Update Cross capacitance authored by Sander de Snoo's avatar Sander de Snoo
...@@ -2,10 +2,10 @@ The chemical potential of the quantum dots used in spin-qubit devices determines ...@@ -2,10 +2,10 @@ The chemical potential of the quantum dots used in spin-qubit devices determines
will be loaded in the quantum dot. The chemical potential is controlled by a plunger gate close to the quantum dot. will be loaded in the quantum dot. The chemical potential is controlled by a plunger gate close to the quantum dot.
However, due to the small distance between quantum dots the potential of a quantum dot is also affected However, due to the small distance between quantum dots the potential of a quantum dot is also affected
by neighboring plunger and barrier gates. This is the capacitive cross-talk, or cross-capacitance, from a gate to by neighboring plunger and barrier gates. This is the capacitive cross-talk, or cross-capacitance, from a gate to
other quantum dots. This cross-capacitance is classical in nature and can be corrected by pulse_lib using other quantum dots. This cross-capacitance is classical in nature and can be corrected by pulse-lib using
"virtual gates". "virtual gates".
A virtual gate is a pulse_lib channel that outputs a pulse sequence on multiple AWG channels A virtual gate is a pulse-lib channel that outputs a pulse sequence on multiple AWG channels
such that only a single chemical potential or single tunnel coupling will be affected by the pulses. such that only a single chemical potential or single tunnel coupling will be affected by the pulses.
Virtual gates are defined by a virtual gate matrix. Virtual gates are defined by a virtual gate matrix.
...@@ -32,13 +32,13 @@ A correct virtual matrix will remove the slant from the lines in the charge stab ...@@ -32,13 +32,13 @@ A correct virtual matrix will remove the slant from the lines in the charge stab
See *Loading a quantum-dot based "Qubyte" register*, C. Volk (2019), for a detailed description of cross-capacitance and virtual gates. See *Loading a quantum-dot based "Qubyte" register*, C. Volk (2019), for a detailed description of cross-capacitance and virtual gates.
# Virtual gate matrix in pulse_lib # Virtual gate matrix in pulse-lib
Pulse_lib inverts cross-capacitance matrix $`M`$ to calculate the voltages on the output channels. Pulse-lib inverts cross-capacitance matrix $`M`$ to calculate the voltages on the output channels.
$`\begin{pmatrix} P1 \\ P2 \\ P3 \end{pmatrix} = M^{-1} \begin{pmatrix} vP1 \\ vP2 \\ vP3 \end{pmatrix}`$ $`\begin{pmatrix} P1 \\ P2 \\ P3 \end{pmatrix} = M^{-1} \begin{pmatrix} vP1 \\ vP2 \\ vP3 \end{pmatrix}`$
The cross-capacitance matrix (real-to-virtual) can be passed to pulse_lib, but also the inverted The cross-capacitance matrix (real-to-virtual) can be passed to pulse-lib, but also the inverted
matrix (virtual-to-real) can be passed. The cross-capacitance matrix has to be a square matrix, because it matrix (virtual-to-real) can be passed. The cross-capacitance matrix has to be a square matrix, because it
must be invertible. The virtual-to-real matrix doesn't have to be square. must be invertible. The virtual-to-real matrix doesn't have to be square.
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