⚛️ quantum physics

3D Integrated Embedded Filters for Superconducting Quantum Circuits

This paper presents the design and experimental validation of novel 3D integrated microwave Purcell filters embedded in multilayer PCBs for superconducting quantum circuits, demonstrating that off-chip integration effectively reduces device complexity while achieving high qubit isolation and compatibility with high-coherence 35-qubit devices.

Original authors: Waqas Ahmad, Gioele Consani, Mohammad Tasnimul Haque, Jacob Dunstan, Brian Vlastakis

Published 2026-03-02

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CC BY 4.0

Original authors: Waqas Ahmad, Gioele Consani, Mohammad Tasnimul Haque, Jacob Dunstan, Brian Vlastakis

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to have a very quiet, private conversation with a friend (the qubit) in the middle of a bustling, noisy train station (the readout line).

In the world of quantum computing, the "friend" is a superconducting qubit, a tiny particle that holds information. To do anything useful with this information, you need to listen to the friend to see what they are saying (readout). However, there's a problem: if the train station is too loud, your friend gets stressed and stops talking (this is called decoherence or losing their quantum state).

For a long time, engineers faced a difficult choice:

Turn down the volume of the train station so your friend stays calm, but then you can't hear them clearly (slow readout).
Turn up the volume so you can hear them instantly, but then your friend gets overwhelmed and stops talking (fast readout, but the qubit dies quickly).

This paper from Oxford Quantum Circuits introduces a clever solution: The 3D Integrated Embedded Filter.

Here is how it works, using simple analogies:

1. The Problem: The "Leaky" Room

Think of the qubit as a delicate soap bubble. The readout line is a giant vacuum cleaner hose attached to the room. If you turn on the vacuum to suck out the air (to read the bubble), the suction is so strong it pops the bubble before you can even look at it. This is called the Purcell Effect. The bubble (qubit) loses its energy too fast because it's too close to the vacuum hose.

2. The Old Solution: Building a Wall Inside the Bubble

Previously, engineers tried to fix this by building a wall inside the room where the bubble lives (on the same silicon chip as the qubit).

The Downside: This wall took up a lot of space. If you wanted to build a city of bubbles (a large quantum computer), you'd run out of room for the bubbles themselves because the walls were too big. It was like trying to build a skyscraper where every apartment had a massive, bulky air filter taking up half the living room.

3. The New Solution: The "Magic Hat" (The 3D PCB Filter)

This paper proposes a new way. Instead of building the wall inside the bubble's room, they built a special hat that sits on top of the room.

The Hat (The PCB): They took a standard circuit board (like the motherboard in a computer, but made of many layers) and built a special filter inside the layers of the board.
The Magic: This hat acts like a noise-canceling headphone or a one-way mirror.
- When the "vacuum cleaner" (readout signal) tries to suck energy out of the bubble, the hat blocks it. It creates a "dead zone" for the bubble's frequency, protecting the bubble from the vacuum.
- However, when the bubble needs to send a message (the readout signal), the hat has a special "window" (a passband) that lets that specific frequency pass through perfectly.

4. The "Swiss Army Knife" Feature: Multiplexing

The coolest part of this new hat is that it's not just for one bubble.

The Old Way: You needed a separate, bulky wall for every single bubble.
The New Way: This single "hat" (filter unit) can protect and listen to nine bubbles at the same time.
Imagine a single security guard who can monitor nine different rooms simultaneously without needing nine different guards. This allows them to pack many more qubits into a small space, making the quantum computer much bigger and more powerful.

5. The Results: A Quiet Conversation

The team tested this on a 35-qubit processor (a small quantum computer).

The Test: They put the qubits in a super-cold fridge (near absolute zero) and turned on the readout.
The Outcome: The qubits stayed alive and happy for a long time (about 84 microseconds). Without this filter, the simulations predicted they would have died in about 39 microseconds because the "vacuum" would have sucked them dry.
The Proof: The fact that the qubits lived longer than the "no-filter" prediction proves the filter is working. It successfully blocked the noise while letting the signal through.

Summary

Think of this paper as inventing a smart, multi-layered shield that sits above the quantum computer chip rather than inside it.

It stops the "noise" from killing the delicate quantum bits.
It lets the "signal" pass through so we can read the data quickly.
It's small enough to fit many qubits in a tiny space.
It can handle nine conversations at once.

This is a major step forward because it means we can build much larger, more complex quantum computers without them falling apart from the noise of trying to listen to them. It's like finally finding a way to hear a whisper in a hurricane without the hurricane blowing you away.

1. Problem Statement

Superconducting quantum processors (QPUs) face a fundamental trade-off between readout speed and qubit coherence.

The Purcell Effect: To achieve fast, high-fidelity readout, readout resonators must be strongly coupled to external transmission lines (high external coupling rate, $\kappa_{ext}$ ). However, this strong coupling creates a dissipative channel that accelerates qubit energy relaxation ( $T_1$ decay) via the Purcell effect.
Scalability Limitations: Traditional solutions involve on-chip Purcell filters (e.g., transmission line bandstops). However, these filters often require significant chip real estate, increasing the footprint of the Quantum Processing Unit (QPU) and complicating routing for large-scale qubit arrays. Furthermore, integrating complex filtering directly onto the qubit substrate increases fabrication complexity and reduces modularity.

2. Methodology

The authors propose a novel 3D-integrated, off-chip Purcell filter embedded within a multilayer Printed Circuit Board (PCB) package. This approach decouples the filtering architecture from the qubit substrate.

Architecture:
- Vertical Integration: The system consists of a superconducting qubit chip (containing qubits and resonators) stacked on top of a multilayer PCB via an aluminum spacer.
- Filter Design: The filter is a triangular-shaped coplanar patch antenna embedded in the middle layer of the PCB. It operates as a bandpass filter centered at the readout frequency (9.8 GHz).
- Multiplexing: The design supports a 9-to-1 multiplexing scheme. Nine input vias on the top PCB layer capacitively couple to nine readout resonators on the qubit chip. A central grounded via acts as an inductive shunting stub to control bandwidth.
- Materials: The PCB uses Rogers RT/duroid 5880 substrates ( $\epsilon_r = 2.2$ ) and Rogers Bondply 2929 pre-preg, with silver-immersion plated copper layers to minimize loss.
Simulation & Modeling:
- Electromagnetic Simulation: Using Ansys HFSS, the authors performed finite-element simulations on both standalone PCB models and coupled models (PCB + QPU).
- Modal Analysis: Used to determine the filter's center frequency, bandwidth, and quality factors ( $Q$ ) without material losses to isolate the Purcell filtering effect.
- Eigenmode Analysis: Simulated the interaction between the qubit, resonators, and the embedded filter to predict radiative decay rates ( $T_{1,rad}$ ).
Experimental Validation:
- A 35-qubit OQC-Toshiko processor was packaged with a PCB containing six tiled filter units (supporting up to 42 resonators, with 35 utilized).
- Measurements were conducted at 11 mK in a dilution refrigerator.
- Characterization: Continuous-wave reflection spectroscopy was used to measure resonator quality factors ( $Q_{int}, Q_{ext}$ ). Time-domain pulse sequences were used to measure qubit coherence times ( $T_1, T_2$ ).

3. Key Contributions

Off-Chip Filter Integration: Demonstrated the first integration of Purcell filters into a multilayer PCB package, removing all filter components from the qubit substrate. This allows for modular development of the qubit stack and the readout/filtering stack.
High-Density Multiplexing: Achieved a 9-to-1 multiplexing capability per filter unit cell, enabling efficient readout of multiple qubits through a single output line while maintaining a compact footprint (the filter fits within a 9-qubit area).
Scalable Tiling: The design is inherently tileable, allowing for the construction of QPUs with arbitrary sizes without increasing the per-qubit footprint or routing complexity.
Shielding: The embedded nature of the patch antenna, shielded by ground planes on both sides, minimizes crosstalk between adjacent filters.

4. Results

Filter Performance:
- Center Frequency: Designed for 9.8 GHz; experimental data showed a passband centered around 10.2 GHz (a ~340 MHz shift attributed to temperature-dependent material property changes).
- Bandwidth: Achieved a 3 dB bandwidth of 0.9 GHz, sufficient for multiplexing multiple resonators.
- Isolation: Simulations predicted a 1000-fold (30 dB) improvement in qubit isolation from the readout port compared to a system without filtering.
Qubit Coherence:
- Radiative Limit Validation: Without the filter, the simulated radiative limit for $T_1$ was ~39 µs. With the filter, the theoretical limit increased to ~22 ms.
- Experimental $T_1$ : The measured median $T_1$ for 18 qubits was 84 µs. Crucially, all measured $T_1$ values exceeded the 39 µs radiative limit of the unfiltered system, confirming that the PCB filter successfully suppresses Purcell decay.
- Other Metrics: Median $T_2$ (Ramsey) was 67 µs, and $T_2$ (Echo) was 110 µs.
Readout Speed: The external quality factors ( $Q_{ext}$ ) of the resonators remained low (high coupling), indicating that the filter did not compromise readout speed. The system successfully demonstrated the simultaneous readout of at least eight multiplexed signals from a single output line.

5. Significance

This work represents a critical step toward fault-tolerant, large-scale quantum computing:

Scalability: By moving filtering off-chip, the approach solves the "footprint problem," allowing QPUs to scale to hundreds or thousands of qubits without the area penalty associated with on-chip filters.
Modularity: It enables a separation of concerns where the qubit fabrication process is decoupled from the complex RF packaging, potentially simplifying manufacturing and yield.
Performance: It proves that high-coherence qubits ( $T_1 > 80$ µs) can coexist with fast, multiplexed readout, a prerequisite for real-time error correction.
Future Outlook: The authors note that this architecture is a precursor to supporting 500+ qubit devices, addressing a major bottleneck in current superconducting quantum hardware scaling.