You should catch up on these vulnerabilities in the canonical question on the subject.
Assuming you are talking about the recent wave of Spectre and Spectre-like vulnerabilities, those are not backdoors, but security vulnerabilities. They generally* allow a local process that is executing on your computer to read memory that they are not otherwise permitted to read. If your adversary is a nation-state actor though, this is the least of your concerns. These attackers usually have access to a large repository of 0days from security contractors. It's more likely that they will exploit a flaw in some exposed service on your router or computer and then escalate privileges using a 0day, known vulnerability, or misconfiguration on your part. If they had to use these vulnerabilities, they would use it to skip the privilege escalation stage and directly read memory.
Normally, a CPU executing code will eventually run into a fork in the road where the specific path it takes depends on some variable. If that variable takes some time to access (e.g. querying hardware peripherals or accessing memory that is not in the CPU cache), then the CPU will engage in an optimization technique dubbed speculative execution. This technique involves speculatively executing both possible paths in code, later discarding the path which it was not supposed to take. The Spectre vulnerabilities typically exploit the fact that this "discarding" is not perfect and still leaves some information behind that a side-channel attack can later discover.
* A few variants allow for a little bit more, such as covert side-channel communication and, in at least one example dubbed NetSpectre, attack certain theoretically vulnerable protocols to read memory over a network very, very slowly. Another variant allows setting read-only patches to read-write in certain, specific situations.