[Paper Review] Spatially correlated classical and quantum noise in driven qubits: The good, the bad, and the ugly

Ji Zou, Stefano Bosco+1 more|arXiv (Cornell University)|Aug 6, 2023

Quantum Computing Algorithms and ArchitectureComputer Science3 citations

TL;DR

This paper presents a theoretical analysis of spatially correlated classical and quantum noise in driven two-qubit systems, revealing that while classical noise only causes correlated decoherence, quantum noise can generate long-range entanglement via coherent interactions such as Ising and Dzyaloshinskii-Moriya coupling. Remarkably, at low temperatures with coherent driving, correlated quantum noise induces on-demand, long-lived entanglement, while $1/f$ noise temporal correlations can even restore lost entanglement.

ABSTRACT

Correlated noise across multiple qubits poses a significant challenge for achieving scalable and fault-tolerant quantum processors. Despite recent experimental efforts to quantify this noise in various qubit architectures, a comprehensive understanding of its role in qubit dynamics remains elusive. Here, we present an analytical study of the dynamics of driven qubits under spatially correlated noise, including both Markovian and non-Markovian noise. Surprisingly, we find that, while correlated classical noise only leads to correlated decoherence without increasing the quantum coherence in the system, the correlated quantum noise can be exploited to generate entanglement. In particular, we reveal that, in the quantum limit, pure dephasing noise induces a coherent long-range two-qubit Ising interaction that correlates distant qubits. In contrast, for purely transverse noise when qubits are subjected to coherent drives, the correlated quantum noise induces both coherent symmetric exchange and Dzyaloshinskii-Moriya interaction between the qubits, as well as correlated relaxation, both of which give rise to significant entanglement. Remarkably, in this case, we uncover that the system exhibits distinct dynamical phases in different parameter regimes. Finally, we reveal the impact of spatio-temporally correlated 1/f noise on the decoherence rate, and how its temporal correlations restore lost entanglement. Our analysis not only offers critical insights into designing effective error mitigation strategies to reduce harmful effects of correlated noise, but also enables tailored protocols to leverage and harness noise-induced correlations for quantum information processing.

Motivation & Objective

• To understand the impact of spatially correlated classical and quantum noise on multi-qubit dynamics in driven qubit systems.
• To distinguish between the detrimental effects (decoherence) and beneficial effects (entanglement generation) of correlated noise.
• To identify conditions under which correlated noise can be harnessed to generate and sustain entanglement in quantum processors.
• To analyze the role of temperature, driving, and noise spectral correlations (e.g., $1/f$) in modulating decoherence and entanglement dynamics.

Proposed method

• Formulates a general master equation framework for two-qubit dynamics under spatially correlated noise, distinguishing classical and quantum noise components.
• Derives noise spectral densities for both Markovian and non-Markovian regimes, including $1/f$ noise with temporal correlations.
• Introduces a rotating frame transformation and uses a time-dependent Hamiltonian to model coherent driving of qubits.
• Solves the master equation for specific initial states (Bell states and product states) to track entanglement evolution via density matrix elements.
• Evaluates entanglement using the concurrence measure, derived from the density matrix components $G_{11}, G_{44}, y(t)$.
• Analyzes the role of temperature via the thermal factor $\alpha = e^{-\beta\hbar\Omega}$, linking classical and quantum noise amplitudes.

Experimental results

Research questions

• RQ1 Can spatially correlated quantum noise generate entanglement in driven two-qubit systems?
• RQ2 How does correlated classical noise affect decoherence, and can it induce entanglement?
• RQ3 What role do temporal correlations in $1/f$ noise play in restoring lost entanglement?
• RQ4 How do temperature and coherent driving influence the balance between decoherence and entanglement generation?
• RQ5 What dynamical phases emerge in the presence of correlated transverse quantum noise under driving?

Key findings

• Correlated quantum noise induces a coherent long-range Ising interaction in the pure dephasing limit, enabling entanglement between distant qubits.
• Under transverse noise with coherent driving, correlated quantum noise generates both symmetric exchange and Dzyaloshinskii-Moriya interactions, leading to significant entanglement.
• The system exhibits distinct dynamical phases depending on the parameter regime, particularly in the presence of transverse noise and driving.
• For Bell-state initial conditions, the final entanglement under correlated quantum noise reaches a maximum value of 1/2 in the quantum limit.
• Temporal correlations in $1/f$ noise can restore entanglement that would otherwise decay, due to coherent revival effects.
• Surprisingly, higher temperatures reduce crosstalk from correlated noise, suggesting a counterintuitive mitigation strategy for certain noise types.