Session B29: Superconducting Qubits: Hamiltonian Engineering and Design Tools

Quantization of Large Superconducting Circuits with Tensor Networks

We introduce a novel method for efficient quantum simulation of large superconducting circuits using matrix product states (MPS) and the density matrix renormalization group (DMRG) technique. We analyze an LC oscillator containing a chain of Josephson junctions, forming a superinductor. We obtain the lowest-lying eigenstates and energies, and calculate physical observables of interest for chain lengths in the range of 5-65 Josephson junctions. We quantify simulation convergence through comparison with exact diagonalization (when possible) and quantum state variance. Our approach reaches far beyond the resource limitations of brute-force exact diagonalization.
  

Towards Total Quantum System Characterization

Quantum enabled technologies promise to deliver the next technological revolution. However, their realization requires a degree of control over quantum systems that is still elusive. The problem stems from our imperfect knowledge of the physical quantities ruling their evolution. To overcome this, system characterization tools such as Hamiltonian learning, noise spectroscopy, and state tomography have been devised. However, the success of each of these schemes often requires the knowledge provided by the other. For example, Hamiltonian learning protocols estimate the parameters of a Hamiltonian ruling the evolution of a set of qubits but require knowledge of any noise affecting them to be successful, while noise spectroscopy protocols can characterize the noise affecting the system of interest but require knowledge of the deterministic part of the Hamiltonian.
In this talk, we will present a limited-access total quantum system characterization tool. We show that it is possible to simultaneously extract the information that Hamiltonian learning, noise spectroscopy, and state tomography of a composite quantum system provide, when only limited-access is available, i.e., when fast and reliable control and measurements are possible in only a subsystem.   

Exact quantization of superconducting circuits

Circuits consisting of weak anharmonic qubits coupled to cavity multimodes are theoretically quatized beyond dispersive regime. In order to do this, we obtain a unitary transformation that diagonalizes harmonic sector of the circuit. Weak anharmonicity does not alter normal mode basis, however it modifies energy levels. using our formalism we we quantize two circuits of 1) a transmon coupled to a resonator, and 2) two transmons coupled to a bus resonator. In both circuits we determine dressed frequencies and Kerr nonlinearities in closed form formulas. Our results are valid for arbitrary frequency detuning and coupling within and beyond dispersive regime.

Reference: MH. Ansari, arXiv:1807.00792   

Numerical Methods for Current Mirror Qubit Simulations

Current Mirror Qubits¹ (CMQs) are an example of “noise insensitive” superconducting qubits predicted to exhibit longer coherence times than conventional superconducting qubits even when exposed to the same noise environment. CMQs also have the advantage of not requiring detailed tune-up or fabrication precision² to achieve noise insensitivity. However, given the large number of circuit components that comprise such qubits, direct numerical diagonalization of the qubit’s Hamiltonian using a product basis is numerically intractable. This presents a challenge for verifying projected noise immunity for realistic circuits that include fabrication imperfections or control offsets. This talk discusses various numerical models for CMQs that address this challenge, and presents initial comparisons between these models and experimental realizations of these qubits.
[1] Alexei Kitaev, arXiv:cond-mat/0609441 (2006)
[2] Dempster et al., PRB 90, 094518 (2014)   

Quantum Engineering Design of Superconducting Qubits

Many novel superconducting qubits have circuits with a large number of quantum components. Such circuits can require "quantum engineering design," i.e., the numerical simulation of a large Hilbert space to determine optimal device performance. For this purpose, we introduce the Villain periodically Continued Harmonic Oscillator Basis (VCHOB). This general method allows for automated and efficient numerical diagonalization of superconducting circuits, increasing the types of circuits for which quantum engineering design is possible.   

Energy-participation approach to the design of quantum Josephson circuits

Superconducting circuits incorporating non-linear devices, such as Josephson tunnel junctions and nanowires, are among the leading platforms for emerging quantum technologies. Promising applications require designing and optimizing circuits with ever-increasing complexity and controlling their dissipative and Hamiltonian parameters to several significant digits. Therefore, there is a growing need for a systematic, simple, and robust approach for precise circuit design, extensible to increased complexity. In this talk, we present such an approach to unify the design of dissipation and Hamiltonians around a single concept — the energy participation, a number between zero and one — in a single-step electromagnetic simulation. This markedly reduces the required number of simulations and allows for robust extension to complex systems. The approach is general purpose, valid for arbitrary non-linear devices and circuit architectures. We present experimental results on a variety of circuit quantum electrodynamics (cQED) devices and architectures, 3D and flip-chip (2.5D), which exhibit percent-level agreement for Hamiltonian parameters over five-orders of magnitude and across a dozen devices.   

Circuit Quantization in the Presence of Time-Dependent External Sources

Circuit quantization serves as a link between physical circuits and quantum Hamiltonians. The standard procedure [1] established decades ago implicitly assumes the external magnetic flux threading a circuit loop to be static. However, time-dependence arises inevitably when flux modulation or noise are considered. Naïve application of the existing circuit-quantization procedure can then lead to inconsistencies in predictions of qubit relaxation times. In this talk, we present a generalized approach to circuit quantization valid in the presence of time-dependent external sources. Our results uncover the reason for the inconsistency and resolve it, and are applicable to a wide range of circuits utilizing time-varying external fields.

[1] M. H. Devoret, Les Houches, Session LXIII 7 (1995)   

Hamiltonian Learning on Superconducting Qubits using Bayesian Inference

Bayesian inference uses Bayes’ theorem to update the probability of a hypothesis and as a result can be used to great effect when trying to learn the Hamiltonian of a quantum system. In comparison to traditional techniques for characterisation it has the benefit of providing statistically relevant information about the learning procedure, enabling more efficient data taking and revealing limits of the model provided to produce the data. It can be used to compare how well different models fit measured data and hence diagnose noise sources. We demonstrate this by applying it to a superconductor semiconductor 'gatemon' qubit and use it to learn the parameters of the Hamiltonian.   

Establishing a physical model for a chain of superconducting qubits

The dynamics in a system of coupled qubits is proven to be computationally hard. Harnessing the computation power associated with these complex dynamics requires controlling the evolution with high fidelity, which in turn requires knowing the physical parameters of the system with high accuracy. Using a few coupled superconducting qubits, we discuss a method for extracting the values of the physical parameters of the system. In addition to the direct spectroscopy of the eigen-modes of the system, we generate controlled dynamics and measure the evolution of certain observables to refine the knowledge of the parameters obtained from spectroscopy. We discuss the accuracy of this calibration technique in terms of the requirements for performing a classically challenging computation.   

Drive-induced lifetime renormalization of superconducting qubits I: Effective Master Equations

We show that number non-conserving terms in the Josephson anharmonicity lead to a renormalization of the lifetime of microwave-driven superconducting qubits. Using a method of unitary transformations, we account for the frequently neglected number non-conserving terms in the Josephson potential, and show that they generate drive- and anharmonicity-dependent corrections of the qubit and readout resonator relaxation rates. Simultaneously, the number-conserving terms yield the known Kerr corrections to the eigenfrequencies of the system. We present our results in the form of effective master equations with renormalized Hamiltonian and collapse operators. Effective master equations provide an efficient tool to extract drive-, state- and anharmonicity-dependent relaxation rates.   

Drive-induced lifetime renormalization of superconducting qubits II: The Readout Problem

Recent experiments found a strong dependence of qubit relaxation rates on the readout drive power. The observed dynamics can not be fully explained by previous theoretical approaches based on the Jaynes-Cummings, Rabi or Kerr based models. We show that an effective master equation that accounts for renormalization of dissipative parameters due to number non-conserving terms inherent in the Josephson nonlinearity captures with good qualitative agreement this strong dependence. We account for a realistic experimental setting with a finite bath temperature and an additional pure dephasing channel, both of which are shown to significantly enhance the qubit relaxation renormalization with drive. Effective master equations for driven Josephson circuits appear to provide an accurate and computationally resource-efficient approach to experimentally relevant settings.   

Computational modeling of decay and hybridization in superconducting circuits

We present a circuit theoretic technique for computing the complex frequencies and eigenmodes of superconducting circuits with radiative loss. We show that the transmon loss rates obtained by our method agree with the established approximation C/Re[Y] away from resonance and do not diverge near resonance. Additionally, we demonstrate that in systems with significant radiative loss, couplings between modes cannot be accurately computed if the loss is neglected. Our simulation technique is useful for designing complex superconducting quantum processors.   

Enablement of near-term quantum processors by architectural yield engineering

Scaling of near-term quantum processors depends on complex architectures where maintaining low gate error rates relies on utilizing the highest coherence times available. In the case of fixed-frequency transmon qubits coupled via cross-resonance gates, multi-qubit operation is feasible as long as the excitation energies of neighboring qubits are similar but non-degenerate. Meeting this condition consistently in a large lattice of qubits requires precise Josephson junction fabrication and accurate frequency forecasting. In this talk, we will compare measured qubit frequencies to resistance measurements of Josephson junctions, and use a statistical model to suggest strategies for useful device yields at the 50 qubit and larger scale.   

Frequency trimming of superconducting fixed-frequency qubits

There has been significant progress to increase the number of superconducting fixed-frequency qubits for multi-qubit gates. The variations in fabrication limits the precision in qubit frequency to within ~ 200 MHz of the design value [1], which could lead to undesired frequency crowding. We developed a frequency trimming process to correct the frequencies of the measured qubits. The frequency trimming involves first a chemical process to remove all on-chip wirebonds, followed by lithography and dry etch to trench the dielectric substrate near the qubit to tune the frequency to the target design value. We present fabrication process details, simulations, and qubit measurements.

[1] S. Rosenblatt et al. , Variability metrics in Josephson Junction fabrication for Quantum Computing circuits, in Proceedings of the APS March Meeting, New Orleans (2017).   

Local trimming of transmon qubit frequency by laser annealing of Josephson junctions

Limited control in the fabrication of Al-AlOx-Al Josephson junctions makes accurate targeting of the qubit transition frequency in superconducting quantum processors an outstanding challenge. We demonstrate a selective increase in junction resistance by localized thermal annealing using a focused diode laser source at room temperature. By tuning the irradiation time and incident laser power, we controllably increase junction resistance by up to 15%. We quantify the success of this targeting method by comparing transmon qubit transition frequencies and coherence before and after laser annealing.