Charging efficiency bursts in a quantum battery with cyclic indefinite causal order

Abstract

Enhancement of quantum battery performance is a popular subject in quantum thermodynamics. An interesting phenomenon is the quick charging effect [Phys. Rev. Res. 6, 023136 (2024)], which has been explored by utilizing a quantum interferometric technique known as superposition of trajectories. A similar technique used to boost quantum battery performance is indefinite causal order. Here, we propose a new charging protocol that utilizes cyclic indefinite causal order, whereby $N$ charging sequences are superposed when utilizing $N$ chargers. We observe charging efficiency bursts when implementing our cyclic indefinite charging protocol. The duration of these bursts increase with $N$. Additionally, we present a circuit model to implement our charging protocol for the two-charger scenario and perform proof-of-concept demonstrations on IonQ, Quantinuum and IBMQ quantum processors. The results validate the existence of charging efficiency bursts as shown by our theoretical analysis and numerical simulations.

Figures (5)

• Figure 1: Illustration of the cyclic indefinite causal order charging protocol for a qubit battery. The quantum battery $Q$ charges with the qubit chargers ($C_1\sim C_N$) in sequences that are elements of the cyclic group $\mathcal{Z}_N$. The charging sequence is controlled by the state $\ket{j}_D$ of the quantum switch $D$. With the quantum switch initialized in the superposition state $\sum_{m=1}^N\ket{m}_D/\sqrt{N}$, the quantum battery experiences a coherent superposition of all charging sequences which results in indefinite causal order. Therefore, the evolved state of the quantum switch $D$, quantum battery $Q$, and chargers $\{C_1,\cdots,C_N\}$ are $U_{\text{tot}}\rho_{\text{in}}U_{\text{tot}}^\dag$, where $\rho_{\text{in}}$ is the total initial state. Finally, measurement is performed on the quantum switch $D$ using projectors $\Pi_k$ to obtain the conditional quantum battery states $\rho_{Q|k}$, which is used for work extraction.
• Figure 2: Performance of qubit battery after charging time $t$. The black solid curves plot the charging efficiency using our cyclic indefinite charging protocol $P_{\text{ICO}}$, while the red dashed curves represent the charging efficiency using a definite charging protocol $P_\text{DCO}$. The results for using $N=2,3,4,5$ chargers in our protocols are shown.
• Figure 3: (a) Quantum circuit for the two-charger cyclic indefinite charging protocol. Here, D,Q,C1,C2 represent the quantum switch, battery qubit, first charger qubit, and second charger qubit, respectively. “Tr” is trace out. (b) Decomposition of the controlled unitary $\mathcal{M}(\theta)$ in (a).
• Figure 4: Charging efficiency of the cyclic indefinite causal order charging protocol with two chargers on quantum devices with respect to total charging time t. The black solid curve represent the charging efficiency of our cyclic indefinite causal order charging protocol $P_\text{ICO}$ predicted by numerical simulations. The red dashed curve represent the charging efficiency of our definite causal order charging protocol $P_\text{DCO}$ predicted by numerical simulations. The blue circles represent results performed on IonQ. The green x represent results performed on IBMQ. The magenta stars represent results performed on Quantinuum. Repetitions for IonQ, IBMQ, Quantinuum are 240000, 20000, 150, respectively. Backend properties are shown in Appendix. \ref{['app:backend']}.
• Figure 5: The configuration of the qubits used on $ibm\_boston$ in our circuit. The control qubit $D$ used qubit 122, the battery qubit $Q$ used qubit 123, the first charger qubit $C_1$ used qubit 124 and the second charger qubit $C_2$ used qubit 136.