Calculating qubit purity/entanglement in a quantum computer

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SUMMARY

This discussion focuses on calculating the "purity of reduced states" in quantum computing, a metric provided by IBM's quantum simulator. The author clarifies that "purity" and "entanglement" are synonymous in this context, as qubits begin in a pure state. A method for calculating these values has been developed, which aligns with results from IBM's simulator across various quantum circuits, including one-qubit gates, CNOT gates, and Toffoli gates. A detailed document outlining this calculation method is available for reference.

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Bob Walance
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I had written a simulator for a quantum computer and wanted to be able to calculate the values of the "purity of reduced states".

"Purity of reduced states" is a quantity that IBM provides on their simulator for each qubit. They used to call it "entanglement", and I believe that the two terms are synonymous since all of the qubits in a quantum computer start out in a pure state.

After struggling to find examples for how to calculate these purity/entanglement values for each qubit, I did finally figure it out. Attached is a document describing how to do this. The values calculated with this method jibe with IBM's simulator for various quantum circuits including simple one-qubit gates, CNOT gates, Toffoli gates, and various combinations of those.

Perhaps someone will find this useful.
 

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