[Quantum Computing] Quantum Parallelism State Calculation

In summary, the resulting state of applying the operator for quantum parallelism should be (1/sqrt(2^4)) * (|0, f(0)> + |0, f(1)> + |1, f(1)> + |1, f(0)>). However, this would be useless to measure and to understand where you are going wrong, it is recommended to apply the operator over the base states and use linearity to get the final state.
  • #1
llha
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TL;DR Summary
Nielsen and Chuang state calculation isn't the full tensor product? But a full tensor product would be useless to measure?
Hi, I'm going through Nielsen and Chuang's Quantum Computation and Quantum Information textbook and I don't really understand this part about quantum parallelism:
1626469417681.png


Shouldn't the resulting state be (1/sqrt(2^4)) * (|0, f(0)> + |0, f(1)> + |1, f(1)> + |1, f(0)>), since the resulting state would be the (normalized) tensor product of (1/sqrt(2)) * (|0> + |1>) and (1/sqrt(2)) * (|f(0)> + f(1)>)?

I understand that would be pretty useless to measure, so I know I'm wrong, but I don't understand where I'm going wrong. Thanks in advance.
 
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  • #2
A state of two qubits can be written in the base ##\left|00\right>, \left|01\right>, \left|10\right>, \left|11\right>##. I would recommend you to apply the operator over these 4 states such that you really understand how the operator works, after that you can write the initial state as a linear combination of those states and use linearity and the previous result to get the final state.
 

FAQ: [Quantum Computing] Quantum Parallelism State Calculation

What is quantum parallelism in quantum computing?

Quantum parallelism is a concept in quantum computing that allows multiple calculations to be performed simultaneously, rather than sequentially. This is made possible by the use of quantum bits, or qubits, which can exist in multiple states at the same time.

How does quantum parallelism improve computation speed?

By allowing for multiple calculations to be performed simultaneously, quantum parallelism can significantly improve computation speed compared to classical computing. This is especially useful for solving complex problems that would take a very long time to solve with classical computing.

What is the role of state calculation in quantum parallelism?

State calculation is a crucial component of quantum parallelism as it involves determining the state of the qubits in a quantum system. This allows for the simultaneous execution of multiple calculations and is essential for achieving the speed and efficiency of quantum computing.

How is quantum parallelism used in real-world applications?

Quantum parallelism has the potential to revolutionize many industries, including finance, drug discovery, and cryptography. For example, it could be used to quickly analyze large datasets for financial forecasting or to simulate the behavior of molecules for drug development.

What are the challenges of implementing quantum parallelism in quantum computing?

One of the main challenges of implementing quantum parallelism in quantum computing is the issue of decoherence, which is the loss of quantum information due to interactions with the environment. This can lead to errors in calculations and is a significant obstacle in achieving reliable quantum parallelism. Other challenges include the development of error-correction techniques and the scaling of quantum systems to handle more complex problems.

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