Programmable Phononic Integrated Circuits

• Programmable Phononic Integrated Circuits are on-chip systems that manipulate quantized acoustic vibrations using engineered waveguides, tunable couplers, and interferometers.
• They achieve high integration density and reconfigurability via piezo-acoustomechanical and thermoacoustic phase-shifting mechanisms with measurable metrics such as low insertion losses.
• PnICs enable advanced signal processing and quantum information transfer, demonstrating high fidelity and robust hybrid integration with electronic and photonic platforms.

Programmable Phononic Integrated Circuits (PnICs) constitute a class of on-chip systems that control and manipulate phonons—the quantized excitations of acoustic vibrations in solid-state platforms—for classical and quantum information processing. They combine engineered waveguides, tunable couplers, interferometers, and phase shifters to deterministically program wave propagation, modal conversion, and interference effects across GHz frequencies. PnICs leverage material platforms such as gallium nitride/sapphire and aluminum nitride/silicon, and incorporate piezo-acoustomechanical and thermoacoustic reconfiguration mechanisms for analog and digital signal control, achieving functionalities that rival silicon photonics and electronics in density, connectivity, and dynamism. Recent work demonstrates large-scale integration (up to 3,000 programmable devices per cm²), high-fidelity quantum state transfer, MHz-frequency selectivity, and robust hybridization with microwave and photonic domains (Xu et al., 30 Oct 2025, Taylor et al., 2021).

1. Functional Architecture and Component Library

Recent PnIC architectures employ fully integrated gigahertz-frequency phononic waveguides formed by acoustic refractive index contrast (e.g., GaN/sapphire, AlN/silicon stacks), supporting quasi-Rayleigh and quasi-Love modes. Core components include:

• Directional Couplers & Y-Splitters: Tunable energy transfer and robust 50:50 splitting for arbitrary waveform routing. For example, a cascading binary tree of 127 Y-splitters creates a 1×128 power splitter with a split ratio of $1 \pm 0.076$ and insertion loss $0.5 \pm 0.37$ dB at 1.5 GHz (Xu et al., 30 Oct 2025).
• Polarization Converters: Adiabatic mode transitions via waveguide width modulation, enabling control of modal polarization through avoided crossings.
• Mach-Zehnder Interferometers (MZIs): Dynamic phase control using integrated heaters effectuates analog tuning with a measured efficiency of 4.03 rad/W for 100 μm devices. Phase-sensitive routing is described by:

$$\mathrm{Output~amplitude} \propto \sqrt{\frac{1+\cos(\alpha P_H+\varphi_0)}{2}}$$

where $P_H$ is heater power, $\alpha$ is the thermoacoustic coefficient (Xu et al., 30 Oct 2025).

• Microring Resonators and Gratings: Modal- and frequency-selective filtering, with achieved bandgaps of 33 MHz in designs spanning 190 μm.

This toolkit supports spatial, modal, and frequency control across parallel channels, affording PnICs multi-domain versatility analogous to photonic IC platforms.

2. Programmability and Reconfigurability Mechanisms

Programmability in PnICs is realized via multiple control modalities:

• Piezo-acoustomechanical Phase Shifting: Voltage-driven strain in integrated piezoelectric actuators induces reversible, deterministic phase changes. The principal mechanism consists of both moving boundary (geometry/density perturbations) and acoustoelastic (strain-dependent elastic moduli) contributions. For ScAlN/silicon actuators, phase shifts of $\pm\pi$ are achievable in 20 μm length at voltages of $\pm50$ V. The accumulated phase over distance $L$ is given by (Taylor et al., 2021):

$\Delta \phi = \Delta k \cdot L + k \cdot \Delta L$

where $\Delta k$ is the change in propagation constant, and $\Delta L$ the strain-induced length change.

• Thermoacoustic Phase Shifting: Integrated heaters provide analog phase tuning with switching times governed by device mechanical resonances (e.g., 14 MHz corresponds to 71 ns).
• Programmable Interferometry: Tunable combinations of beam-splitters and phase shifters permit arbitrary SU(N) transformations:

$$U(2) = i \begin{pmatrix} e^{i\phi/2}\sin{\theta/2} & e^{i\phi/2}\cos{\theta/2} \ e^{-i\phi/2}\cos{\theta/2} & -e^{-i\phi/2}\sin{\theta/2} \end{pmatrix}$$

Cascaded networks constitute universal linear processors for classical and quantum signals.

3. Large-Scale Integration and Performance Metrics

PnICs achieve ultra-high integration density by leveraging strong acoustic confinement, short coupling lengths, and scalable architectures:

Device Type	Integration Density (cm²)	Functional Metric
Y-splitters	~3,300	50:50 splitting
Full PnIC	~3,000	128-output splitter

The 1×128 splitter demonstrates uniform output amplitudes of 6.5 ± 1 pm, with total losses below 10 dB for 128-parallel outputs (Xu et al., 30 Oct 2025). Frequency demultiplexers (21-port AAWGs) achieve 3.8 MHz channel spacing with Q~400 and adjacent channel isolation exceeding 10 dB.

Quantum circuits using trapped ions offer programmable beam-splitter gates with operation errors of ~1%, preparation/detection fidelities above 94%, and Hong-Ou-Mandel visibilities of 99.7% (Chen et al., 2022). Programmable quantum memories operating at 5.14 GHz can achieve 96.9% state transfer fidelity, with practical limits (delay, round-trip times) reducing this to 89.0% (Taylor et al., 2021).

4. Quantum Information Processing Capabilities

PnICs establish a platform for quantum and hybrid information transfer:

• Linear Quantum Processing: Deterministic control of phonon Fock and Gaussian states using SU(N) interferometers and phase shifters. This extends demonstration of boson sampling and quantum tomography to phononic systems.
• Programmable Quantum Memory: Dynamically reconfigurable phonon cavities allow switching between strongly coupled ("write/read") and weakly coupled ("storage") regimes using voltage-tunable phase shifters. Input–output theory (SLH formalism) models the system, with cavity field update given by:

$$\dot{a}_c = -\frac{1}{2}\left(4\kappa_e\cos^2\frac{\theta(t)}{2}+\kappa_i\right)a_c - 2\sqrt{\kappa_e}\cos\frac{\theta(t)}{2}a_{\mathrm{in}}$$

State transfer is governed by an optimal phase trajectory derived for exponential input profiles.

• Hybrid Quantum Networks: PnICs are compatible with cryogenic environments; SOI and piezoelectric platforms mediate coupling to superconducting qubits and photonic circuits. The density, modal control, and low dissipation position PnICs as connectives in hybrid quantum computing architectures.

5. Advanced Signal Processing and Hybrid Integration

The phononic circuit paradigm enables parallel, programmable RF and microwave spectral processing:

• Frequency Demultiplexing: MHz-scale arrayed waveguide gratings route gigahertz phonon signals into multiple parallel outputs based on phase gradients:

$\Delta\phi(f) = \beta(f)\Delta L$

Channel mapping follows:

$$\beta_s(f)d \cdot \theta_{out,n} + \Delta\phi(f) = 2\pi m$$

• Synthesizers and Arbitrary Waveform Generation: MZIs allow amplitude/phase modulation in each frequency channel, supporting on/off ratios up to 29 dB.
• Hybrid Chips: The "Zhengfu" architecture (Xu et al., 30 Oct 2025) foresees co-integration of phononic, electronic, and photonic functionalities for signal transfer, processing, and transduction.

A plausible implication is that massive parallelism and programmability in the acoustic domain portend new architectures for analog AI accelerators, low-noise sensor arrays, and multi-domain communications processors.

6. Scalability, Limitations, and Outlook

Scalability in PnICs is substantiated by architecture that grows with device size and number of functional blocks:

• Mode Count Scaling: Trapped ion phononic networks can be extended to ~100 modes (ions), with robust connectivity and deterministic control (Chen et al., 2022). Photonic-like unfavorable scaling of loss and preparation/detection (as $0.3^N$ in optics) is replaced by more favorable factors ($0.96^N$) in phononic platforms.
• Propagation Loss and Integration Constraints: The current loss (2.4 dB/mm) in high-density circuits is primarily due to propagation and substrate leakage; further improvement is expected via waveguide engineering.
• Dynamic Control Limitations: Realistic phase shifter speed is bounded by mechanical resonance frequencies; delay times (e.g., 60 ns) set performance limits for quantum state transfer in memory protocols (Taylor et al., 2021).

While no published PnIC results document multi-qubit hybrid algorithms at scale, current programmable architectures and fidelity figures suggest readiness for extension to quantum simulation, hybrid machine learning, and system-level quantum interconnects across modalities.

7. Summary Table of Experimental Metrics

System/Component	Metric	Platform
1×128 splitter	6.5 ± 1 pm output, 0.5 ± 0.37 dB loss	GaN/sapphire PnIC (Xu et al., 30 Oct 2025)
21-port demux (AAWG)	3.8 MHz channel, >10 dB isolation	GaN/sapphire PnIC (Xu et al., 30 Oct 2025)
Quantum memory transfer	96.9% ideal, 89.0% with delay	AlN/silicon piezo PnIC (Taylor et al., 2021)
Phononic network tomography	94.5 ± 1.95% (single), 93.4 ± 3.15% (two phonon)	Trapped ion chain (Chen et al., 2022)

Programmable Phononic Integrated Circuits define a scalable, reconfigurable, and high-density platform for acoustic information processing—supporting advanced classical, quantum, and hybrid signal operations. Their integration with electronic and photonic domains establishes the phononic IC as the third technological pillar of on-chip information technology (Xu et al., 30 Oct 2025).