Читать книгу Principles of Superconducting Quantum Computers - Daniel D. Stancil - Страница 29

The Bell and Deutsch examples have illustrated several important characteristics of quantum computing:

 Results are (usually) statistical: When a classical program is executed, you obtain the same result each time. However, when a quantum circuit is executed, multiple results are possible with probabilities determined by the magnitude squared of the amplitudes of each state. Consequently, in general a circuit must be executed a large number of times, with the results of the computation extracted from a histogram of the measured outcomes.It is possible, however, for the outcome to be one particular state with probability 1. This is the case for Deutsch’s algorithm, for example. We know the answer for certain after one execution (assuming the quantum machine is error-free). So it’s not the case that a quantum algorithm must be probabilistic, but the most interesting algorithms tend to be that way.

 Quantum parallelism: Arranging for the input state to be a superposition allows the calculation to consider multiple cases at once. However, it is not as easy to capitalize on this as it might sound. As indicated in the previous bullet, even though the output state may contain the complete solution, a single measurement will yield only one state with a probability given by the squared magnitude of the amplitude of the state in the solution of the problem.

 Exponential scaling: The number of cases that can be considered scales as 2N, where N is the number of qubits. Beyond about 50 qubits, a general quantum processor cannot be simulated by a supercomputer; said differently, a processor with of order 50 or more qubits is capable of computations not possible on the best classical computers. However, if the quantum program is restricted to certain types of gates, then the operation of the quantum computer can be efficiently simulated by a classical computer.

 Quantum interference: When multiple cases are considered using superposition, the goal of the quantum circuit is to arrange for the amplitudes of correct answer(s) to add constructively, while arranging for the incorrect answer(s) to add destructively.

 Asking the right question: Although the output state of a quantum calculation will generally contain information about many possibilities, making a measurement collapses the state and therefore only gives a single result. In the Deutsch Problem, two classical function calls would not only tell you whether the function was constant or balanced, but it would tell you precisely what the function was. In contrast, the quantum calculation answers the question about whether the function is constant or balanced in one function call (which requires consideration of both cases), but it does not tell you which of the two possible functions it is.