Principles of Quantum Computing — III : Quantum Circuit and Measurement
#Quantum30 Cohort 04
Day 08
Date: 25th March, 2024.
Computation, as discussed earlier, is a process of manipulating the states of a physical system. A quantum computer takes a quantum state as the input and controls the state to increase the probability of finding the answer in the output state for the computation. For instance, Shor’s Algorithm manipulates the quantum states to find prime factors of a large number. A significant difference between a classical (electronic) circuit and a quantum circuit is the intermediate states in the circuits.
In a classical electronic circuit, we can measure the intermediate state since 0 and 1 in binary is represented by voltages (e.g., 0 volts and 5 volts) on a node in the circuit. Thus, it is possible to find an error (e.g., 2.5 volts) by measuring the voltage in the circuit.
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However, in a quantum circuit, the intermediate states are likely to be in a superposition state. If the superposition state is measured, the quantum state is corrupted and becomes one of the two orthogonal based states ( i.e., |0⟩ or |1⟩ at the time of measurement with the probabilities |α⟩² and |β⟩².
For example, when the photons in the equation (6) are measured, one of the four states,
e.g., |ψ₁⟩|ψ₂⟩ = |0⟩|1⟩ is observed with an equal probability i.e., 1/4, but all other information about the original state (6) is lost by the measurement.
In other words , the measurement is a one-way operation that doesn’t allow us to find the original state from the measured result similar to classical one-way function, e.g., hash.
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