State preparations and the Rubik's cube

State preparation — the process of loading a known probability mass function or setting a quantum system to a certain known state — is a critical part of quantum algorithm development. It is also important in hybrid classical/quantum algorithms that perform some quantum calculation, which needs to start in a known state, measure the state, perform some classical calculation and then repeat this process as necessary, using different starting states for each iteration.

Is it difficult to prepare a certain quantum state? Quite so. I spoke with Ian Mason recently and he likened state preparation to reversing a Rubik’s cube. If I gave you a scrambled Rubik’s cube, you could learn how to solve and unscramble it. But if I gave you a solved cube and asked you to scramble it to a precisely known state, how difficult would that be?

The process of reversing a cube would be even more difficult if certain constraints were given. For instance: do this in no more than a certain number of steps, or perhaps a certain rotation is not allowed.

Preparing a quantum state is even more difficult. Qubits have an infinite number of states. Qubits can be entangled. Today’s quantum computers have limitations in terms of the type of gates that can be used (analogous to prohibiting certain cube rotations), the number of ancilla qubits that can be used, not to mention the overall stability of the circuit which effectively limits the depth of the circuit — the number of steps you can take.

Fortunately, preparing states while accounting for a given set of constraints is very easy with the Classiq platform. Watch this short demo from our head of algorithms to see just how easy. If only reversing a Rubik’s cube was this easy…

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