In theory the Nexus 4 could connect to Verizon's "XLTE" network which is band 4 (assuming you have a modded or older baseband flashed), but even if it did work it would work with data only as Verizon's 3G network is CDMA and the Nexus 4 does not support VoLTE nor CDMA. I do know my Nexus 4 can sometimes see Verizon when I search for networks, but I have never tried popping in a Verizon SIM.