Now that we understand how to set up a quantum computer, at least in theory, how can it be used to perform actual calculations? Just like in the classical case, the process boils down to three steps. First, our set of qubits must be prepared, or initialized, into a starting state. Then, we would have to perform a set of operations to manipulate those states while performing a particular algorithm. Finally, we would need to be able to read out the answer.
This schematic represents the steps required for computation using a two-spin qubit. When you first put your qubits together, each will be in some arbitrary superposition. After initialization, they collapse into a well-defined superposition of your choosing. You then perform a set of operations, each of which scrambles the composition of the qubit’s superposition. Finally, you take a measurement to read-out the answer. You will detect just one particular state, though with a probability given as the square of its coefficient following the last operation (in this case, 33 percent).
To see how all this could be done, let’s return to our three-qubit system. During the initialization step, we would set the values of each of the coefficients (a, b, etc.) to some precise value. For example, we could set a = 1 and the rest equal to zero. This would be equivalent to putting the system squarely into the Ψ0 state, or (0,0,0). We would then perform our operation(s), which is equivalent to scrambling up the various values of the coefficients in specific ways that are determined by our algorithm. At the end of these operations, the final state of the system will have a set of coefficients that is different from those of the initial state.
ATOM TRAP
While it is tempting to think that quantum computers gain their speed by performing multiple computations on qubits in parallel, this is not the case. That’s because a key step to computation is measurement, which will collapse the qubit into one random component state. Once collapsed, you’ve lost all benefits of superposition and have to start over. Instead, quantum computers derive their speed by taking advantage of interference effects between the quantum states. To get the most out of a quantum computer specific quantum algorithms, designed to take advantage of quantum interference, are needed.
Finally, we would need to read the state of the qubit. This is done by taking some form of measurement, the details of which will depend on whether your qubits are based on electron spins, atomic states, or something else entirely. When a measurement is made, we will collapse the qubit into one, and only one, of its component states. Any single measurement could potentially read out any of the component states, with a probability given by the square of each particular coefficient (e.g., |a|2 or |f|2). By running the algorithm a number of times and recording the measurement results, you can use statistics to work out what the final state was and therefore determine the result of the quantum computation.
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