representation of the drive operator can compound during driven evolution, resulting in different predicted error generators and correction pulses. A mismatch in the accumulated AC Stark phase provides one illustrative di- agnostic of this dynamical model dependence. We further demonstrate that the model Hamiltonian informs the choice of control framework: Omitting relevant leakage pathways or higher-order error channels can lead to an overly restricted correction strategy. Including these channels motivates an extended correction framework that improves the gate performance using the same physical control resources.High-fidelity quantum control relies on accurate models of driven dynamics. We examine this re- quirement for single-qubit gates in superconducting transmons by comparing control pulses derived from the standard Duffing approximation and from a Hamiltonian constructed by diagonalizing the transmon eigenbasis. Using the same correction-pulse construction for both models, we show that correction fields derived from the Duffing approximation can substantially reduce the gate error pre- dicted by that model while remaining less effective when combined with an independently calibrated baseline pulse in the diagonalized-transmon model. In the fast-gate regime, such transferred correc- tions can even fail to improve over the uncorrected diagonalized-transmon baseline. We show that small model-dependent differences in both the energy spectrum and the representation of the drive operator can compound during driven evolution, resulting in different predicted error generators and correction pulses. A mismatch in the accumulated AC Stark phase provides one illustrative di- agnostic of this dynamical model dependence. We further demonstrate that the model Hamiltonian informs the choice of control framework: Omitting relevant leakage pathways or higher-order error channels can lead to an overly restricted correction strategy. Including these channels motivates an extended correction framework that improves the gate performance using the same physical control resources.

quant-pharXiv:2607.27111Jul 30, 20260 citations

Effective Hamiltonians for interacting superconducting qubits: local basis reduction and the Schrieffer–Wolff transformation

Gioele Consani, Paul A. Warburton

Abstract An open question in designing superconducting quantum circuits is how best to reduce the full circuit Hamiltonian which describes their dynamics to an effective two-level qubit Hamiltonian which is appropriate for manipulation of quantum information. Despite advances in numerical methods to simulate the spectral properties of multi-element superconducting circuits (Yurke B and Denker J S 1984 Phys. Rev. A 29 1419, Reiter F and Sørensen A S 2012 Phys. Rev. A 85 032111 and Amin M H et al 2012 Phys. Rev. A 86 052314), the literature lacks a consistent and effective method of determining the effective qubit Hamiltonian. Here we address this problem by introducing a novel local basis reduction method . This method does not require any ad hoc assumption on the structure of the Hamiltonian such as its linear response to applied fields. We numerically benchmark the local basis reduction method against other Hamiltonian reduction methods in the literature and report specific examples of superconducting qubits, including the capacitively-shunted flux qubit, where the standard reduction approaches fail. By combining the local basis reduction method with the Schrieffer–Wolff transformation we further extend its applicability to systems of interacting qubits and use it to extract both non-stoquastic two-qubit Hamiltonians and three-local interaction terms in three-qubit Hamiltonians.Abstract An open question in designing superconducting quantum circuits is how best to reduce the full circuit Hamiltonian which describes their dynamics to an effective two-level qubit Hamiltonian which is appropriate for manipulation of quantum information. Despite advances in numerical methods to simulate the spectral properties of multi-element superconducting circuits (Yurke B and Denker J S 1984 Phys. Rev. A 29 1419, Reiter F and Sørensen A S 2012 Phys. Rev. A 85 032111 and Amin M H et al 2012 Phys. Rev. A 86 052314), the literature lacks a consistent and effective method of determining the effective qubit Hamiltonian. Here we address this problem by introducing a novel local basis reduction method . This method does not require any ad hoc assumption on the structure of the Hamiltonian such as its linear response to applied fields. We numerically benchmark the local basis reduction method against other Hamiltonian reduction methods in the literature and report specific examples of superconducting qubits, including the capacitively-shunted flux qubit, where the standard reduction approaches fail. By combining the local basis reduction method with the Schrieffer–Wolff transformation we further extend its applicability to systems of interacting qubits and use it to extract both non-stoquastic two-qubit Hamiltonians and three-local interaction terms in three-qubit Hamiltonians.

arXiv:1912.00464New Journal of PhysicsMar 26, 202020 citations

Numerical analysis of effective models for flux-tunable transmon systems

Hannes Lagemann, Dennis Willsch, Madita Willsch +3 more

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 Schr\"odinger 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 nonadiabatic 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.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 Schr\"odinger 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 nonadiabatic 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.

arXiv:2201.02402Physical Review AAug 26, 20226 citations

Fast CZ gate in hybrid fluxonium-transmon systems with tunable couplers

Peng Xu, Yunlong Wang, Yuechen Mu +4 more

Hybrid superconducting architectures combining different types of qubits offer a promising platform for exploiting their complementary advantages, yet high-fidelity entangling gates remain challenging because of strong nonlinearities and residual qubit-qubit interactions. Here, we propose a high-fidelity controlled-Z (CZ) gate for a hybrid circuit comprising a fluxonium qubit, a fixed-frequency transmon qubit, and a flux-tunable transmon coupler. By modulating only the external magnetic flux applied to the coupler, the qubit-qubit interaction is dynamically engineered for conditional-phase accumulation while the residual interaction is suppressed at idle, mitigating spectator-induced errors. We employ a low-dimensional Fourier-cosine pulse parameterization and a physically motivated cost function to independently suppress conditional-phase errors and leakage from the computational subspace. Numerical simulations demonstrate that a microwave-free CZ gate can be realized within $25 \mathrm{ns}$ , with an average gate fidelity exceeding $99.99\%$ and leakage below $10^{-5}$ . Using experimentally relevant superconducting-qubit parameters and accounting for decoherence, the proposed scheme maintains a CZ-gate fidelity of approximately $99.9\%$ . We further extend the analysis to larger coupled architectures and find that the CZ-gate infidelity remains below $10^{-4}$ in the presence of spectator qubits. These results establish single-parameter flux control as a simple and robust approach for realizing high-fidelity entangling gates in heterogeneous superconducting quantum architectures.Hybrid superconducting architectures combining different types of qubits offer a promising platform for exploiting their complementary advantages, yet high-fidelity entangling gates remain challenging because of strong nonlinearities and residual qubit-qubit interactions. Here, we propose a high-fidelity controlled-Z (CZ) gate for a hybrid circuit comprising a fluxonium qubit, a fixed-frequency transmon qubit, and a flux-tunable transmon coupler. By modulating only the external magnetic flux applied to the coupler, the qubit-qubit interaction is dynamically engineered for conditional-phase accumulation while the residual interaction is suppressed at idle, mitigating spectator-induced errors. We employ a low-dimensional Fourier-cosine pulse parameterization and a physically motivated cost function to independently suppress conditional-phase errors and leakage from the computational subspace. Numerical simulations demonstrate that a microwave-free CZ gate can be realized within $25 \mathrm{ns}$, with an average gate fidelity exceeding $99.99\%$ and leakage below $10^{-5}$. Using experimentally relevant superconducting-qubit parameters and accounting for decoherence, the proposed scheme maintains a CZ-gate fidelity of approximately $99.9\%$. We further extend the analysis to larger coupled architectures and find that the CZ-gate infidelity remains below $10^{-4}$ in the presence of spectator qubits. These results establish single-parameter flux control as a simple and robust approach for realizing high-fidelity entangling gates in heterogeneous superconducting quantum architectures.

quant-pharXiv:2609.14197Sep 15, 20260 citations

Multi-level Control in Large-anharmonicity High-coherence Capacitively Shunted Flux Quantum Circuits

Muhammet Ali Yurtalan

Superconducting devices as quantum bits (qubits) are one of the most promising candidates for implementing a practical quantum computer. Over the last decade, quantum coherence times of superconducting qubits have been continuously improved. Operating qubits in noise insensitive points, eliminating the participation of the lossy materials, and better isolation from environment increased the decoherence times from nanoseconds to tens of microseconds. One recent approach on the qubit design is to shunt the Josephson junctions with large capacitors to reduce the sensitivity to noise and to redistribute the stored electromagnetic energy in a well-engineered area. This approach was first applied on charge qubits and later adopted to other types of superconducting qubits. \n \nIn this thesis, we present the design and the characterization of a three-Josephson junction superconducting circuit with three large shunt capacitors. We present experiments on decoherence in the circuit used as a qubit. The qubit relaxation time T₁ is reaching as high as 47 μs and the spin-echo dephasing time T₂ = 9.4 μs. In addition, we present spectroscopy experiments and decoherence characterization in the qutrit subspace formed by the lowest three energy levels. The spectroscopy data is in excellent agreement with the complete circuit model based on the system capacitance matrix. At the flux symmetry point, the circuit has a large anharmonicity, defined as the difference between the 1-2 and 0-1 transition frequencies, approaching 2π × 3.7 GHz, which is enabling fast single qubit operations. We performed randomized benchmarking with the qubit gates with a duration of 1.62 ns and an average gate fidelity of 99.9%. \n \nMoreover, we present experiments with multi-level control in qutrit subspace, formed by the lowest three energy levels. We demonstrate a single step experimental implementation of a generalized Walsh-Hadamard gate. We use a decomposition of the quantum gate into two unitary operations, one implemented by an off-diagonal Hamiltonian and the other implemented by a diagonal Hamiltonian. The off-diagonal Hamiltonian is obtained by the simultaneous driving of the transitions between levels 0-1, 1-2, and 0-2, with the latter being a two-photon process. The diagonal Hamiltonian is effectively implemented by appropriately shifting the phases of adjacent pulses. The gate is characterized using tomography process and the average fidelity exceeds 90%, in good agreement with numerical simulations that take into account the multi-level structure of the system.Superconducting devices as quantum bits (qubits) are one of the most promising candidates for implementing a practical quantum computer. Over the last decade, quantum coherence times of superconducting qubits have been continuously improved. Operating qubits in noise insensitive points, eliminating the participation of the lossy materials, and better isolation from environment increased the decoherence times from nanoseconds to tens of microseconds. One recent approach on the qubit design is to shunt the Josephson junctions with large capacitors to reduce the sensitivity to noise and to redistribute the stored electromagnetic energy in a well-engineered area. This approach was first applied on charge qubits and later adopted to other types of superconducting qubits. \n \nIn this thesis, we present the design and the characterization of a three-Josephson junction superconducting circuit with three large shunt capacitors. We present experiments on decoherence in the circuit used as a qubit. The qubit relaxation time T₁ is reaching as high as 47 μs and the spin-echo dephasing time T₂ = 9.4 μs. In addition, we present spectroscopy experiments and decoherence characterization in the qutrit subspace formed by the lowest three energy levels. The spectroscopy data is in excellent agreement with the complete circuit model based on the system capacitance matrix. At the flux symmetry point, the circuit has a large anharmonicity, defined as the difference between the 1-2 and 0-1 transition frequencies, approaching 2π × 3.7 GHz, which is enabling fast single qubit operations. We performed randomized benchmarking with the qubit gates with a duration of 1.62 ns and an average gate fidelity of 99.9%. \n \nMoreover, we present experiments with multi-level control in qutrit subspace, formed by the lowest three energy levels. We demonstrate a single step experimental implementation of a generalized Walsh-Hadamard gate. We use a decomposition of the quantum gate into two unitary operations, one implemented by an off-diagonal Hamiltonian and the other implemented by a diagonal Hamiltonian. The off-diagonal Hamiltonian is obtained by the simultaneous driving of the transitions between levels 0-1, 1-2, and 0-2, with the latter being a two-photon process. The diagonal Hamiltonian is effectively implemented by appropriately shifting the phases of adjacent pulses. The gate is characterized using tomography process and the average fidelity exceeds 90%, in good agreement with numerical simulations that take into account the multi-level structure of the system.

Apr 5, 20190 citations

25 \mathrm{ns}

, with an average gate fidelity exceeding

99.99\%

and leakage below

10^{-5}

. Using experimentally relevant superconducting-qubit parameters and accounting for decoherence, the proposed scheme maintains a CZ-gate fidelity of approximately

99.9\%

. We further extend the analysis to larger coupled architectures and find that the CZ-gate infidelity remains below

10^{-4}

in the presence of spectator qubits. These results establish single-parameter flux control as a simple and robust approach for realizing high-fidelity entangling gates in heterogeneous superconducting quantum architectures.