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arXiv:2010.01016 · Physical Review Letters

Spin-Boson Quantum Phase Transition in Multilevel Superconducting Qubits

Kuljeet Kaur, Théo Sépulcre, Nicolas Roch, Izak Snyman, Serge Florens, Soumya Bera

Published Dec 3, 2021• 28 citations
arXivHTMLPDF

Abstract

Superconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, by building on nonlinear elements that are often idealized as two-level qubits. A classic example is given by a charge qubit that is capacitively coupled to a transmission line, which leads to the celebrated spin-boson description of quantum dissipation. We show that the intrinsic multilevel structure of superconducting qubits drastically restricts the validity of the spin-boson paradigm due to phase localization, which spreads the wave function over many charge states. Numerical renormalization group simulations also show that the quantum critical point moves out of the physically accessible range in the multilevel regime. Imposing charge discreteness in a simple variational state accounts for these multilevel effects, which are relevant for a large class of devices.

DOI
10.1103/physrevlett.127.237702

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Superconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, by building on nonlinear elements that are often idealized as two-level qubits. A classic example is given by a charge qubit that is capacitively coupled to a transmission line, which leads to the celebrated spin-boson description of quantum dissipation. We show that the intrinsic multilevel structure of superconducting qubits drastically restricts the validity of the spin-boson paradigm due to phase localization, which spreads the wave function over many charge states. Numerical renormalization group simulations also show that the quantum critical point moves out of the physically accessible range in the multilevel regime. Imposing charge discreteness in a simple variational state accounts for these multilevel effects, which are relevant for a large class of devices.
Superconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, both at the analog and digital levels. Their building blocks are often idealized as two-level qubits, drawing powerful analogies to quantum spin models. For a charge qubit that is capacitively coupled to a transmission line, this analogy leads to the celebrated spin-boson description of quantum dissipation. We put here into evidence a failure of the two-level paradigm for realistic superconducting devices, due to electrostatic constraints which limit the maximum strength of dissipation. These prevent the occurence of the spin-boson quantum phase transition for transmons, even up to relatively large non-linearities. A different picture for the many-body ground state describing strongly dissipative transmons is proposed, showing unusual zero point fluctuations.
We present a multilevel quantum theory of decoherence for a general circuit realization of a superconducting qubit. Using electrical network graph theory, we derive a Hamiltonian for the circuit. The dissipative circuit elements (external impedances, shunt resistors) are described using the Caldeira-Leggett model. The master equation for the superconducting phases in the Born-Markov approximation is derived and brought into the Bloch-Redfield form in order to describe multilevel dissipative quantum dynamics of the circuit. The model takes into account leakage effects, i.e., transitions from the allowed qubit states to higher excited states of the system. As a special case, we truncate the Hilbert space and derive a two-level (Bloch) theory with characteristic relaxation (T1){(T}_{1})(T1​) and decoherence (T2){(T}_{2})(T2​) times. We apply our theory to the class of superconducting flux qubits; however, the formalism can be applied for both superconducting flux and charge qubits.
We study quantum critical phenomena in the microwave scattering of the subohmic spin-boson system, which exhibits a quantum phase transition at a critical system-reservoir coupling. By relating the reflection coefficient of a microwave with the dynamic susceptibility of the subohmic spin-boson system, we clarify the appearance of quantum critical phenomena in microwave scattering. Further, we propose experimental setups to realize the subohmic spin-boson system in a superconducting circuit composed of a charge qubit and a dissipative transmission line.
The new superconductivity theory that attributes the U(1)U(1)U(1) superconductivity phase to a Berry phase arising from many-body wave functions is applied to the circuit quantization for superconducting qubits. The phase-charge duality required for the occurrence of superconductivity in the standard theory becomes irrelevant in the new theory, and the absence of a dissipative quantum phase transition in Josephson junctions is explained. It is shown that a charge-decaying term leads to the compact phase description, and the appearance of Shapiro steps is explained without introducing normal current.
Quantum processors based on superconducting circuitry have reached the scale of hundreds of qubits and demonstrated computational capabilities that challenge state-of-the-art classical methods for carefully designed problems. Despite these advances, fundamental questions persist over how to best improve and scale the computational power of this emerging technology. Most transmon-based quantum processors encode information in two-level systems, or qubits, leaving the rich multilevel structure of the transmon largely unexploited. In this thesis, we demonstrate how the capabilities of these devices can be meaningfully extended by harnessing this intrinsic multilevel structure to encode qudits — d-level quantum systems that access a larger and more connected Hilbert space than their qubit counterparts. We begin by demonstrating universal single-qudit operation before turning to microwave-activated entanglement to realize scalable two-qudit gates. We present a high-fidelity, fully entangling two-qutrit CZ gate based on a novel tunable cross-Kerr mechanism. We further explore two-qudit gates that selectively entangle subspaces of the full Hilbert space via two-photon multipartite Raman transitions, employing these operations to generate large entangled states across a transmon array. To address the noisy nature of near-term qudit computation, we introduce and characterize error suppression techniques for qudit circuits, including dynamical decoupling and quantum error mitigation. We then synthesize these directions by exploring simulations of quantum systems that have innate multilevel interactions and are therefore well tailored to qudit operation. First we investigate digital quantum simulations of collective neutrino oscillations and the spin-1 truncated Abelian Higgs model, finding error mitigation methods critical for improving circuit performance. Finally, out of equilibrium --- or Floquet --- spin-1 systems are realized using an array of 15 superconducting qutrits to probe a novel Z3 discrete time crystalline (DTC) phase of matter with intrinsically chiral interactions. This DTC result demonstrates that native qudit hardware provides powerful access to non-equilibrium phases rooted in higher discrete symmetries, opening a route to a broader landscape of dynamical orders beyond the Z2 Ising paradigm.
We theoretically propose and analyze a Josephson-like magnetic tunnel junction (MTJ) structure that exhibits quantum spin dynamics analogous to those in superconducting Josephson junctions. By exploiting the isomorphism between the equations of motion for low-dissipation MTJs with easy-plane anisotropy and the Josephson phase dynamics, we construct a theoretical framework for realizing spintronic qubits. Within this framework, we identify the physical parameters, such as anisotropy constants, Gilbert damping, spin current amplitude, and geometric factors, that govern the transition from classical to quantum behavior. We show that different types of spintronic qubits, including analogs of charge, flux, and transmon superconducting qubits, can be implemented depending on the hierarchy of energy scales. A Hamiltonian formalism is developed for each regime, enabling an analytical treatment of the two-level quantum dynamics and estimation of coherence times. In particular, we demonstrate that the spin current can be used not only to excite but also to stabilize the qubit states through dissipation control. These findings provide a route toward integrating spintronic qubits into complementary metal-oxide-semiconductor compatible architectures and lay the groundwork for a fully spintronic platform for quantum computation.