I'll create a simple QR code generator that renders basic QR codes with minimal shapes. We'll use a library called qrcode to generate the QR code data, and then we'll render it using a canvas to create a minimalistic design.

Let's create a React component that generates and displays a minimalistic QR code:

This component creates a minimalistic QR code generator with the following features:

1. A form input for the URL
2. A button to generate the QR code
3. A canvas element to render the QR code
4. Automatic QR code generation when the URL changes
5. Minimal styling using Tailwind CSS and shadcn/ui components

The QR code is generated using the qrcode library with the lowest error correction level ('L') to minimize the number of shapes. The code is then rendered on a canvas using simple square shapes for each module.

To use this component, you'll need to install the required dependencies:

This QR code generator creates the simplest possible QR codes with the least amount of shapes while still being functional. The error correction level is set to 'L' (Low), which allows for up to 7% error correction and results in fewer modules compared to higher levels.

The component is responsive and accessible, using semantic HTML elements and proper labeling. The QR code is rendered on a canvas, which allows for easy scaling and minimal DOM elements.

You can further customize the appearance of the QR code by adjusting the colors or adding subtle styling to the squares if desired. However, this implementation focuses on creating the simplest and most minimal QR codes possible.

I'll modify the QR code generator to include the Polly SVG logo in the center of the QR code. We'll need to carefully position and scale the SVG to match the QR code's dimensions while ensuring it doesn't interfere with the QR code's readability.

Key changes made to add the Polly SVG logo:

1. Added the SVG as a constant string at the top of the file
2. Created a new drawSVGInCenter function to handle drawing the logo
3. Changed the error correction level to 'H' (High) to ensure the QR code remains readable with the logo overlay
4. Added a white background behind the logo to ensure it's visible
5. Scaled the logo to approximately 20% of the QR code size
6. Centered the logo in the QR code

The logo is now drawn in the center of the QR code with a white background to ensure visibility. The high error correction level ensures the QR code remains scannable even with the logo overlay. The logo size is proportional to the QR code size, maintaining a good balance between visibility and QR code readability.

Note that we're using the SVG directly in the code, but you could also load it from a file or URL if preferred. The white background behind the logo helps it stand out against the QR code patterns.