The authors propose a Floquet qubit that is the superconducting circuit analog of a mechanical Kapitza pendulum. Under periodic driving, the bit and phase flip rates of the emerging qubit states are exponentially suppressed with respect to the ratio of the effective Josephson energy to charging energy. A cooling scheme to protect the system against charge noise is also proposed.
The authors propose a Floquet qubit that is the superconducting circuit analog of a mechanical Kapitza pendulum. Under periodic driving, the bit and phase flip rates of the emerging qubit states are exponentially suppressed with respect to the ratio of the effective Josephson energy to charging energy. A cooling scheme to protect the system against charge noise is also proposed.
Quantum control and noise protection of a Floquet 0−π qubit
Time-periodic systems allow engineering new effective Hamiltonians from limited physical interactions. For example, the inverted position of the Kapitza pendulum emerges as a stable equilibrium with rapid drive of its pivot point. In this work, we propose the Kapitzonium: a Floquet qubit that is the superconducting circuit analog of a mechanical Kapitza pendulum. Under periodic driving, the emerging qubit states are exponentially protected against bit and phase flips caused by dissipation, which is the primary source of decoherence of current qubits. However, we find that dissipation causes leakage out of the Floquet qubit subspace. We engineer a passive cooling scheme to stabilize the qubit subspace, which is crucial for high fidelity quantum control under dissipation. Furthermore, we introduce a hardware-efficient fluorescence-based method for qubit measurement and discuss the experimental implementation of the Floquet qubit. The proposed Kapitzonium is one of the simplest Floquet qubits that can be realized with current technology -- and it already has many intriguing features and capabilities. Our work provides the first steps to develop more complex Floquet quantum systems from the ground up to realize large-scale protected engineered dynamics.
Floquet engineering is a powerful method that can be used to modify the properties of interacting many-body Hamiltonians via the application of periodic time-dependent drives. Here, we consider the physics of an inductively shunted superconducting Josephson junction in the presence of Floquet drives in the fluxonium regime and beyond, which we dub the frozonium artificial atom. We find that in the vicinity of special ratios of the drive amplitude and frequency, the many-body dynamics can be tuned to that of an effectively linear bosonic oscillator, with additional nonlinear corrections that are suppressed in higher powers of the drive frequency. By analyzing the inverse participation ratios between the time-evolved frozonium wavefunctions and the eigenbasis of a linear oscillator, we demonstrate the ability to achieve a novel dynamical control using a combination of numerical exact diagonalization and Floquet-Magnus expansion. We discuss the physics of resonances between quasi-energy states induced by the drive and ways to mitigate their effects. We also highlight the enhanced protection of frozonium against external sources of noise present in experimental setups. This work lays the foundation for future applications in quantum memory and bosonic quantum control using superconducting circuits.
In the past few decades, quantum computation has become an active area of research due to prospects to execute high-efficiency quantum algorithms. Quantum algorithms promise to accelerate many practical computation problems, but they can not be managed on classical computers. While a vast amount of time and effort has been invested into this field, executing a quantum algorithm is still a difficult task. One major obstacle is decoherence, which can be induced by the environment. To better protect information against noises, designs for a quantum computer have quickly improved. However, many new designs lack systematic analysis. \n \nIn the first part of the thesis, we investigate a type of superconducting-circuit-based qubit design proposed recently. The qubit, inspired by the current-mirror effect, is called the "zero-pi qubit". In Chapter 2, we derived an approximated model through concrete mathematical calculations and simulations of the zero-pi qubit. The model is concise and accurately describes the qubit system. Based on the model, we further estimate the decoherence time of the qubit. The dephasing time due to the flux noise and the charge noise exceed 40 s, and the relaxation process is well-protected against flux noise and charge noise. \n \nIn the second part of the thesis, Chapter 3, we explore the qubit control in the strong driving regime. Driving a qubit with a strong signal is an approach to shorten the operation time, thus suppressing the influence of the decoherence. We achieve strong driving condition experimentally and observe complicated qubit dynamics, which is not predicted by any conventional model. We then propose a model based on Floquet theory which accurately describes the dynamics of the qubit.
We propose a superconducting qubit based on engineering the first and second harmonics of the Josephson energy and phase relation E J 1 cos φ and E J 2 cos 2 φ . By constructing a circuit such that E J 2 is negative and | E J 1 | ≪ | E J 2 | , we create a periodic potential with two nondegenerate minima. The qubit, which we dub “harmonium,” is formed from the lowest-energy states of each minimum. Bit-flip protection of the qubit arises due to the localization of each qubit state to their respective minima, while phase-flip protection can be understood by considering the circuit within the Born-Oppenheimer approximation. We demonstrate with time-domain simulations that single- and two-qubit gates can be performed in approximately 100 ns. Finally, we compute the qubit coherence times using numerical diagonalization of the complete circuit in conjunction with state-of-the-art noise models. We estimate out-of-manifold heating times on the order of milliseconds, which can be treated as erasure errors using conventional dispersive readout. We estimate pure-dephasing times on the order of many tens of milliseconds, and bit-flip times on the order of seconds.
High-coherence qubits, which can store and manipulate quantum states for long times with low error rates, are necessary building blocks for quantum computers. Here we propose a driven superconducting erasure qubit, the Floquet fluxonium molecule, which minimizes bit-flip rates through disjoint support of its qubit states and suppresses phase flips by a novel second-order insensitivity to flux-noise dephasing. We estimate the bit-flip, phase-flip, and erasure rates through numerical simulations, with predicted coherence times of approximately 50 ms in the computational subspace and erasure lifetimes of about 500 μ s . We also present a protocol for performing high-fidelity single-qubit rotation gates via additional flux modulation, on timescales of roughly 500 ns, and propose a scheme for erasure detection and logical readout. Our results demonstrate the utility of drives for building new qubits that can outperform their static counterparts. Published by the American Physical Society 2024
We develop and characterize a symmetry-protected superconducting qubit that offers simultaneous exponential suppression of energy decay from charge and flux noises, and dephasing from flux noise.The qubit consists of a Cooper-pair box (CPB) shunted by a superinductor, forming a superconducting loop.Provided the offset charge on the CPB island is an odd number of electrons, the qubit potential corresponds to that of a cos (φ/2) Josephson element, preserving the parity of fluxons in the loop via Aharonov-Casher interference.In this regime, the logical-state wavefunctions reside in disjoint regions of Hilbert space, thereby ensuring protection against energy decay.By switching the protection on, we observe a tenfold increase of the decay time, reaching up to 100 μs.Though the qubit is sensitive to charge noise, the sensitivity is much reduced in comparison with the charge qubit, and the charge-noise-induced dephasing time of the current device exceeds 1 μs.Implementation of full dephasing protection can be achieved in the next-generation devices by combining several cos(φ/2) Josephson elements in a small array.