Demonstration of a quantum comparator on an ion-trap quantum device

TL;DR

Problem: efficiently compare two $n$-bit integers on a quantum processor with reversible, coherent circuits. Method: implemented a Cuccaro-style adder-based quantum comparator on a trapped-ion device (Reimei) with all-to-all connectivity, achieving linear-depth in $n$ and using $2n+2$ qubits; tested for $n=3,5,7,9$ without postselection. Contributions: first large-scale demonstration of quantum comparison on hardware, with conventional success near $(98 ext%,97 ext%,97 ext%,95 ext%)$ and ancilla-inclusive success up to $(69 ext%)$ at $n=9$, and analysis of error modes. Significance: establishes quantum comparison as a viable arithmetic primitive on current quantum hardware and provides a benchmark for scaling modular-arithmetic circuits in quantum algorithms.

Abstract

Quantum computers are believed to solve a class of computational problems that are based on modular arithmetic faster than classical computers. Among the arithmetic building blocks, comparison of integer pairs is a primitive. Here we report its demonstration in the Reimei quantum computer at RIKEN, whose trapped-ion architecture provides all-to-all qubit connectivity together with high gate fidelities. We observe high success probabilities for bit widths n = 3, 5, 7, and 9: Under a conventional output-only success criterion we obtain 95% at n=9; under a stricter criterion additionally requiring the ancilla to be correct, the success is 69% at n=9. These results demonstrate reliable quantum comparison at scales far beyond those previously achieved experimentally, not only for comparators but also in the broader context of quantum arithmetic circuits.

Figures (4)

• Figure 1: Quantum comparator circuit adopted in this work, exemplified for $n=3$. The circuit is adapted from Ref. Gouzien2023. The third qubit from the top is a clean ancilla qubit used for borrow propagation, and the total number of qubits is $2n+2$.
• Figure 2: Experimental quantum circuit used in this work, exemplified for $n=3$. The circuit consists of preparation of an input state using Hadamard gates, the comparator shown in Fig. \ref{['fig:circuit']}, and measurement of all qubits in the computational basis.
• Figure 3: The success count under the conventional criterion (see Sec. \ref{['sec:conventional']}) is plotted as a function of bit width $n$. Obtained from $100$ experimental shots for each $n$.
• Figure 4: Histograms of the four outcome categories introduce as a stricter criterion in Sec. \ref{['sec:strict']}. Obtained from $100$ experimental shots for each bit width $n$.