Syncopated Dynamical Decoupling for Suppressing Crosstalk in Quantum Circuits

TL;DR

This work tackles the challenge of crosstalk in quantum circuits, particularly static $ZZ$ interactions, which hinder high‑fidelity two‑qubit gates. It introduces a discrete optimization framework in the superoperator (Pauli) representation to design syncopated dynamical decoupling sequences that suppress $ZZ$ crosstalk while preserving single‑qubit decoherence protection, using time‑shifting, frequency‑doubling, and operator‑alternation. The authors validate the approach on a Rigetti Aspen superconducting device, demonstrating that syncopated DD reduces Ramsey beating caused by $ZZ$ crosstalk and separates crosstalk from $1/f$ noise, with quantitative estimates of $J$ and the dispersive parameter $\chi$ that align with hardware fits. They further show circuit‑level benefits: applying syncopated DD to idle qubits in a QAOA circuit improves performance, and combining it with randomized compiling yields additional gains, indicating practical scalability for error mitigation in near‑term quantum hardware.

Abstract

Theoretically understanding and experimentally characterizing and modifying the underlying Hamiltonian of a quantum system is of utmost importance in achieving high-fidelity quantum gates for quantum computing. In this work, we explore the use of dynamical decoupling (DD) in characterizing and suppressing undesired two-qubit couplings as well as the underlying single-qubit decoherence, both significant hurdles to achieving precise quantum control and realizing quantum computing on many hardware prototypes. Through discrete search of dynamical decoupling sequences, we identify sequences that protect against decoherence and selectively target unwanted two-qubit interactions of general form. On a transmon-qubit-based superconducting quantum device, we identify separate white and 1/f noise components underlying the single-qubit decoherence and a static ZZ coupling between pairs of qubits. A family of syncopated dynamical decoupling sequences is found and their efficiency demonstrated in two-qubit benchmarking experiments. The syncopated decoupling technique significantly boosts performance in a realistic algorithmic quantum circuit.

Figures (9)

• Figure 1: In Pauli basis $\{XX, YY, ZZ\}$, demonstration of DD sequence $(\text{I}\pi_X, \pi_X\pi_Y, \text{I}\pi_X, \pi_X\pi_Y)$ for the Heisenberg Hamiltonian. (a) Toggling-frame sequence representation. The initial (original) Hamiltonian is represented as the first column. Each following column shows the updated Hamiltonian after each DD pulse applied in sequential order. The zero sum of each row indicates that the corresponding term is averaged out in the effective Hamiltonian, i.e., decoupling achieved. (b) Action of the first pulse $I\pi_X$ updated $\vec{v}_0$ into $\vec{v}_1$. (c) Matrix representation of a $\frac{\pi}{2}$ pulse.
• Figure 2: Illustration of DD schemes $(x,y)$ on a two-qubit system subject to a $ZZ$ coupling. DD sequence $x$ and $y$ are applied to each qubit individually. (a) Scheme (XXXX,NONE). Decoherence on the first qubit, as well as $ZZ$ coupling, are canceled out by the DD sequence, while decoherence on the second qubit remains. (b) Synchronized DD Scheme (XXXX,XXXX). When the same sequence is applied to both qubits synchronously, individual decoherence is removed, but the $ZZ$ coupling between them is unaffected. (c) Syncopated DD scheme (XXXX, XX). This scheme averages out $ZZ$ coupling as well as single-qubit decoherence on both qubits. (d) Syncopated DD scheme (XX-CPMG, XX). Shifting one sequence can also achieve syncopation, with fewer pulses overall. The pulse duration is exaggerated for illustration purposes.
• Figure 3: The experimental setup is shown in (a). The qubit is prepared in the $\ket +$ state, remains there for some idle time, in which a decoupling sequence is applied, and undergoes the pre-measurement rotation. The result should be a characteristic Ramsey decay curve, where the physical detuning can be extracted from the frequency of the oscillation and the dephasing rate can be extracted from the envelope. When the neighbour is in the (b)$\ket +$ state, the detuning is negligible but a characteristic beating frequency of 18.1Khz is visible. With the (c) syncopated DD sequences, the characteristic beating is suppressed and we recover the expected curve. The $\Gamma_{1/f}$ dephasing rate is reduced from $28.5\pm2.6$kHz to $19.2\pm1.4$kHz, indicating improved protection from decoherence.
• Figure 4: A fully-connected crosstalk graph with 6 qubits is depicted, with crosstalk represented by solid lines. (Top) The JAZZ-based approach to measuring the crosstalk proceeds by changing the state of the qubits one-by-one, and measuring the detuning in each state. $N(N-1)$ measurements (2 for each edge) are required to characterize all crosstalks. (Bottom) Syncopated dynamical decoupling is used to decouple static crosstalks, allowing simultaneous measurement of crosstalks. The decoupled edges are depicted by dotted gray lines, while each pair under study is coloured. This requires $N-1$ measurements.
• Figure 5: The average decay envelope of each qubit when different DD schemes are applied. DD applied to Qubit 101 alone is shown in red, to Qubit 102 alone is shown in black. Synchronized and syncopated DD are shown in blue and teal, respectively. The error bands reflect the standard error of the parameter estimate over the set of experiments. The syncopated DD provides the best protection to both qubits.

Theorems & Definitions (3)

• Theorem 1
• proof
• Corollary 1.1