Undergrad Calculating qubit purity/entanglement in a quantum computer

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The discussion focuses on calculating the "purity of reduced states" in a quantum computer simulator, a metric previously referred to as "entanglement." The author successfully developed a method to compute these values, which align with those provided by IBM's simulator for various quantum circuits. The document detailing this calculation method is shared for others to utilize. The purity values are consistent across different gate operations, including one-qubit gates and CNOT gates. This information may benefit others working with quantum computing simulations.
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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Thread 'Two equivalent statements of time reversal symmetric Hamiltonian'

Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?
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