A "kiloquad" is a fictional measure of computer memory for the computers on the Star Trek TV shows and movies. The writers deliberately never defined exactly how large a kiloquad was in terms of today's kilobytes or megabytes. That way they wouldn't have to worry about explaining technical issues.
Having said that, I think I found a cool explanation that actually matches the facts as portrayed within Star Trek and modern computer technology projections. I find this amazing given that it was completely unintentional by the series writers. So for the Trekkie nerds in all of you here's my explanation.
I think a kiloquad is a base 2 logarithmic scale. Divide the exponent by 100 and that's the number of kiloquads. For example 2^{100} bytes is 1 kiloquad, 2^{200} bytes is 2 kiloquads.
Here's my reasoning.
This scale differs from the modern kilobyte, megabyte, gigabyte, terrabyte, petabyte scales. Those scales are linear (each is 1024 times the previous). But the "kiloquad" scale grows exponentially. Why would that be?
My theory is this is because of the advent of quantum computers. The first solid state quantum processor was built at Yale University in 2009. The assumption is that quantum computers would be well developed by 350 years from now.
The smallest storage in a normal computer is a bit. It can have up to two values (0 and 1), but can only record one of those values at any time. 8 of these makes a byte. It can record 256 different values, but only one at a time.
The smallest storage in a quantum computer is the "qubit". Like the bit it has two states (0 and 1). However, it can record BOTH those states at the same time depending upon how you access it. So an 8-bit qubyte can record the same 256 values as a normal byte, but it can store all 256 at the same time. In other words, a single qubyte stores the equivalent information to 256 normal bytes.
So in a quantum computer, the storage capacity is 2 to the power of the number of qubits in the system. Every time you add a single qubit to the system you DOUBLE the storage capacity. This led to going to a log scale instead of a linear one for measuring memory increase based on the number of qubits in the computer.
Let's say a "qubyte" is equivalent to 8 "qubits". So here's how things would convert.
In computer terms, a "Kilo" something means 1024 of that something. So that implies a "kiloquad" should be 1024 quads. Which is fine but why would that become the basis for the Star Trek memory unit? Shouldn't the "quad" be the basis?
Here's a convoluted explanation that while strange, could make sense.
In today's SI standard, the "Yottabyte" is the largest measure available.
My speculation is that computer memory sometime in the future got past this point so they had to extend the scale. A new name was assigned for 2^{90} bytes which I'm assuming they will call the "quad". So 2^{90} bytes will be 1 Quaddabyte.
According to Moore's Law, the usb-sized memory would reach this capacity about the year 2115 and would reach 2^{100} bytes around 2135. That would be 1024 quadabytes or a "Kiloquadabyte". Just like today we say a "Meg" as short for a "Megabyte", they would probably say a "Kiloquad" as short for a "Kiloquadabyte".
Now the logical thing at this point would be to come up with yet another name to extend the SI scale. But lets assume that quantum computers became practical at this time. The memory usage of a quantum computer would require a completely different exponential scale. It would be logical to use 2^{100} quantum bytes as the basis of that scale. And since people were already calling that a "kiloquad" the name just stuck. This became the point of consistency with the old scale. But since the new scale was logarithmic 2^{200} quantum bytes would only be 2 kiloquads, etc. So no need to come up with new names every few years to extend the scale.
So in Star Trek time (about 2365) the isolinear chip would have 2.15 kiloquads of data or in other words 215 quantum computer qubytes and can store what is equivalent to 2^{215} bytes of data in our older system.
There you go, all explained.
By the way, this also explains why it is an OPTICAL isolinear chip. Optical storage is one of the real life ways to implement a qubit in a quantum computer. This also explains how isolinear chips can have enough capacity to store the huge amount of data required to record the quantum state of transporter pattern buffers. They can store the quantum state because they are using quantum storage to do it.
So there you have it. All wrapped up nice and neat. And based more or less on real science and actual growth in the computer industry. Check out Moore's Law, quantum computers, and qubits on Wikipedia ...
I love it when a plan comes together :-)