🔬 mesoscale physics

Engineering two-qubit gates via anisotropic exchange in germanium spin qubits

This paper demonstrates that by leveraging strong spin-orbit interaction in germanium hole spin qubits and utilizing full vector magnetic field control, researchers can engineer anisotropic exchange interactions to continuously tune the interaction Hamiltonian, enabling the realization of native single-pulse iSWAP gates and facilitating spin-based quantum simulation.

Original authors: Leonardo Massai, Bence Hetényi, Eoin G. Kelly, Inga Seidler, Konstantinos Tsoukalas, Michele Aldeghi, Alexei Orekhov, Lisa Sommer, Marta Pita-Vidal, Uwe von Lüpke, Stephan Paredes, Stephen W. Bedell

Published 2026-08-18

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Leonardo Massai, Bence Hetényi, Eoin G. Kelly, Inga Seidler, Konstantinos Tsoukalas, Michele Aldeghi, Alexei Orekhov, Lisa Sommer, Marta Pita-Vidal, Uwe von Lüpke, Stephan Paredes, Stephen W. Bedell, Felix J. Schupp, Matthias Mergenthaler, Gian Salis, Andreas Fuhrer, Patrick Harvey-Collard

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

In the quest to build a quantum computer, scientists are searching for tiny, controllable systems that can hold information in a state of superposition, existing in multiple possibilities at once. One promising candidate for this role is the "spin" of a single particle trapped inside a semiconductor chip. Imagine a tiny magnet, the size of an atom, that can point up or down, or even a mix of both. In recent years, researchers have found that using "holes"—the absence of an electron in a crystal lattice—within germanium chips offers unique advantages. These holes interact strongly with their environment in a way that allows scientists to control them with electricity rather than just magnetic fields, making them fast and potentially easier to manage. However, for a quantum computer to solve complex problems, these individual particles must be able to talk to one another, swapping information or changing each other's states. This conversation is mediated by a force called exchange interaction, which usually acts like a simple, uniform handshake between two neighbors. But in the germanium system, the rules of this handshake are far more complicated and interesting than previously thought.

A team of researchers at IBM Research Europe has now mapped out exactly how this conversation happens between two hole spins in a germanium chip. They discovered that the interaction is not a simple, uniform force but a complex, directional one that changes depending on how the magnetic field is oriented. By carefully adjusting the direction of the magnetic field, they found they could turn the interaction on and off, and even reverse its nature. In a standard setup, two quantum bits would interact in a fixed way, limiting the types of operations they could perform. Here, the researchers showed that by simply rotating the magnetic field, they could tune the interaction from a positive value, through zero, to a negative value. This ability to flip the sign of the interaction is a rare and powerful tool, allowing for a level of control that was previously impossible with these materials.

The team worked with a device containing two tiny traps, known as quantum dots, holding a single hole spin each. They placed this device in a magnetic field and used a technique called spectroscopy to listen to the "voice" of the spins. By measuring the frequency at which the spins flipped, they could deduce the strength and direction of the force connecting them. They found that this force splits into two distinct parts: one that acts like a push or pull along a specific line, and another that acts like a sideways swap. The researchers mapped out how these two parts changed as they rotated the magnetic field in three-dimensional space. They observed that the "push or pull" part could be made to vanish completely, and then reappear with the opposite effect. This means that at a specific angle, the spins stop influencing each other's energy levels in the usual way, while the "sideways swap" part remains active.

This discovery allowed the scientists to engineer a specific type of quantum gate, a fundamental building block for quantum logic. By aligning the magnetic field to the precise angle where the push-pull interaction vanished, they were left with only the sideways swap force. They then applied a single, short electrical pulse to the chip, causing the two spins to swap their states perfectly. This operation, known as an iSWAP gate, is a crucial step for quantum computing, but it is notoriously difficult to achieve in systems where the interaction is fixed and isotropic. In this germanium system, the researchers achieved this gate in just 56 nanoseconds. They verified the success of the operation by measuring the state of the spins before and after the pulse, confirming that the two particles had indeed exchanged their information with high accuracy.

The study also revealed that the behavior of these spins is deeply tied to the shape of the magnetic response of the material itself, known as the g-tensor. The researchers measured this shape for each individual spin and found that their slight misalignment was the key to creating the directional interaction. Because the two spins responded to the magnetic field in slightly different directions, the force between them became anisotropic, meaning it depended on the angle of the field. This finding suggests that the geometry of the material is not just a background detail but a primary control knob for quantum operations. The team measured the stability of the spins and found they could maintain their quantum state for over 21 microseconds, a duration that is among the best reported for this type of system.

While the experiment demonstrated a high-fidelity gate, the researchers noted that the performance was limited by the difficulty of reading out the state of the spins at that specific magnetic angle, rather than by a flaw in the gate mechanism itself. The study provides a clear blueprint for how to manipulate quantum interactions not by changing the hardware, but by simply turning a magnetic dial. This approach offers a new path for building quantum computers where the logic gates are defined by the orientation of a global field, rather than by complex, individual wiring for every single operation. The ability to tune the interaction from positive to negative, and to isolate specific types of quantum motion, opens the door to simulating complex physical systems and performing calculations that were previously out of reach. By understanding and harnessing these directional forces, the researchers have shown that germanium is a versatile platform capable of supporting the next generation of quantum hardware.

Technical Summary: Engineering Two-Qubit Gates via Anisotropic Exchange in Germanium Spin Qubits

Problem and Context
Germanium hole spin qubits offer a versatile platform for quantum information processing, characterized by strong intrinsic spin-orbit interaction (SOI). While SOI is well-understood in the context of single-qubit properties—enabling electrically tunable g-tensors and operational sweet spots—its influence on the two-qubit exchange interaction remains largely unexplored. In standard isotropic Heisenberg exchange, the coupling is a scalar constant. However, in systems with strong SOI, site-dependent g-tensors and spin-flip tunnelling cause the exchange coupling to become an anisotropic tensor, $J(\vec{B})$ . This anisotropy introduces distinct longitudinal ( $J_\parallel$ ) and transverse ( $J_\perp$ ) components. Understanding and controlling the ratio between these components is critical, as it dictates the native two-qubit gate set (e.g., controlled-phase vs. SWAP-like gates) and influences gate fidelity and crosstalk. Prior to this work, while anisotropic exchange was observed indirectly in singlet-triplet qubits, its direct measurement and exploitation for gate engineering in Loss-DiVincenzo single-hole spin qubits had not been achieved.

Methodology
The authors experimentally investigated a gate-defined double quantum dot (DQD) fabricated in a strained Ge/SiGe heterostructure, coupled to a single-hole transistor (SHT) for charge sensing. The study utilized full vector control of the external magnetic field $\vec{B}$ to map the exchange interaction.

Single-Qubit Characterization: The g-tensors for two hole spin qubits ( $Q_1$ and $Q_2$ ) were characterized via adiabatic rapid passage (ARP) spectroscopy at a fixed magnetic field magnitude ( $B=60$ mT). This established the orientation of the principal axes ( $\vec{g}_{x'}, \vec{g}_{y'}, \vec{g}_{z'}$ ) and the Euler angles describing the g-tensor rotation in the lab frame.
Spectroscopic Mapping: To resolve the exchange tensor, the team performed state spectroscopy at two operating points: a "J-off" point for single-qubit manipulation and a "J-on" point for two-qubit interaction. By preparing specific initial states ( $|\downarrow\downarrow\rangle$ , $|\uparrow\downarrow\rangle$ , $|\downarrow\uparrow\rangle$ ) and applying broadband ARP pulses, they measured the four transition frequencies of the exchange-coupled system as a function of the magnetic field direction ( $\phi_B, \theta_B$ ).
Decomposition: The measured frequencies were used to extract the longitudinal exchange $J_\parallel$ and the quadrature sum of the Zeeman detuning and transverse exchange, $(E_{\Delta g}^2 + |J_\perp|^2)^{1/2}$ .
Gate Engineering: Based on the spectroscopic maps, the authors identified a specific magnetic field orientation where $J_\parallel = 0$ and the Zeeman detuning $E_{\Delta g} = 0$ , while $J_\perp$ remained non-zero. They utilized this condition to engineer a Hamiltonian dominated purely by transverse exchange.

Key Results

Anisotropic Exchange Mapping: The study successfully mapped the longitudinal ( $J_\parallel$ ) and transverse components of the exchange tensor. The results confirmed that $J_\parallel$ is highly sensitive to the magnetic field orientation, varying from positive values to zero and even to effectively negative values.
Negative Longitudinal Exchange: The authors reported the first direct measurement of effectively negative longitudinal exchange ( $J_\parallel < 0$ ) in spin qubits. This was evidenced by "inverted" exchange-split spin transitions, where the frequency branches diverged with opposite signs compared to the conventional positive exchange regime.
Gate Dynamics: The research demonstrated that $J_\parallel$ drives controlled-phase (CPhase) oscillations, while $J_\perp$ (in conjunction with detuning) drives SWAP-like oscillations. The frequencies of these oscillations matched the spectroscopic predictions.
Baseband iSWAP Gate: By tuning the magnetic field to a specific orientation where $J_\parallel = 0$ and $E_{\Delta g} = 0$ , the authors engineered a pure transverse (XY) interaction. This enabled the implementation of a single-pulse baseband iSWAP gate. The gate was calibrated using amplitude sweeps and phase corrections, achieving a process fidelity of approximately 60% (limited primarily by state preparation and measurement errors), which corresponds to an estimated underlying gate fidelity of ~87%.

Significance and Claims
The paper claims that linking the geometry of single-qubit g-tensors to exchange anisotropy establishes a method for "native Hamiltonian engineering." By simply reorienting the global magnetic field, the interaction Hamiltonian can be continuously tuned. This capability allows for:

Continuous Control: The ability to tune the interaction from conventional positive exchange, through zero, to negative exchange.
Access to New Gate Sets: The realization of gates, such as the single-pulse iSWAP, that are unattainable under isotropic exchange conditions.
Scalability Implications: The authors posit that characterizing and engineering g-tensor geometry is a prerequisite for scaling hole spin qubit arrays. They suggest that targeted heterostructure development could align these tensors to enable simultaneous long coherence, baseband single- and two-qubit gates, and shuttling, positioning germanium as a uniquely versatile platform for scalable quantum hardware.

The work provides the first comprehensive characterization of anisotropic exchange in germanium and demonstrates a proof-of-concept for using magnetic field orientation as a control knob for two-qubit interactions.

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