Mechanical Resonator-based Quantum Computing

TL;DR

MRQC introduces a mechanical-resonator-based quantum computing platform where a superconducting transmon qubit operates as the CPU while densely spaced mechanical phonon modes in an HBAR serve as RAM. The authors demonstrate a universal gate set including single-qubit operations and fast two-qubit Cφ gates implemented via off-resonant JC interactions, enabling execution of QFT and QPF on three phonon modes. Tomography and randomized benchmarking quantify performance, yielding single-qubit RB fidelities around 95% and no-SPAM two-qubit gate fidelities near 89%, while the QFT3 protocol shows notable SPAM- and decoherence-limited infidelity, with simulations attributing much of the error to transmon decoherence and SPAM. This work validates mechanical resonators as scalable quantum memories and highlights a concrete path toward hardware-efficient quantum random-access memory integrated with superconducting processors.

Abstract

Hybrid quantum systems combine the unique advantages of different physical platforms with the goal of realizing more powerful and practical quantum information processing devices. Mechanical systems, such as bulk acoustic wave resonators, feature a large number of highly coherent harmonic modes in a compact footprint, which complements the strong nonlinearities and fast operation times of superconducting quantum circuits. Here, we demonstrate an architecture for mechanical resonator-based quantum computing, in which a superconducting qubit is used to perform quantum gates on a collection of mechanical modes. We show the implementation of a universal gate set, composed of single-qubit gates and controlled arbitrary-phase gates, and showcase their use in the quantum Fourier transform and quantum period finding algorithms. These results pave the way toward using mechanical systems to build crucial components for future quantum technologies, such as quantum random-access memories.

Figures (11)

• Figure 1: Operating principle of MRQC and randomized benchmarking.A, Image of the $\hbar$BAR device. The transmon qubit is fabricated on the bottom chip (false-colored blue), while the mechanical modes reside within the HBAR chip on top (false-colored orange). B, General principle of the MRQC architecture. A generic conventional quantum circuit containing single- and two-qubit gates is depicted on the left, while the equivalent circuit implemented in MRQC is shown on the right. C, Randomized-benchmarking results for single-phonon gates for three different modes (colors) compared to single-transmon gates (black).
• Figure 2: Arbitrary controlled-phase gate protocol.A, Sequence for implementing a $C_{\phi}$ operation composed of two off-resonant transmon-phonon interactions and a Z-rotation operation in the middle. The Z-rotation is decomposed into a series of X- and Y-rotations. B, Measured and theoretical evolution of the transmon $|{e}\rangle$ state populations during the $C_{\phi}$ gate for four different initial states. Gray and black vertical dashed lines show the point at which the Z-rotation is applied and the point at which the $C_{\phi}$ gate is completed, respectively. C, Dependence of the detuning $\Delta$ (purple), interaction time $t_{int}$ (green) and Z-rotation $\theta$ (red) on the target controlled phase $\phi$ (see Supplementary Information). For later analysis of measured gate fidelities, note that a larger $\phi$ require a smaller $\Delta$ and a longer $t_{int}$.
• Figure 3: Arbitrary controlled-phase gate process tomography.A, Process tomography sequence of an arbitrary $C_{\phi}$ gate. The choice of initial states and measurement axes are determined by $R_{sp}$ and $R_m$ pulses, respectively. B, Ideal (left) and reconstructed (right) process matrices $\chi$ of a $C_{\pi}$ gate. The implemented $C_{\pi}$ gate yields a fidelity $F_{\pi} = 85.7\%$ including SPAM errors. C, Measured fidelities of multiple repetitions of $C_{\pi}$ gates with SPAM errors. The exponential fit to the data allows us to extract the no-SPAM fidelity of $\mathscr{F}_{\pi}=89.2\%$. Error bars are determined by repeating the experiment ten times and calculating the standard deviation. D, Measured (transparent) and simulated (opaque) no-SPAM infidelities $1-\mathscr{F}_{\phi}$ of eight $C_{\phi}$ gates with $\phi = k \pi/8$. E, Measured $C_{\pi/4}$, $C_{\pi/2}$ and $C_{\pi}$ gate infidelities $1-\mathscr{F}_{\phi}$ for three different phonon modes (see Supplementary Information A for details on the modes' properties).
• Figure 4: Quantum Fourier transform and quantum period finding measurements.A, QFT sequence for one (green), two (red) and three (black) phonon modes. B, Reconstructed $\chi$ matrix amplitudes of a three phonon QFT sequence for an ideal operation (1), simulation without SPAM (2), simulation with SPAM (3), and experimentally measured (4). Index labels on x- and y-axes correspond to combinations of 3-element tensor products of Pauli operators (see Supplementary Information D). C, Measured (transparent) and simulated (opaque) infidelity of the QFT operations with SPAM. D, Sequence for a quantum period finding algorithm on a function with period $r=2$. Ideal intermediate states during the algorithm are shown in pink. E, Measured population results of the QPF algorithm shown in D. We observe clear population peaks in states $|{0}\rangle$ and $|{4}\rangle$, corresponding to $r=2$.
• Figure S1: Randomized benchmarking protocol and simulation.A, Sequence for the single-phonon gate randomized benchmarking. $U_i$ are randomly chosen from a set of gates given in Table. \ref{['gateset']}, while $U_{corr}$ is chosen such that it reverts the state of the transmon to state $|{g}\rangle$ in the ideal case. B, Simulated single-phonon gate randomized benchmarking of phonon mode 1. The obtained average Clifford gate fidelity of $F=95.66\%$ agrees well with the measured values found in the main text.