The Qt spectrum demo has a different .pro file structure to the other demos, as it consists not just of an executable, but also a DLL:

spectrum/
    spectrum.pro
    spectrum.pri
    app/
        app.pro
    3rdparty/
        fftreal/
            fftreal.pro

In order to ensure that the demo can be launched by qtdemo, the .pro files contains DESTDIR directives which put the binaries (both spectrum.exe, built by app.pro, and fftreal.dll, built by fftreal.pro) into ${BUILD_ROOT}/debug or ${BUILD_ROOT}/release depending on the build configuration. This is done as follows:

# In spectrum.pri
win32 {
    build_pass {
        CONFIG(release, release|debug): spectrum_build_dir = /release
        CONFIG(debug, release|debug): spectrum_build_dir = /debug
    }
}

# In fftreal.pro
TEMPLATE = lib
TARGET = fftreal
DESTDIR = ../..$${spectrum_build_dir}

# In app.pro
TEMPLATE = app
TARGET = spectrum
LIBS += -L..$${spectrum_build_dir}
LIBS += -lfftreal
DESTDIR = ..$${spectrum_build_dir}

The problem is that QtCreator does not run a build_pass step, so the spectrum_build_dir variable never gets set. This means that it always tries to launch a binary from ${BUILD_ROOT}/spectrum.exe