Pulse-level control for quantum resource preparation

Abstract

Minimizing the time required for quantum state preparation is crucial to mitigate decoherence and enable practical quantum algorithms on near-term hardware. In this work, we introduce a technique for quantum state preparation in transmon-qubit systems using optimized electromagnetic pulse sequences rather than discrete quantum gates. By directly targeting quantum correlations instead of specific target states, we identify minimal-time pulse protocols that optimize relevant entanglement resources, such as concurrence and the three-tangle for two and three qubit systems, respectively. For the figures of merit considered, this approach successfully achieves maximal entanglement in each case: Bell, GHZ and W like states. Beyond state preparation, the resource-oriented nature of the approach leads to a reduced effective expressivity of the control scheme, a feature that represents an advantage in algorithmic settings where excessive control freedom is known to hinder performance.

Figures (21)

• Figure 1: (color online) Pulse scheme required to prepare the maximally entangled state eq. (\ref{['distri dos qubits']}). The scheme shows two local pulses (cyan) applied to qubits 0 and 1 (channels D0 and D1, respectively). Afterwards, a pulse is sent to qubit 0 (channel U0, yellow pulse) with frequency of qubit 1 (target qubit) in order to produce entanglement.The diagram show that the duration of entire pulse sequence is 989.0 $dt$
• Figure 2: Probability distribution of the state eq. (\ref{['distri dos qubits']}) in the computational basis, where we can show large populations in the states $|00\rangle$ and $11\rangle$. This state exhibit a nearly maximal value of negativity $\mathcal{N}(\rho_{01}) = 0.499$.
• Figure 3: Gaussian Square pulse scheme used to obtain a Bell-type state between qubits zero and one, considering three energy levels. The pulse widths were previously adjusted from those obtained in the square-pulse case, figure (\ref{['1']}). In this way, only the amplitude and $\sigma$ parameters were varied, where $\sigma$ indicates the smoothness of the envelope edges.The diagram also shows that the execution time is 1379.0 $dt$.
• Figure 4: Probability distribution in the computational basis for the two-qubit state eq. (\ref{['psi_gauss']}). This distribution is obtained by applying the pulse sequence of Figure (\ref{['fig: pulse_bell2_gaussian']}) and keeping the first two levels per system, so that we consider two qubits. Here, negativity achieves the value $\mathcal{N}(\rho_{01}) = 0.499$.
• Figure 5: Square-pulse scheme used to generate the GHZ state. Three local pulses (cyan) are applied on channels D0, D1, and D2, and two cross-frequency pulses (yellow) are applied on channels U0 and U1. The U0 pulse is sent to qubit 0 at the resonance of qubit 1, and the U1 pulse is sent to qubit 1 at the resonance of qubit 2, enabling the required correlations. It can be observed that the duration of the entire pulse pattern is 2848.0 $dt$.