You need to choose one of the high-speed interfaces that are available on the PC, and implement that in your FPGA (or by a companion chip of some sort) including any upper protocol layers that are needed to be able to exchange data with an app running on the PC.
A SERDES alone won't cut it. Now if this was a SERDES coupled to an Ethernet MAC (or MAC+PHY), which in turn could be used with an internal MCU/CPU core, that would be starting to make sense.
As for other choices, you have already mentioned USB, another possibility is the PCI-e, or the parallel PCI in the older days... On the host PC, you can talk to the USB stuff using LibUSB from the user space. Custom PCI or PCI-e hardware needs a kernel-space driver.
For really high throughput (efficient use of the bandwidth available), you will need to implement buffering / block transfers / DMA stuff. The existing PC interfaces have all that, but you'll need to support that on part of your custom device...
EDIT:
For one-off lab setups, companies that make industrial "data acquisition" interface cards for the PC, tended to also have a model for high-speed parallel digital I/O. I recall the PCI-1755 from Advantech (phased out long ago) that could do 32 bits at 20 MHz = 80 MBytes per second. The external bus was transported over cabling borrowed from SCSI. Internally on the parallel PCI bus, the board was using bus-master DMA. Nowadays, I'd take a look if National Instruments have something, and I know for a fact that Adlink have a whole family of products in that vein.
The PCI interface on a number of industrial IO boards used to be implemented using "slave bridges" by PLX (years ago acquired by Avago, now Broadcom). I remember universal chips such as PCI-9052, PCI-9030, PCI-9056 or PCI-9656 - the latter two can do BM-DMA. As PLX got assimilated, it looked like the these chips were doomed, I guess some even got phased out - and I'm quite surprised to see some of them listed and stocked by Mouser, but look at the prices :-) I believe that there used to be similar chips with a PCI-e interface, but I may be wrong. At the time when it looked like those PLX slave bridges were gone, vendors like Advantech have redesigned many of their boards to use FPGA's for a PCI interface - which made their designs more proprietary and less publically documented. On one board that used to have a PCI slave bridge chip, on a recent revision I have found a chip by Actel - which looks more like an FPGA. Actel's list of IP cores contains several interesting interface blocks, such as PCI-e.
I've also found a stand-alone SERDES transceiver by Texas Instruments, the TLK2501. I'm wondering of this would be compatible with your existing FPGA design. Couple its parallel 16bit local bus to some DMA-capable slave bridge by Broadcom (ex-PLX) and it might as well work...
Chris Stratton has mentioned SATA. That doesn't sound stupid at all. I've even found some SATA host IP core for some Xilinx FPGA that features the necessary differential driver and receiver. Sata Target chips or IP cores are difficult to find though - probably because SATA target boxes are only made by a couple large vendors: two hard drive brands, and maybe some DVD-ROM makers. A number of flash SSD target controllers have a SATA-compatible interface... The target-mode HBA chips used in SATA disk drives (spinning rust) are traditionally made by Marvell, LSI and maybe other such vendors - some are likely private chip models, where a public datasheet isn't even available...