Presentation Information
[ED4-03]A method to analyze and improve AQFP sensitivity to trapped flux
*Coenrad Johann Fourie1 (1. Stellenbosch University (South Africa))
Keywords:
AQFP,Flux Trapping,Operating Margins
Adiabatic quantum-flux parametron (AQFP) logic operates with ultralow switching energy that makes it ideal for use near qubits. However, large-scale systems—such as those needed for multi-qubit interface and control—remain vulnerable to magnetic flux trapped during cooldown. It is frequently observed that AQFP operating margins undergo large shifts between heat-cool cycles, that some AQFP circuits sometimes have very narrow margins that require multiple heat-cool cycles to find a stable operating point, and that AFQP circuits often get stuck in always-0 or always-1 states.
Such margin shifts have been investigated in multiple studies, and flux trapping as pinned vortices in ground planes or as fluxons in engineered moats has been demonstrated to be a primary cause [1]. It has been shown through modelling and simulation, and verified experimentally, that the supercurrent circulating around a pinned vortex or around the moat in which a fluxon is trapped couples magnetically to nearby circuit inductors and clock lines. This coupling induces current in the nearby circuits that shift operating points and thus deteriorates operating margins.
The densification of AQFP layouts to enable better integration scale for large systems shrinks the available space around individual cells where moats can be placed to create low-energy sites for fluxons to trap, and to prevent Pearl vortex pinning near the AQFP cells. However, where moats are too close to the circuit structures, the coupling from the moats also influences circuit operation. This is problematic because moats are by their very design highly likely to capture flux.
Dense AQFP integration thus requires moat design and cell layout that minimize the shift in operating margins when the moats trap flux. To achieve that, we need to determine how sensitive a cell is to a fluxon at any given location, use that to optimize the AQFP cell layout to depress the sensitivity landscape where moats are likely to be placed, and then find moat patterns that create the least disturbance to the operating point of the circuit.
We approach this by using a sweep analysis where a Pearl vortex is progressively scanned across the cell layout area and the minimum operating margin for the circuit calculated from a margin analysis simulation at each scan point. This is processed as a sensitivity map overlayed with the cell structure, from which areas where the least (or no) flux are tolerated and areas where the most flux can be tolerated are identified. Moats are then placed in areas with highest tolerance (or least sensitivity), and the moat patterns are adjusted for minimum disturbance to the cell operating margins. We show that symmetry between moats and layout structures is essential to reduce sensitivity.
This method is then applied to existing AQFP circuit layouts, such as a known fluxon-sensitive output driver stage depicted in Fig. 1, to obtain improved moat configurations that will enable denser placement and to identify tweaks to the layout that enhance symmetry between moats and critical circuit elements.
Such margin shifts have been investigated in multiple studies, and flux trapping as pinned vortices in ground planes or as fluxons in engineered moats has been demonstrated to be a primary cause [1]. It has been shown through modelling and simulation, and verified experimentally, that the supercurrent circulating around a pinned vortex or around the moat in which a fluxon is trapped couples magnetically to nearby circuit inductors and clock lines. This coupling induces current in the nearby circuits that shift operating points and thus deteriorates operating margins.
The densification of AQFP layouts to enable better integration scale for large systems shrinks the available space around individual cells where moats can be placed to create low-energy sites for fluxons to trap, and to prevent Pearl vortex pinning near the AQFP cells. However, where moats are too close to the circuit structures, the coupling from the moats also influences circuit operation. This is problematic because moats are by their very design highly likely to capture flux.
Dense AQFP integration thus requires moat design and cell layout that minimize the shift in operating margins when the moats trap flux. To achieve that, we need to determine how sensitive a cell is to a fluxon at any given location, use that to optimize the AQFP cell layout to depress the sensitivity landscape where moats are likely to be placed, and then find moat patterns that create the least disturbance to the operating point of the circuit.
We approach this by using a sweep analysis where a Pearl vortex is progressively scanned across the cell layout area and the minimum operating margin for the circuit calculated from a margin analysis simulation at each scan point. This is processed as a sensitivity map overlayed with the cell structure, from which areas where the least (or no) flux are tolerated and areas where the most flux can be tolerated are identified. Moats are then placed in areas with highest tolerance (or least sensitivity), and the moat patterns are adjusted for minimum disturbance to the cell operating margins. We show that symmetry between moats and layout structures is essential to reduce sensitivity.
This method is then applied to existing AQFP circuit layouts, such as a known fluxon-sensitive output driver stage depicted in Fig. 1, to obtain improved moat configurations that will enable denser placement and to identify tweaks to the layout that enhance symmetry between moats and critical circuit elements.