Improving initial-state-dependent quantum circuit optimization by introducing state labels

TL;DR

Two key improvements are introduced: the state label manager that reduces unnecessary state measurements and the $CX$-pair removal process that eliminates redundant gate pairs that significantly reduce the number of two-qubit gates.

Abstract

While the capabilities of quantum hardware have significantly advanced in recent years, executing quantum algorithms as quantum circuits at the lowest possible cost remains crucial, regardless of the hardware progress. We are developing a quantum-state-dependent circuit optimizer called AQCEL. Our guiding principle, implemented as the AQCEL optimization protocol, is to optimize quantum circuits by measuring the states of the control qubits to identify and eliminate unnecessary control operations. In this paper, we introduce two key improvements: the state label manager that reduces unnecessary state measurements and the $CX$-pair removal process that eliminates redundant gate pairs. These enhancements significantly reduce the number of two-qubit gates, improving the fidelity of quantum circuits executed on quantum hardware. To demonstrate the effectiveness of our method, we apply AQCEL to quantum circuits for the quantum parton shower algorithm. Experimental results using the IBM quantum computer show a substantial reduction in gate counts and an improvement in fidelity compared to the conventional optimization technique as well as the original AQCEL protocol. Our findings highlight the potential of state-dependent circuit optimization for enhancing the performance of quantum algorithms on near-term quantum devices.

Figures (10)

• Figure 1: Example of how redundant $CX$ pairs appear and how to remove them. (a) Aqcel will decompose a multi-qubit controlled operator into $RCCX$ gates (illustrated as $CCX$ gates in the figure) and a single controlled-$U$ gate. (b) Aqcel can eliminate redundant control operations depending on the states of qubits. (c) Redundant $CX$ pairs can be removed once they are identified as redundant.
• Figure 2: Example of the workflow of the optimization and state labeling. (a) State measurements are performed to identify redundant control operations at the first gate, denoted as gate A. From the measurements, the gate is replaced by a $CX$ gate, and the labels of the control and target qubits are updated. (b) Since the label of the control qubit is $\mathbf{0/1}$ in the second gate denoted as gate B, we can identify that this control operation is necessary and cannot be removed. (c) Since the gate C is paired with the gate A, it is replaced by a $CX$ gate as for the gate A. In addition, the state of the target qubit should return to the $\mathbf{0}$ state.
• Figure 3: Quantum circuit of the QPS algorithm with ${N_{\rm evol}}$ = 2. The initial number of particles is one and the state is $f_1$. The coupling constants are $g_1$, $g_2$, and $g_{12}$. The $X$ operators are shown in dark blue, while the $Ry$ operators are shown in dark red. The number outside the $Ry$ box indicates the rotation angle.
• Figure 4: Hellinger fidelity between the distribution of bitstrings measured on the noiseless simulator for the 1-step QPS circuit and measured on the $ibm\_fez$ backend for the optimized circuit as a function of noise threshold parameter in Aqcel. The red circles and blue squares show the Aqcel with and without the state label manager, respectively.
• Figure 5: Optimized 1-step QPS circuit using Aqcel (a) w/o $CX$-pair removal and (b) w/ $CX$-pair removal. The colored boxes in the left figure show applicable parts of $CX$-pair removal, and the corresponding parts are shown in the same color in the right figure.