But as antimatter pairs are dangerous because their annihilation is powerful, we should build the "antimatter factory" in orbit in space (or should we?), we can't only rely on nuclear reactors, as they would be to costly to send in space. I've read that to power these lasers, we would need 2,000 kilometer square (20 times Paris' surface area) of photovoltaic panels.
I won't check the numbers, and as others have already told you, your energy requirements are way too high. If properly controlled - there is the difficulty - you only need around 8 kWh per pair. Since a solar panel will yield around 200 W per square meter, that's 40 square meters per hour: with 4 square meters you need ten hours, with 400 square meters you're ready in 1/10th hour, or six minutes.
But that's the minimum energy, not considering losses, not considering anything. How efficient matter-antimatter production is, it depends on your technology. With magnetic capture coils ready to snatch the antiproton, your energy requirements might increase to perhaps around 4000 m2h.
The problem now becomes that at energy densities way below those required for proton-antiproton pair formation, lots of other particle-antiparticle pairs will form. So the "spontaneous creation" method is either unfeasible or requires a way of separating and removing all those unwanted particles and if possible recycle their energy, meanwhile capturing those proton/antiproton pairs popping up every now and then.
What you need instead is a way of duplicating the cosmic ray smashing mechanism - accelerate protons at tremendous speeds using massive electric fields, bombarding larger nuclei so that enough protons create the conditions for a particle/antiparticle creation, and find a way for capturing the antiprotons. It can be done, for a cost.
Then you have another difficulty, that of storing those antiprotons. They're negatively charged and strongly repel one another - granted, they've got so much energy that you need very few of them, but as ℏe said...
And all matter is a
mixture of positive protons and negative electrons which are
attracting and repelling with this great force. So perfect is the
balance, however, that when you stand near someone else you don’t feel
any force at all. If there were even a little bit of unbalance you
would know it. If you were standing at arm’s length from someone and
each of you had one percent more electrons than protons, the repelling
force would be incredible. How great? Enough to lift the Empire State
Building? No! To lift Mount Everest? No! The repulsion would be enough
to lift a “weight” equal to that of the entire Earth!
...so you really want to produce also a lot of antielectrons (positrons) and make antihydrogen. Except that hydrogen is neutral and cannot be held in place by ordinary electromagnetic fields. And you need to keep it in a vacuum, but how do you keep a gas in a vacuum? So you need to supercool and weakly compress it using diamagnetism.
All this will impact your power demands, unless you come up with some other means of containing antiprotons that also allows for antiprotons to be easily extracted and annihilated (remember, each pair only gives out about 8 kWh). There are ways, but not so economical.