Inductively shunted superconducting qubits, such as the unimon qubit, combine high anharmonicity with protection from low-frequency charge noise, positioning them as promising candidates for the implementation of fault-tolerant superconducting quantum computers. In this work, we develop accurate closed-form approximations for the frequency and anharmonicity of the unimon qubit that are also applicable to any single-mode superconducting qubits with a single-well potential profile, such as the quarton qubit or the kinemon qubit. We use these results to theoretically explore the single-qubit gate fidelity and coherence times across the parameter space of qubits with a single-well potential. We find that the gate fidelity can be optimized by tuning the Hamiltonian to (1) a high qubit mode impedance of 1 – 2 k Ω , (2) a low qubit frequency of 1 GHz, (3) and a perfect cancellation of the linear inductance and the Josephson inductance attained at a flux bias of half flux quantum. According to our theoretical analysis, the proposed qubit parameters have the potential to enhance the single-qubit gate fidelity of the unimon beyond 99.99%, even without significant improvements to the dielectric quality factor or the flux noise density measured for the first unimon qubits. Furthermore, we compare unimon, transmon, and fluxonium qubits in terms of their energy spectra and qubit coherence subject to dielectric loss and 1 / f flux noise in order to highlight the advantages and limitations of each qubit type.
Inductively shunted superconducting qubits, such as the unimon qubit, combine high anharmonicity with protection from low-frequency charge noise, positioning them as promising candidates for the implementation of fault-tolerant superconducting quantum computers. In this work, we develop accurate closed-form approximations for the frequency and anharmonicity of the unimon qubit that are also applicable to any single-mode superconducting qubits with a single-well potential profile, such as the quarton qubit or the kinemon qubit. We use these results to theoretically explore the single-qubit gate fidelity and coherence times across the parameter space of qubits with a single-well potential. We find that the gate fidelity can be optimized by tuning the Hamiltonian to (1) a high qubit mode impedance of 1 – 2 k Ω , (2) a low qubit frequency of 1 GHz, (3) and a perfect cancellation of the linear inductance and the Josephson inductance attained at a flux bias of half flux quantum. According to our theoretical analysis, the proposed qubit parameters have the potential to enhance the single-qubit gate fidelity of the unimon beyond 99.99%, even without significant improvements to the dielectric quality factor or the flux noise density measured for the first unimon qubits. Furthermore, we compare unimon, transmon, and fluxonium qubits in terms of their energy spectra and qubit coherence subject to dielectric loss and 1 / f flux noise in order to highlight the advantages and limitations of each qubit type.
Abstract Superconducting qubits seem promising for useful quantum computers, but the currently wide-spread qubit designs and techniques do not yet provide high enough performance. Here, we introduce a superconducting-qubit type, the unimon, which combines the desired properties of increased anharmonicity, full insensitivity to dc charge noise, reduced sensitivity to flux noise, and a simple structure consisting only of a single Josephson junction in a resonator. In agreement with our quantum models, we measure the qubit frequency, ω01/(2π), and increased anharmonicity α/(2π) at the optimal operation point, yielding, for example, 99.9% and 99.8% fidelity for 13 ns single-qubit gates on two qubits with (ω01, α) = (4.49 GHz, 434 MHz) × 2π and (3.55 GHz, 744 MHz) × 2π, respectively. The energy relaxation seems to be dominated by dielectric losses. Thus, improvements of the design, materials, and gate time may promote the unimon to break the 99.99% fidelity target for efficient quantum error correction and possible useful quantum advantage with noisy systems.
Quantum computers utilize qubits to store and process quantum information. In superconducting quantum computers, qubits are implemented as quantum superconducting resonant circuits. The circuits are operated only at the two energy states, which form the computational basis for the qubit. To suppress leakage to uncomputational states, superconducting qubits are designed to be anharmonic oscillators, which is achieved using one or more Josephson junctions, a nonlinear superconducting element. One of the main challenges in developing quantum computers is minimizing the decoherence caused by environmental noise. Decoherence is characterized by two coherence times, T1 for depolarization processes and T2 for dephasing. This thesis reviews and investigates the decoherence properties of superconducting qubits. The main goal of the thesis is to analyze the tradeoff between anharmonicity and dephasing in a qubit unimon. Recently developed unimon incorporates a single Josephson junction shunted by a linear inductor and a capacitor. Unimon is tunable by external magnetic flux, and at the half flux quantum bias, the Josephson energy is partially canceled by the inductive energy, allowing unimon to have relatively high anharmonicity while remaining fully protected against low-frequency charge noise. In addition, at the sweet spot with respect to the magnetic flux, unimon becomes immune to first-order perturbations in the flux. The sweet spot, however, is relatively narrow, making unimon susceptible to dephasing through the quadratic coupling to the flux noise. In the first chapter of this thesis, we present a comprehensive look into the basic theory of superconducting qubits, starting with two-state quantum systems, followed by superconductivity and superconducting circuit elements, and finally combining these two by introducing circuit quantum electrodynamics (cQED), a framework for building superconducting qubits. We follow with a theoretical discussion of decoherence in two-state quantum systems, described by the Bloch-Redfield formalism. We continue the discussion by estimating decoherence using perturbation theory, with special care put into the dephasing due to the low-frequency 1/f noise. Finally, we review the theoretical model of unimon, which is used in the numerical analysis. As a main result of this thesis, we suggest a design parameter regime for unimon, which gives the best ratio between anharmonicity and T2.
Quantum processors with native multi-qubit gates may offer very efficient implementations of near-term quantum algorithms on noisy hardware. Here, we introduce the multiunimon, a superconducting multimode circuit that encodes multiple qubits and enables native multi-qubit gates in a device consisting of a single Josephson junction embedded in a coplanar waveguide structure. Closely related to the unimon qubit, it inherits properties such as high anharmonicity, full protection against low-frequency charge noise, and partial protection against flux noise. By designing such a three-qubit device with Josephson-to-inductive energy ratio above unity and using a leakage-aware encoding scheme for the computational states, we simulate all twelve different controlled-controlled-NOT gates with a mean fidelity of 99.5% with simple sine-squared pulses of comparable length to single-qubit gates. The performance is limited by incoherent errors dominated by dielectric loss. With improvements in noise protection, design, and pulse shaping, the simulations suggest that fidelities approaching 99.99% are within reach. Our results demonstrate the potential of the multiunimon as a highly connected multi-qubit unit for larger superconducting quantum processors.
Abstract Superconducting qubits seem promising for useful quantum computers, but the currently wide-spread qubit designs and techniques do not yet provide high enough performance. Here, we introduce a superconducting-qubit type, the unimon, which combines the desired properties of increased anharmonicity, full insensitivity to dc charge noise, reduced sensitivity to flux noise, and a simple structure consisting only of a single Josephson junction in a resonator. In agreement with our quantum models, we measure the qubit frequency, ω01/(2π), and increased anharmonicity α/(2π) at the optimal operation point, yielding, for example, 99.9% and 99.8% fidelity for 13 ns single-qubit gates on two qubits with (ω01, α) = (4.49 GHz, 434 MHz) × 2π and (3.55 GHz, 744 MHz) × 2π, respectively. The energy relaxation seems to be dominated by dielectric losses. Thus, improvements of the design, materials, and gate time may promote the unimon to break the 99.99% fidelity target for efficient quantum error correction and possible useful quantum advantage with noisy systems.
Superconducting circuits provide a promising approach for constructing a large-scale quantum computer in the future. In theory, a fault-tolerant quantum computer is suitable for efficiently simulating quantum-mechanical systems, such as molecules, or factorizing large integers - to name a few examples. However, reaching a practical quantum advantage will probably require scaling up the number of qubits in current quantum-processing units by several orders of magnitude while retaining high controllability and high coherence of individual qubits. In this thesis, we first provide a review of the most common superconducting qubit types in order to shed light on the factors that affect the coherence, anharmonicity, and operation of single qubits. Using the insight gained from the review, we theoretically study a novel superconducting qubit circuit that consists of a grounded coplanar waveguide resonator incorporating an embedded Josephson junction in the center conductor of the resonator. The non-linear Josephson junction renders the normal modes of the resonator anharmonic, as a result of which one of the normal modes can be utilized to implement a qubit. The studied circuit, nicknamed as the coplanarium, may provide a high-coherence superconducting qubit since it contains no isolated superconducting islands rendering the qubit immune to dephasing arising from low-frequency charge noise. We derive the quantum Hamiltonian of the distributed circuit from first principles both with and without an external magnetic flux. Using numerical calculations based on our theoretical results, we show that the anharmonicity of the coplanarium qubit can exceed 500 MHz for a qubit frequency of 5 GHz at a flux-insensitive sweet spot if an appropriate external magnetic flux is applied. Importantly, the parameter values used in the numerical simulations are experimentally feasible, and the characteristic impedance of the resonator needs to be no greater than Z0 = 100 Omega. The relatively high anharmonicity can be attributed to a partial cancellation of the quadratic potential-energy terms associated with the Josephson junction and the linear inductance of the resonator. In conclusion, the promising coherence and anharmonicity properties may render the coplanarium qubit an interesting alternative for reducing leakage errors, and the ratio between coherence times and the duration of quantum logic gates in superconducting quantum processors.
We consider a superconducting half-wavelength resonator that is grounded at its both ends and contains a single Josephson junction. Previously this circuit was considered as a unimon qubit in the single-mode approximation where dc-phase-biasing the junction to π leads to increased anharmonicity and 99.9% experimentally observed single-qubit gate fidelity. Inspired by the promising first experimental results, we develop here a theoretical and numerical model for the detailed understanding of the multimode physics of the unimon circuit. To this end, first, we consider the high-frequency modes of the unimon circuit and find that even though these modes are at their ground state, they imply a significant renormalization to the Josephson energy. We introduce an efficient method to fully account for the relevant modes and show that unexcited high-lying modes lead to corrections in the qubit energy and anharmonicity. Interestingly, provided that the junction is offset from the middle of the circuit, we find strong cross-Kerr coupling strengths between a few low-lying modes. This observation paves the way for the utilization of the multimode structure, for example, as several qubits embedded into a single unimon circuit. Published by the American Physical Society 2024