Mapping exchange phase in quantum dots with 3D tomography

Researchers at Sandia National Laboratories have developed a new technique for mapping the exchange interaction within silicon-germanium quantum dot devices, employing the max-flow/min-cut phase unwrapping method, originally used in digital holography, to create a three-dimensional phase volume. The work addresses longstanding challenges in extracting the exchange interaction coefficient, which helps to understand and improve spin qubit performance. Confirming the method’s robustness, the team increased scan resolution to validate minimal device drift. This approach may provide detailed information useful for understanding device variability and optimizing qubit control. Si/SiGe Quantum Dot Exchange Interaction Fundamentals Researchers at Sandia National Laboratories are using a technique akin to phase-shifting digital holography to map the accumulated phase of spin qubits within a Si/SiGe quantum dot device, a method traditionally employed in fields like optical imaging. This approach allows for the creation of a three-dimensional phase volume, derived from a series of two-dimensional measurements, revealing subtle variations in the exchange interaction critical for qubit control. The work focuses on pulses applied to specific gates, P2, B2 and P3, to manipulate the exchange interaction between spins on quantum dots two and three, inducing a rotational phase shift around the Jn-axis of the Bloch sphere.

The team’s method addresses longstanding difficulties in extracting the exchange interaction coefficient, J(V), as a function of gate electrode voltages, a parameter essential for accurately simulating device performance and mitigating the effects of disorder. Conventional coherent measurements of exchange yield a cosine of the accumulated phase, which is the time integral of the exchange interaction itself; however, inverting this cosine to determine J(V) is prone to ambiguity and sensitivity to noise. To overcome these challenges, the researchers implemented the max-flow/min-cut phase unwrapping method, or PUMA, originally developed for other applications, to robustly unwrap the phase in three-dimensional voltage space. The device itself was fabricated by Corp.’s quantum device foundry, mirroring designs used in other quantum computing efforts, and operates using a three-electron-spin exchange-only qubit encoding. Coherent qubit control is achieved by applying voltage pulses to the quantum dot plunger and barrier gates, effectively switching the Heisenberg exchange interaction between neighboring quantum dots on and off. The Heisenberg interaction Hamiltonian for the system is defined as H = J12(V(t)) + J23(V(t)), where Jz≡ J12 and Jn≡ J23 represent the exchange interactions between quantum dots 1-2 and 2-3, respectively, and Si are spin operators. “This is important for simulating the effects of noise on the gate electrodes, which requires a reasonably accurate model for J(V),” the researchers note, highlighting the need for precise characterization of the exchange interaction. The resulting 3D phase volume provides detailed information about the exchange interaction landscape, enabling optimization of qubit control pulses and potentially improving qubit fidelity.

The team’s approach allows for the identification of a minimal-gradient π exchange pulse point in voltage space, a specific target for achieving precise and efficient qubit manipulation. This level of control helps to minimize errors and maximize the coherence of quantum computations. The work represents a step toward a more complete understanding of the factors influencing qubit performance in Si/SiGe quantum dot devices. 3D Tomography for Mapping Accumulated Exchange Phase Extracting precise data on accumulated phase is now possible through a novel three-dimensional mapping technique, allowing for more accurate modeling of spin qubit behavior. Researchers developed a method to build a volumetric model of integrated exchange, a function of three gate electrode voltages, to better understand how voltage controls electron spin-spin interactions within a silicon-based quantum dot device. This approach moves beyond simply calibrating control pulses, offering a pathway to understand the underlying physics governing qubit performance.

The team overcame inherent difficulties in measuring exchange interactions, which typically manifest as a modulated cosine of accumulated phase, by incorporating techniques from fields outside of traditional quantum computing. This combination enabled robust extraction of the accumulated phase, φ, despite the challenges of inverting a cosine and mitigating noise during phase unwrapping. The use of PUMA, originally developed for other imaging applications, demonstrates an innovative cross-disciplinary approach to quantum measurement. PUMA Algorithm Enables Robust 3D Phase Unwrapping The team’s method directly inputs wrapped phase data into PUMA, a technique that converts the phase into a graph and estimates its value by minimizing energy on that graph through binary optimizations and max-flow/min-cut calculations. The robustness of this phase extraction and unwrapping procedure was tested by deliberately increasing scan resolution to 300×300 pixels, requiring approximately 12 hours to complete a set of four phase raster scans. This extended measurement time allowed for assessment of device drift, a potential source of error in phase measurements, and confirmed the method’s resilience to even minimal calibration shifts. Following the unwrapping process, a phase derivative value (PDV) is applied to identify regions of high-confidence phase. Upon building a model of the extracted phase information, the researchers optimize over the model to locate a minimal-gradient π exchange pulse point in voltage space. PUMA’s reliance on binary optimizations, successive adjustments to refine the phase estimate, is efficiently computed through max-flow/min-cut calculations. This computational strategy allows for the unwrapping of the phase despite its integral nature, which introduces ambiguity when inverting the cosine function.

The team’s approach represents an advancement in the ability to model and optimize these quantum systems.

Voltage Space Optimization of π Exchange Pulses This detailed examination of phase behavior was performed on a 12-QD Si/SiGe Tunnel Falls device, allowing for the construction of a three-dimensional model of integrated exchange as a function of the three voltages applied to the gate electrodes.

The team’s approach addresses a cross-section of the full voltage space during an exchange pulse, typically defined by the three gate electrodes controlling a pair of quantum dots and the potential barrier between them. Maintaining consistent electrostatic potential difference, or detuning, between the quantum dots during pulsing is critical, as is compensating for capacitive effects from barrier gate pulses. Beyond model building, the extracted phase information offers multiple benefits, including improved understanding of device variability and enhanced calibration of device models. “We may compare simulated phase from atomistic models incorporating disorder with the phase voltage dependence of measured devices,” the researchers state, highlighting the potential for connecting experimental results with microscopic modeling.

Device Variability Analysis via Exchange Phase Mapping Extracting the accumulated phase of exchange interactions in silicon spin qubits now benefits from a technique mirroring methods used in phase-shifting digital holography, enabling detailed three-dimensional mapping of the exchange landscape. Researchers at Sandia National Laboratories applied this measurement approach to a 12-quantum dot Intel Si/SiGe Tunnel Falls device, generating a phase volume from a series of two-dimensional measurements. This advancement addresses challenges inherent in directly analyzing voltage-dependent exchange, typically obscured by trigonometric functions of accumulated phase.

The team’s automated analysis pipeline, completed in approximately one minute, builds a model of high-confidence phase data and facilitates simulations of device operation. This model incorporates experimental non-idealities, such as skew, allowing for realistic pulsing trajectories through phase space and intuitive visualization of exchange phase control. Applications of Direct Phase Unwrapping for Qubit Control This approach addresses inherent difficulties in determining the exchange interaction coefficient, which helps to understand both simulating device behavior and achieving high-fidelity qubit operation. The resulting 3D phase mapping enables the design of tailored voltage trajectories for qubit control, optimizing exchange phase coherence even with device-specific imperfections. An accurate understanding of voltage-dependent phase also facilitates direct comparison with simulated data generated from microscopic physical models, potentially revealing the origins of non-ideal electronic structures within the device. This capability extends beyond control optimization, offering a pathway to calibrate the impulse response of the control signal path, a challenging task given the millikelvin operating temperatures of dilution refrigerators.

The team’s work builds on a substantial body of research in phase unwrapping algorithms developed over the past three decades across diverse scientific disciplines, including interferometric synthetic aperture radar, magnetic resonance imaging and optical interferometry. Recognizing the nuances of different approaches, whether the wrapped phase is directly measured, derived from a trigonometric function, or relies on input carrier frequencies, the researchers adapted existing techniques to the specific challenges of quantum dot characterization. “Because of this, and the fact that phase unwrapping is a nontrivial problem, especially when considering robustness to a variety of different types of noise, researchers in disparate fields have generated a large body of work on phase unwrapping algorithms over the past 30+ years,” the paper states. Measurements were conducted on an industrially manufactured silicon-based device enriched with isotopically purified silicon-28, a material chosen to minimize spin decoherence. The device’s architecture, featuring quantum dots, allowed for precise control of exchange interactions between electron spins through applied voltage pulses. This experimental setup enabled the acquisition of phase data as a function of these voltage-driven interactions, providing the foundation for the 3D phase reconstruction. The method’s reliability was demonstrated through the analysis of data from this device, confirming its potential for broader application in characterizing complex quantum systems. 👉 More information🗞 Three-dimensional tomography of exchange phase in voltage space in a Si/Si−Ge quantum dot device✍️ Dylan Albrecht, Sarah Thompson, N. Tobias Jacobson and Ryan Jock🧠 DOI: http://link.aps.org/doi/10.1103/7572-brsj More like thisQuantum PhysicsQuantum systems may bypass slow driving with a new measurement shortcutQuantum PhysicsA theory predicts power laws for errors during quantum annealing runsPhysicsResidual coherence dominates entanglement in neutrino oscillation, study findsQuantum Error CorrectionA shifted operating point prevents controller stall in quantum error correctionStay currentSee today’s quantum computing news on Quantum Zeitgeist for the latest breakthroughs in qubits, hardware, algorithms, and industry deals. Tags: