Universal composite phase gates with tunable target phase

TL;DR

This work develops universal composite phase gates by applying a Cayley–Klein parametrization to design even-numbered nominal $π$-pulse sequences that accumulate a tunable phase $Φ$ while suppressing leakage terms for arbitrary dynamical phase $α$. A compact analytic phase law yields a one-parameter family of gates for any even $N$, with leading off-diagonal leakage $U_{12}$ canceled to high order, enabling broad, flat high-fidelity plateaus under pulse-area and detuning errors. Numerical simulations in a two-level system show that these gates outperform comparable Torosov-type sequences for the same total pulse count, and validations with shaped pulses confirm envelope-robustness of the universality. The approach offers a simple, versatile route to robust, tunable phase control in quantum information processing and related coherent-control tasks.

Abstract

We present a systematic method for constructing universal composite phase gates with a continuously tunable target phase. Using a general Cayley--Klein parametrization of the single-pulse propagator, we design gates from an even number of nominal $π$ pulses and derive analytic phase families by canceling, order by order in a small deviation parameter, the leading contributions to the undesired off-diagonal element of the composite propagator, independently of the dynamical phase. The resulting sequences provide intrinsic robustness against generic control imperfections and parameter fluctuations and remain valid for arbitrary pulse shapes. Numerical simulations in a standard two-level model confirm high-order error suppression and demonstrate broad, flat high-fidelity plateaus over wide ranges of simultaneous pulse-area and detuning errors, highlighting the efficiency of the proposed universal composite phase gates for resilient phase control in quantum information processing.

Figures (5)

• Figure 1: Numerical fidelity landscapes for the target phase gate $\mathbf{G}(\Phi)$ for our four-pulse universal composite phase gate (top) and the universal six-pulse gate UPh6a of Torosov et al.Torosov (bottom). The contours labeled $m$ indicate fixed infidelity $1-F=10^{-m}$.
• Figure 2: Numerical fidelity landscapes for the target phase gate $\mathbf{G}(\Phi)$ for our eight-pulse universal composite phase gate (top left) compared with phase-gate constructions based on pairs of universal $\pi$-pulse sequences (UPh10a, UPh14a, UPh26a) Torosov. Contour labels indicate fixed infidelity $1-F=10^{-m}$.
• Figure 3: One-dimensional cross-sections of the infidelity for our universal composite phase gates compared with the Torosov sequences. Top row: $N=4$ (solid blue) versus UPh6a (dashed orange). Bottom row: $N=8$ (solid blue) versus UPh10a (dashed orange) and UPh14a (dash-dotted green). Left column: infidelity versus pulse-area error $\epsilon_A$ at $\delta=0$. Right column: infidelity versus normalized detuning $\delta$ at $\epsilon_A=0$.
• Figure 4: Numerical fidelity landscapes for the target phase gate $\mathbf{G}(\Phi)$ for our universal composite phase gates of 4, 8, 12 and 20 pulses constructed using the general phase formula \ref{['eq:phase_law_general_Phi']}. Contour labels indicate fixed infidelity $1-F=10^{-m}$.
• Figure 5: Numerical fidelity landscapes for the target phase gate $\mathbf{G}(\Phi)$ for our universal composite phase gates (same phase patterns as Fig. \ref{['fig:4_8_12_and_20_pulse']}), computed by solving the time-dependent Schrödinger equation with truncated-Gaussian pulse envelopes. Contour labels indicate fixed infidelity $1-F=10^{-m}$.