I have installed Debian 11.4 (bullseye) with KDE on my lenovo Thinkpad X1 Carbon Gen 10.
The hardware is as follows:
00:00.0 Host bridge: Intel Corporation Device 4621 (rev 02)
- Subsystem: Lenovo Device 22e7 Flags: bus master, fast devsel, latency 0, IOMMU group 0
Capabilities: [e0] Vendor Specific Information: Len=14 <?>
00:02.0 VGA compatible controller: Intel Corporation Device 46a6 (rev 0c) (prog-if 00 [VGA controller])
- Subsystem: Lenovo Device 22e7 Flags: bus master, fast devsel, latency 0, IRQ 176, IOMMU group 1 Memory at 603c000000 (64-bit, non-prefetchable) [size=16M] Memory at 4000000000 (64-bit, prefetchable) [size=256M] I/O ports at 2000 [size=64] Expansion ROM at 000c0000 [virtual] [disabled] [size=128K]
Capabilities: [40] Vendor Specific Information: Len=0c <?> Capabilities: [70] Express Root Complex Integrated Endpoint, MSI 00 Capabilities: [ac] MSI: Enable+ Count=1/1 Maskable+ 64bit- Capabilities: [d0] Power Management version 2 Capabilities: [100] Process Address Space ID (PASID) Capabilities: [200] Address Translation Service (ATS) Capabilities: [300] Page Request Interface (PRI) Capabilities: [320] Single Root I/O Virtualization (SR-IOV) Kernel driver in use: i915 Kernel modules: i915
00:04.0 Signal processing controller: Intel Corporation Device 461d (rev 02)
- Subsystem: Lenovo Device 22e7 Flags: bus master, fast devsel, latency 0, IRQ 177, IOMMU group 2 Memory at 603d180000 (64-bit, non-prefetchable) [size=128K] Capabilities: [90] MSI: Enable+ Count=1/1 Maskable- 64bit- Capabilities: [d0] Power Management version 3
Capabilities: [e0] Vendor Specific Information: Len=0c <?> Kernel driver in use: proc_thermal_pci Kernel modules: processor_thermal_device_pci
00:06.0 PCI bridge: Intel Corporation Device 464d (rev 02) (prog-if 00 [Normal decode])
- Flags: bus master, fast devsel, latency 0, IRQ 122, IOMMU group 3 Bus: primary=00, secondary=04, subordinate=04, sec-latency=0 I/O behind bridge: [disabled] Memory behind bridge: bc200000-bc2fffff [size=1M] Prefetchable memory behind bridge: [disabled] Capabilities: [40] Express Root Port (Slot+), MSI 00 Capabilities: [80] MSI: Enable+ Count=1/1 Maskable- 64bit- Capabilities: [90] Subsystem: Lenovo Device 22e7 Capabilities: [a0] Power Management version 3 Capabilities: [100] Advanced Error Reporting Capabilities: [220] Access Control Services Capabilities: [200] L1 PM Substates Capabilities: [150] Precision Time Measurement Capabilities: [280] Virtual Channel Capabilities: [a30] Secondary PCI Express
Capabilities: [a90] Data Link Feature <?> Capabilities: [a9c] Physical Layer 16.0 GT/s <?> Capabilities: [edc] Lane Margining at the Receiver <?> Kernel driver in use: pcieport
00:07.0 PCI bridge: Intel Corporation Device 466e (rev 02) (prog-if 00 [Normal decode])
- Flags: bus master, fast devsel, latency 0, IRQ 123, IOMMU group 4 Bus: primary=00, secondary=20, subordinate=49, sec-latency=0 I/O behind bridge: 00003000-00003fff [size=4K] Memory behind bridge: b0000000-bc1fffff [size=194M] Prefetchable memory behind bridge: 0000006000000000-000000601bffffff [size=448M] Capabilities: [40] Express Root Port (Slot+), MSI 00 Capabilities: [80] MSI: Enable+ Count=1/1 Maskable- 64bit- Capabilities: [90] Subsystem: Lenovo Device 22e7 Capabilities: [a0] Power Management version 3 Capabilities: [100] Advanced Error Reporting Capabilities: [220] Access Control Services Capabilities: [150] Precision Time Measurement Capabilities: [a00] Downstream Port Containment Capabilities: [a30] Secondary PCI Express
Capabilities: [a90] Data Link Feature <?> Capabilities: [ba0] Physical Resizable BAR Kernel driver in use: pcieport
00:07.2 PCI bridge: Intel Corporation Device 462f (rev 02) (prog-if 00 [Normal decode])
- Flags: bus master, fast devsel, latency 0, IRQ 124, IOMMU group 5 Bus: primary=00, secondary=50, subordinate=79, sec-latency=0 I/O behind bridge: 00004000-00004fff [size=4K] Memory behind bridge: a2000000-ae1fffff [size=194M] Prefetchable memory behind bridge: 0000006020000000-000000603bffffff [size=448M] Capabilities: [40] Express Root Port (Slot+), MSI 00 Capabilities: [80] MSI: Enable+ Count=1/1 Maskable- 64bit- Capabilities: [90] Subsystem: Lenovo Device 22e7 Capabilities: [a0] Power Management version 3 Capabilities: [100] Advanced Error Reporting Capabilities: [220] Access Control Services Capabilities: [150] Precision Time Measurement Capabilities: [a00] Downstream Port Containment Capabilities: [a30] Secondary PCI Express
Capabilities: [a90] Data Link Feature <?> Capabilities: [ba0] Physical Resizable BAR Kernel driver in use: pcieport
00:08.0 System peripheral: Intel Corporation Device 464f (rev 02)
- Subsystem: Lenovo Device 22e7 Flags: fast devsel, IRQ 255, IOMMU group 6 Memory at 603d1da000 (64-bit, non-prefetchable) [disabled] [size=4K] Capabilities: [90] MSI: Enable- Count=1/1 Maskable- 64bit-
Capabilities: [a0] Vendor Specific Information: Len=14 <?> Capabilities: [dc] Power Management version 2 Capabilities: [f0] PCI Advanced Features
00:0a.0 Signal processing controller: Intel Corporation Device 467d (rev 01)
- Subsystem: Lenovo Device 22e7 Flags: fast devsel, IOMMU group 7 Memory at 603d1c0000 (64-bit, non-prefetchable) [size=32K] Capabilities: [70] Express Root Complex Integrated Endpoint, MSI 00 Capabilities: [d0] Power Management version 3
Capabilities: [100] Designated Vendor-Specific: Vendor=8086 ID=0002 Rev=1 Len=16 <?> Capabilities: [110] Designated Vendor-Specific: Vendor=8086 ID=0003 Rev=1 Len=16 <?> Capabilities: [120] Designated Vendor-Specific: Vendor=8086 ID=0004 Rev=1 Len=16 <?>
00:0d.0 USB controller: Intel Corporation Device 461e (rev 02) (prog-if 30 [XHCI])
- Subsystem: Lenovo Device 22e7 Flags: bus master, medium devsel, latency 0, IRQ 175, IOMMU group 8 Memory at 603d1b0000 (64-bit, non-prefetchable) [size=64K] Capabilities: [70] Power Management version 2 Capabilities: [80] MSI: Enable+ Count=1/8 Maskable- 64bit+
Capabilities: [90] Vendor Specific Information: Len=14 <?> Capabilities: [b0] Vendor Specific Information: Len=00 <?> Kernel driver in use: xhci_hcd Kernel modules: xhci_pci
00:0d.2 USB controller: Intel Corporation Device 463e (rev 02) (prog-if 40 [USB4 Host Interface])
- Subsystem: Lenovo Device 22e7 Flags: bus master, fast devsel, latency 0, IRQ 16, IOMMU group 8 Memory at 603d140000 (64-bit, non-prefetchable) [size=256K] Memory at 603d1d9000 (64-bit, non-prefetchable) [size=4K] Capabilities: [80] Power Management version 3 Capabilities: [88] MSI: Enable- Count=1/1 Maskable- 64bit+ Capabilities: [a0] MSI-X: Enable+ Count=16 Masked- Kernel driver in use: thunderbolt Kernel modules: thunderbolt
00:0d.3 USB controller: Intel Corporation Device 466d (rev 02) (prog-if 40 [USB4 Host Interface])
- Subsystem: Lenovo Device 22e7 Flags: bus master, fast devsel, latency 0, IRQ 16, IOMMU group 8 Memory at 603d100000 (64-bit, non-prefetchable) [size=256K] Memory at 603d1d8000 (64-bit, non-prefetchable) [size=4K] Capabilities: [80] Power Management version 3 Capabilities: [88] MSI: Enable- Count=1/1 Maskable- 64bit+ Capabilities: [a0] MSI-X: Enable+ Count=16 Masked- Kernel driver in use: thunderbolt Kernel modules: thunderbolt
00:14.0 USB controller: Intel Corporation Device 51ed (rev 01) (prog-if 30 [XHCI])
- Subsystem: Lenovo Device 22e7 Flags: bus master, medium devsel, latency 0, IRQ 141, IOMMU group 9 Memory at 603d1a0000 (64-bit, non-prefetchable) [size=64K] Capabilities: [70] Power Management version 2 Capabilities: [80] MSI: Enable+ Count=1/8 Maskable- 64bit+
Capabilities: [90] Vendor Specific Information: Len=14 <?> Capabilities: [b0] Vendor Specific Information: Len=00 <?> Kernel driver in use: xhci_hcd Kernel modules: xhci_pci
00:14.2 RAM memory: Intel Corporation Device 51ef (rev 01)
- Subsystem: Lenovo Device 22e7 Flags: fast devsel, IOMMU group 9 Memory at 603d1d0000 (64-bit, non-prefetchable) [disabled] [size=16K] Memory at 603d1d7000 (64-bit, non-prefetchable) [disabled] [size=4K] Capabilities: [80] Power Management version 3
00:14.3 Network controller: Intel Corporation Device 51f0 (rev 01)
- Subsystem: Intel Corporation Device 0090 Flags: bus master, fast devsel, latency 0, IRQ 16, IOMMU group 10 Memory at 603d1cc000 (64-bit, non-prefetchable) [size=16K] Capabilities: [c8] Power Management version 3 Capabilities: [d0] MSI: Enable- Count=1/1 Maskable- 64bit+ Capabilities: [40] Express Root Complex Integrated Endpoint, MSI 00 Capabilities: [80] MSI-X: Enable+ Count=16 Masked- Capabilities: [100] Latency Tolerance Reporting
Capabilities: [164] Vendor Specific Information: ID=0010 Rev=0 Len=014 <?> Kernel driver in use: iwlwifi Kernel modules: iwlwifi
00:15.0 Serial bus controller [0c80]: Intel Corporation Device 51e8 (rev 01)
- Subsystem: Lenovo Device 22e7 Flags: bus master, fast devsel, latency 0, IRQ 27, IOMMU group 11 Memory at 4017000000 (64-bit, non-prefetchable) [size=4K] Capabilities: [80] Power Management version 3
Capabilities: [90] Vendor Specific Information: Len=14 <?> Kernel driver in use: intel-lpss Kernel modules: intel_lpss_pci
00:16.0 Communication controller: Intel Corporation Device 51e0 (rev 01)
- Subsystem: Lenovo Device 22e7 Flags: bus master, fast devsel, latency 0, IRQ 178, IOMMU group 12 Memory at 603d1d5000 (64-bit, non-prefetchable) [size=4K] Capabilities: [50] Power Management version 3 Capabilities: [8c] MSI: Enable+ Count=1/1 Maskable- 64bit+
Capabilities: [a4] Vendor Specific Information: Len=14 <?> Kernel driver in use: mei_me Kernel modules: mei_me
00:16.3 Serial controller: Intel Corporation Device 51e3 (rev 01) (prog-if 02 [16550])
- Subsystem: Lenovo Device 22e7 Flags: 66MHz, fast devsel, IRQ 19, IOMMU group 12 I/O ports at 2060 [size=8] Memory at bc301000 (32-bit, non-prefetchable) [size=4K] Capabilities: [40] MSI: Enable- Count=1/1 Maskable- 64bit+ Capabilities: [50] Power Management version 3 Kernel driver in use: serial
00:1f.0 ISA bridge: Intel Corporation Device 5182 (rev 01)
- Subsystem: Lenovo Device 22e7 Flags: bus master, fast devsel, latency 0, IOMMU group 13
00:1f.3 Audio device: Intel Corporation Device 51c8 (rev 01) (prog-if 80)
- Subsystem: Lenovo Device 22e7 Flags: bus master, fast devsel, latency 64, IRQ 195, IOMMU group 13 Memory at 603d1c8000 (64-bit, non-prefetchable) [size=16K] Memory at 603d000000 (64-bit, non-prefetchable) [size=1M] Capabilities: [50] Power Management version 3
Capabilities: [80] Vendor Specific Information: Len=14 <?> Capabilities: [60] MSI: Enable+ Count=1/1 Maskable- 64bit+ Kernel driver in use: snd_hda_intel Kernel modules: snd_hda_intel, snd_sof_pci_intel_tgl
00:1f.4 SMBus: Intel Corporation Device 51a3 (rev 01)
- Subsystem: Lenovo Device 22e7 Flags: medium devsel, IRQ 16, IOMMU group 13 Memory at 603d1d4000 (64-bit, non-prefetchable) [size=256] I/O ports at efa0 [size=32] Kernel driver in use: i801_smbus Kernel modules: i2c_i801
00:1f.5 Serial bus controller [0c80]: Intel Corporation Device 51a4 (rev 01)
- Subsystem: Lenovo Device 22e7 Flags: fast devsel, IOMMU group 13 Memory at a0800000 (32-bit, non-prefetchable) [size=4K]
04:00.0 Non-Volatile memory controller: Samsung Electronics Co Ltd NVMe SSD Controller PM9A1/980PRO (prog-if 02 [NVM Express])
- Subsystem: Samsung Electronics Co Ltd Device a801 Flags: bus master, fast devsel, latency 0, IRQ 16, NUMA node 0, IOMMU group 14 Memory at bc200000 (64-bit, non-prefetchable) [size=16K] Capabilities: [40] Power Management version 3 Capabilities: [50] MSI: Enable- Count=1/32 Maskable- 64bit+ Capabilities: [70] Express Endpoint, MSI 00 Capabilities: [b0] MSI-X: Enable+ Count=130 Masked- Capabilities: [100] Advanced Error Reporting Capabilities: [168] Alternative Routing-ID Interpretation (ARI) Capabilities: [178] Secondary PCI Express
Capabilities: [198] Physical Layer 16.0 GT/s <?> Capabilities: [1bc] Lane Margining at the Receiver <?> Capabilities: [214] Latency Tolerance Reporting Capabilities: [21c] L1 PM Substates Capabilities: [3a0] Data Link Feature <?> Kernel driver in use: nvme Kernel modules: nvme
For the installation with netinst I used an old ethernet usb
The first problem with the Thinkpad X1 is the netinst installation of Debian 11.4 with KDE. When the installation finishes and reboots, then KDE does not start. It is a problem with the SDDM display manager
If you change the display manager to GDM the KDE boots but HDMI does not work, I think it is some incompatibility with kernel 5.10.
The easy solution is to install with netinst Debian 11.4 and not choose to install any graphical environment, only ssh server.
Once Debian is installed without a graphical environment, boot up and login as root.
The goal is to install Kernel 5.18 from Debian backports, so we have to add the repository to /etc/apt/source.list, I also added the contrib non-free.
My source.list file is like this:
deb http://deb.debian.org/debian/ bullseye main contrib non-free
deb-src http://deb.debian.org/debian/ bullseye main contrib non-free
deb http://security.debian.org/debian-security/ bullseye-security main contrib non-free
deb-src http://security.debian.org/debian-security/ bullseye-security main contrib non-free
deb http://deb.debian.org/debian/ bullseye-updates main contrib non-free
deb-src http://deb.debian.org/debian/ bullseye-updates main contrib non-free
deb http://deb.debian.org/debian/ bullseye-backports main contrib non-free
And now we write:
apt-get update
apt-get upgrade
apt-get install linux-image-5.18.0-0.deb11.3-amd64 linux-headers-5.18.0-0.deb11.3-amd64
I also put the headers in case one day I need to install a driver from a manufacturer (for example a new ethernet usb).
Once the installation is complete, we do the following:
reboot now
and login as root
Now let's install KDE , I did it like this: (but there are several ways to do it):
apt install kde-full sddm
Now let's enable sound:
tee /etc/modprobe.d/sof-fix.conf <<<'options snd-intel-dspcfg dsp_driver=1' now it will have sound, the only thing that won't work is the external microphone, you will have to use the headphones to talk.
And now we write:
reboot now
Now if everything has worked fine, Debian will boot with KDE and will have sound and HDMI will work.
Once in KDE, download the WIFI and Bluetooth firmware and install it.
For this we download the latest kernel firmware from the URL:
https://git.kernel.org/pub/scm/linux/kernel/git/firmware/linux-firmware.git/
Assuming the downloaded file is linux-firmware-20220815.tar.gz
From the terminal we do:
cd Downloads
tar xvzf linux-firmware-20220815.tar.gz
cd linux-firmware-20220815
su
cp intel/ibt-0040-0041.ddc /lib/firmware/intel/.
cp iwl* /lib/firmware/.
We now install the tlp to improve battery management:
apt-get install tlp tlp-rdw
apt-get install tp-smapi-dkms acpi-call-dkms
Now we reboot from KDE
On start-up it will detect the WIFI and Bluetooth.
And now you have the Thinkpad X1 Carbon Gen 10 with Debian 11 and KDE running perfectly. 
note: If you need to virtualise any windows with Virtualbox, you must assign more than one processor to the windows virtual machine or you will have problems.