Dissipative Dynamics of Graph-State Stabilizers with Superconducting Qubits

Liran Shirizly, Grégoire Misguich, and Haggai Landa

Phys. Rev. Lett. 132, 010601 – Published 3 January 2024

Abstract

We study experimentally and numerically the noisy evolution of multipartite entangled states, focusing on superconducting qubit devices accessible via the cloud. We find that a valid modeling of the dynamics requires one to properly account for coherent frequency shifts, caused by stochastic charge-parity fluctuations. We introduce an approach modeling the charge-parity splitting using an extended Markovian environment. This approach is numerically scalable to tens of qubits, allowing us to simulate efficiently the dissipative dynamics of some large multiqubit states. Probing the continuous-time dynamics of increasingly larger and more complex initial states with up to 12 coupled qubits in a ring-graph state, we obtain a good agreement of the experiments and simulations. We show that the underlying many-body dynamics generate decays and revivals of stabilizers, which are used extensively in the context of quantum error correction. Furthermore, we demonstrate the mitigation of 2-qubit coherent interactions (crosstalk) using tailored dynamical decoupling sequences. Our noise model and the numerical approach can be valuable to advance the understanding of error correction and mitigation and invite further investigations of their dynamics.

Received 8 August 2023
Revised 21 November 2023
Accepted 29 November 2023

DOI:https://doi.org/10.1103/PhysRevLett.132.010601

Physics Subject Headings (PhySH)

Open quantum systems Quantum benchmarking Quantum circuits Quantum entanglement Quantum information processing Quantum information with solid state qubits

Superconducting qubits

Tensor network methods

Quantum Information, Science & Technology

Authors & Affiliations

Liran Shirizly ^1,*, Grégoire Misguich^2,†, and Haggai Landa^1,‡

¹IBM Quantum, IBM Research - Israel, Haifa University Campus, Mount Carmel, Haifa 31905, Israel
²Université Paris-Saclay, CNRS, CEA, Institut de Physique Théorique, 91191 Gif-sur-Yvette, France

^*liran.shirizly@ibm.com
^†gregoire.misguich@ipht.fr
^‡haggaila@gmail.com

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 132, Iss. 1 — 5 January 2024

Reuse & Permissions

Access Options

Article part of CHORUS

Accepted manuscript will be available starting 2 January 2025.

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
(a) This Letter focuses on the dynamics of an open quantum system with a density matrix $ρ (t)$ of 12 qubits in a ring. (b) For superconducting qubits, the qubit levels (with frequency $ω_{i}$ ) are split due to charge-parity fluctuations that manifest effectively as a Bernoulli stochastic variable shifting the qubit frequency by $\pm ν_{i}$ . (c) To model the charge-parity splitting in a many-body simulation reproducing the experiment dynamics, each qubit $Q_{i}$ is coupled to a fictitious two-level system [with levels denoted by $e$ , $o$ (even, odd)] initialized to a diagonal mixed state, which is traced over at the end of a calculation. The model further includes energy relaxation time ( $T_{1, i}$ ), dephasing time ( $T_{2, i}$ ), and 2-qubit $Z Z$ crosstalk ( $ζ_{i, j}$ )—see the text for details.
Reuse & Permissions
Figure 2
(a) A single qubit’s mean $x y$ projection of the Bloch vector ( $\sqrt{⟨ X ⟩^{2} + ⟨ Y ⟩^{2}}$ ) as a function of time after being initialized to the $| + ⟩$ state in a Ramsey experiment, plotted together with $⟨ Z ⟩$ whose amplitude grows as the qubit’s ground state becomes populated at a rate equal to $1 / T_{1}$ . The shrinking of the $x y$ projection and its revival is reminiscent of a non-Markovian process. (b) A characterization of $ν$ and $Δ$ of Eq. (1) together with the decoherence time $T_{2}$ from the data points in an identical Ramsey experiment with the lines showing a fit of the data according to Eqs. (2) and (3).
Reuse & Permissions
Figure 3
(a) Dynamics of the middle qubit among three that are initialized to the product state $| + ⟩^{\otimes 3}$ . The experiment measurements are given by the points (with statistical error bars) and the lines are taken from simulation data. The multiple frequencies visible in the oscillations of the shown qubit result from the combination of its parity oscillations, detuning error, and $Z Z$ coupling to two neighbors (with different coupling strengths)—see the text for a detailed discussion. (b) The dynamics of the $Z_{1} X_{2} Z_{3}$ stabilizer of a similar $3 Q$ chain initialized in a graph state and of the middle qubit’s $⟨ X ⟩$ . In this figure and in Fig. 4, the lines show simulation data that, once the Hamiltonian and noise parameters have been determined, do not involve any adjustable parameters.
Reuse & Permissions
Figure 4
(a) The dynamics of the $12 Q$ -ring graph-state stabilizers’ mean decoherence, as measured in the experiment (points) and extracted from simulations (lines). The presented measure that ideally equals 1 is shown with and without intermediate dynamical decoupling sequences, which cancel the effect of frequency shifts, charge-parity fluctuations, and $Z Z$ coupling; see the text for details. (b) Using the data of the same simulations, we can see how the fidelity of $ρ (t)$ with the ideal $12 Q$ state is significantly improved when using the DD sequence canceling the coherent Hamiltonian errors.
Reuse & Permissions

Physical Review Letters