⚛️ quantum physics

Fock State Generation and SWAP using a Rabi-Driven Qubit

This paper presents a tunable, Rabi-driven qubit-mediated protocol that enables the deterministic generation of high-photon-number Fock states and high-fidelity SWAP operations in isolated high-Q cavity modes without compromising their coherence, thereby offering a scalable pathway for bosonic quantum computing.

Original authors: Natan Karaev, Eliya Blumenthal, Shay Hacohen-Gourgy

Published 2026-04-09

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Natan Karaev, Eliya Blumenthal, Shay Hacohen-Gourgy

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 build a super-fast, super-secure computer using light (photons) instead of electricity. In this world, the basic building blocks of information aren't just "on" or "off" (like 0 and 1); they are specific, countable packets of light called Fock states. Think of a Fock state as a specific number of marbles in a jar: 0 marbles, 1 marble, 5 marbles, etc.

The challenge scientists face is: How do you put exactly 5 marbles in a jar, or move those 5 marbles from Jar A to Jar B, without spilling any or accidentally adding extra ones?

This paper, by researchers at the Technion in Israel, presents a clever new way to do exactly that. Here is the story of their discovery, explained simply.

The Problem: The "Strong Hand" vs. The "Glass Jar"

Traditionally, to move these light-packets (photons) around, scientists used a "strong hand." They connected the light jar (the cavity) very tightly to a control switch (the qubit).

The Analogy: Imagine trying to move a delicate glass jar filled with water using a giant, heavy metal clamp. The clamp works fast, but it's so heavy and tight that it shakes the jar, cracks the glass, or lets water leak out. In physics terms, this "strong coupling" ruins the isolation of the light, causing errors.

The researchers wanted a way to move the marbles using a gentle touch (weak coupling) that wouldn't break the jar, but they needed it to be fast and precise.

The Solution: The "Rhythmic Push" (Rabi Driving)

The team invented a method that acts like a metronome or a rhythmic push.

The Setup: They have a "Memory Jar" (a high-quality cavity that holds light for a long time) and a "Control Switch" (a qubit). Usually, the switch barely touches the jar.
The Magic Trick: Instead of grabbing the jar, they "tick" the switch very fast (this is the Rabi drive).
The Sideband: They also gently "tick" the jar at a specific rhythm that matches the switch.
The Result: When these two rhythms sync up, something magical happens. Even though the switch is only weakly connected to the jar, the rhythmic pushing creates a temporary, strong bridge. It's like two people on a swing: if you push them at just the right moment, you can make them go very high, even with a light touch.

This bridge allows them to:

Create Fock States: They can push exactly 1, 2, 3, 4, or 5 marbles into the jar, one by one, with high precision.
Swap States: They can take the marbles from Jar A and instantly swap them with the empty Jar B.

What They Actually Did

The researchers built a superconducting "flute" (a special metal box that traps microwaves) and tested their theory.

The Marble Counting: They successfully created states with up to 5 photons (marbles) in less than 2 microseconds. That's faster than a camera flash!
The Swap: They moved a single photon from one mode to another in about 2 microseconds.
The Entanglement (The "Spooky" Connection): They used their swapping method to create a Bell State.
- The Analogy: Imagine you have two jars. You put a marble in one, but you don't know which one. You create a state where the marble is simultaneously in Jar A and Jar B until you look. This is "entanglement," the "spooky action at a distance" Einstein talked about. They proved their method can create this complex, linked state reliably.

Why This Matters

This is a big deal for the future of quantum computing for three reasons:

Safety First: Because they use a "weak" connection that only becomes strong when they want it to, the delicate light jars don't get damaged. The system is more stable.
Speed: Even though the connection is weak, the "rhythmic push" makes the process incredibly fast.
Scalability: The method is like a recipe. If you can make 5 marbles, you can theoretically make 50 or 500 just by adjusting the timing. This opens the door to building much larger, more complex quantum computers.

The Bottom Line

Think of this research as inventing a gentle, high-speed robotic arm that can pick up delicate glass marbles and move them between jars without ever shaking the jars. Before this, you needed a giant clamp that risked breaking the glass. Now, we have a precise, rhythmic tool that makes building the quantum computers of the future much safer and more reliable.

The researchers admit their current setup isn't perfect (the "glass" still has tiny cracks), but they've proven the method works. With better materials in the future, this technique could become the standard way we build the next generation of super-computers.

1. Problem Statement

The paper addresses two critical bottlenecks in bosonic quantum computing architectures:

Deterministic Fock State Generation: Creating specific photon number states ( $|n\rangle$ ) is currently difficult. Conventional methods require strong qubit-cavity coupling, which compromises the high-quality factor ( $Q$ ) and isolation of the cavity modes. Existing protocols often rely on complex optimal control, highly tailored waveforms, or extreme parameter calibration, making them sensitive to perturbations and difficult to scale.
Quantum State Transfer (SWAP): Efficiently transferring quantum information between modes (either within the same cavity or between different cavities) is essential for dual-rail architectures and scaling. However, achieving rapid SWAP operations in systems with weakly coupled qubits (necessary for preserving mode isolation) is a fundamental trade-off. Current on-demand methods often require specific photon counts or complex drive waveforms.

The core challenge is to achieve fast, deterministic, and high-fidelity Fock state generation and SWAP operations in weakly coupled systems without sacrificing the isolation required for long coherence times.

2. Methodology

The authors propose a tunable mechanism that leverages a Rabi-driven qubit to mediate strong, on-demand interactions between a qubit and high- $Q$ cavity modes, despite the underlying weak static coupling.

System Architecture:
- Hardware: A superconducting aluminum "flute" cavity containing two high- $Q$ modes (Memory 1 and Memory 2) and a transmon qubit. A separate stripline resonator is used for readout.
- Coupling Strategy: The qubit is weakly coupled to the memory modes via dispersive shifts ( $\chi$ ).
Theoretical Mechanism:
- Rabi-Driven Sideband Interaction: The qubit is driven by a strong Rabi drive ( $\Omega_R$ ). Simultaneously, the memory modes are driven at a frequency detuned by $\Omega_R$ .
- Effective Hamiltonian: In the frame of the Rabi drive, the system transforms into a set of "dressed states" ( $|+\rangle, |-\rangle$ ). The sideband drives induce an effective Jaynes-Cummings interaction between the qubit and the cavity modes.
- Tunable Coupling: The effective coupling strength $g_i$ is proportional to the drive amplitude and the dispersive shift ( $g_i \propto |\chi_i|\bar{a}_i$ ). This allows the researchers to induce strong interactions ( $g$ ) on demand while keeping the static physical coupling weak.
Protocols:
1. Fock State Generation:
  - Initialize the qubit and memory mode.
  - Pump excitations into the qubit via Rabi drive phase shifts.
  - Transfer excitations to the memory mode by activating the Rabi drive for a specific duration $\tau_n$ .
  - For higher photon numbers ( $n$ ), the process is iterative. The required time scales as $\tau_n = \tau_1 / \sqrt{n}$ because the effective coupling rate for state $|n\rangle$ scales as $g\sqrt{n+1}$ .
2. Fock State SWAP:
  - Drive both memory modes and the qubit to create symmetric sideband coupling ( $g_1 = g_2 = g$ ).
  - The system evolves as an anti-symmetric mode. For a single photon ( $|1\rangle$ ), the swap occurs at a rate of $\sqrt{2}g$ , resulting in a time $\tau'_1 = \pi/(\sqrt{2}g)$ .
  - For $n > 1$ , the non-linearity of the qubit (limited to one excitation) creates complex dynamics, resulting in either a SWAP or $-SWAP$ gate depending on whether $n$ is even or odd.
3. Bell State Generation:
  - By initializing the qubit in the excited dressed state and performing a SWAP pulse for half the duration ( $\tau'_1/2$ ), the system generates a maximally entangled Bell state: $(|1, 0\rangle + |0, 1\rangle) / \sqrt{2}$ .

3. Key Contributions

Weak-Coupling to Strong-Interaction Conversion: Demonstrated a method to achieve strong, controllable Jaynes-Cummings coupling in systems that are inherently weakly coupled, preserving cavity isolation.
Analytical Waveforms: The protocols use simple, analytical pulse sequences (Rabi drives and sideband drives) rather than complex numerical optimal control, making them robust and easier to implement.
Scalability: The method inherently scales to higher photon numbers and faster operational regimes, as the operation time decreases with higher photon counts ( $\tau_n \propto 1/\sqrt{n}$ ).
Dual-Rail Compatibility: Successfully demonstrated the generation of Bell states, a prerequisite for dual-rail quantum error correction architectures.

4. Experimental Results

The experiments were conducted using a superconducting flute cavity with the following parameters:

Rabi Frequency: $\Omega_R/2\pi = 6$ MHz.
Effective Coupling: $g/2\pi \approx 0.182$ MHz.
Coherence: Memory modes had $T_1 \approx 136-145$ $\mu$ s; Qubit $T_1 \approx 22.8$ $\mu$ s.

Key Findings:

Fock State Generation:
- Deterministically generated Fock states up to $|n=5\rangle$ .
- Operation times were < 2 $\mu$ s per photon.
- Fidelities: Measured via Wigner characteristic functions.
  - $|1\rangle$ : 91.64%
  - $|2\rangle$ : 82.38%
  - $|3\rangle$ : 75.82%
  - $|4\rangle$ : 69.39%
  - $|5\rangle$ : 62.98%
- Analysis: Fidelity degradation for higher $n$ was attributed primarily to drive ramp-up/down times (200 ns) causing dephasing via changing Stark shifts, rather than fundamental methodological limits.
Fock State SWAP:
- Demonstrated SWAP of a $|1\rangle$ state in approximately 2.27 $\mu$ s.
- Achieved a fidelity of 68.44%.
- The operation functioned as a $-SWAP$ gate (SWAP with a phase flip), consistent with theory.
Bell State Generation:
- Successfully generated the dual-rail Bell state $(|1, 0\rangle + |0, 1\rangle) / \sqrt{2}$ .
- Joint Wigner characteristic function measurements showed clear coherence between the two memory modes, matching theoretical predictions.

5. Significance and Future Outlook

Robust Pathway for Bosonic Computing: This work establishes a robust pathway for scalable bosonic quantum computing by enabling complex operations on modes that remain strictly weakly coupled to qubits. This preserves the high- $Q$ isolation necessary for long coherence times while overcoming the speed limitations of weak coupling.
Performance Potential: The authors note that current performance is limited by baseline coherence and drive ramp artifacts, not the fundamental method. Simulations suggest that with:
- Shorter ramp times (20 ns),
- Higher $T_2$ coherence times,
- Reduced Two-Level System (TLS) density,
- Stronger drives,
- ...fidelities for high-photon Fock states could exceed 90% even at $n=5$ .
Impact: The ability to deterministically generate and swap Fock states rapidly in weakly coupled systems is a cornerstone for future fault-tolerant quantum devices, particularly those utilizing dual-rail encoding and bosonic error-correcting codes.