Understanding Qubit Errors: A Study on Quasiparticle-Induced Errors in Schrödinger Cat Qubits

Researchers from the University of Grenoble Alpes have studied the theory of quasiparticle-induced errors in driven-dissipative Schrödinger cat qubits. The study focuses on understanding qubit decoherence, a key factor in improving performance. The research discusses the effects of residual Bogolyubov quasiparticles in Schrödinger cat qubits, which are operated under nonequilibrium conditions.

The team presents a microscopic derivation of the master equation for cat qubits, allowing them to determine the conditions under which the quasiparticles contribute significantly to qubit errors. The study also explores the role of superconducting circuits in realizing qubits and the noise sources in Schrödinger cat qubits.

What is the Theory of Quasiparticle-Induced Errors in Driven-Dissipative Schrödinger Cat Qubits?

The theory of quasiparticle-induced errors in driven-dissipative Schrödinger cat qubits is a study conducted by Kirill S Dubovitskii, Denis M Basko, Julia S Meyer, and Manuel Houzet from the University of Grenoble Alpes, France. The research focuses on understanding the mechanisms of qubit decoherence, a crucial prerequisite for improving the performance of qubits. The study discusses the effects of residual Bogolyubov quasiparticles in Schrödinger cat qubits, either of the dissipative or Kerr type.

The major difference from previous studies of quasiparticles in superconducting qubits is that the Schrödinger cat qubits are operated under nonequilibrium conditions. An external microwave drive is needed to stabilize cat states, superpositions of coherent degenerate eigenstates of an effective stationary Lindbladian in the rotating frame. The researchers present a microscopic derivation of the master equation for cat qubits and express the effect of the quasiparticles as dissipators acting on the density matrix of the cat qubit. This enables them to determine the conditions under which the quasiparticles substantially contribute to the qubit errors.

How Do Superconducting Circuits Contribute to the Realization of Qubits?

Superconducting circuits represent one of the most promising physical platforms for realizing qubits, the elementary building blocks of quantum computers. Operational superconducting qubits include transmon, fluxonium, and many others. All qubits are subject to errors due to their environment, and quantum error correction imposes a huge overhead cost in any quantum computer architecture.

A single logical qubit must be represented by many physical qubits. Then, qubits with intrinsic protection against some errors may reduce this cost and offer a technological advantage. One way to implement such intrinsic protection is to encode the qubit states in a bosonic degree of freedom, well separating the two states in the phase space, thus reducing their sensitivity to local noise. This separation can be achieved via an interplay between a microwave drive and nonlinear couplings such as Schrödinger cat qubits have been successfully fabricated in recent years.

What are the Noise Sources in Schrödinger Cat Qubits?

Like other superconducting qubits based on Josephson junctions, Schrödinger cat qubits are subject to various noise sources such as photon escape, dielectric loss, and finally residual Bogolyubov quasiparticles. Even though superconducting qubits are operated at very low temperatures so that hardly any quasiparticles should be present in thermal equilibrium, typically a significant number of residual nonequilibrium quasiparticles can still be detected.

Presumably generated by rare energetic events such as cosmic rays, dilute quasiparticles recombine very slowly and it is well established that their density normalized to the Cooper pair density is usually in the range xqp105-108. Many experiments studying the coherence of transmon or fluxonium qubits are successfully described taking into account residual quasiparticles via the theory developed in Refs 24-26. As qubits are improved by eliminating other error sources, Bogolyubov quasiparticles are likely to ultimately limit the coherence times.

How Does the Driven Nature of Schrödinger Cat Qubits Affect Their Interaction with Residual Quasiparticles?

The fundamental difference between the conventional qubits such as transmon or fluxonium and cat qubits is that the former are based on stationary eigenstates of a static Hamiltonian while the latter rely on a strong microwave drive. In fact, the qubit states are stationary only in a fast rotating reference frame whose frequency is determined by a device-dependent combination of the natural frequencies of the circuit and the drive.

The cat qubit states may be eigenstates of an engineered Kerr-like bosonic Hamiltonian or form the stationary manifold of a two-photon dissipative Lindbladian. This poses the question of how the driven Kerr qubit or driven-dissipative dissipative qubit nature of the Schrödinger cat qubits affects their interaction with the residual quasiparticles. The present paper is dedicated to a theoretical investigation of this question.

What is the Role of the Master Equation in Identifying Errors in Kerr and Dissipative Cat Qubits?

In the study, the researchers start from the quasiparticle tunneling Hamiltonian and calculate the rates of various errors in Kerr and dissipative cat qubits. To identify these errors, it is convenient to use the phenomenological master equation, which became a standard tool for the description of the cat qubits dynamics.

The master equation describes undesired relaxation processes for the qubit characterized by the rates κ, typically referred to as single photon loss/gain rates, and κϕ, pure dephasing rate, and lead to various errors. Typically, the photon loss rate κ<κϕ. A master equation similar to 1 is often used for conventional static qubits like transmon.