Why Isn't the Federal Reserve Buying Recession Insurance?: No Longer Fresh at Project Syndicate

Note to Self: Quantum Computing Notes: CNOT Gates

Bases:

|++> = [+ |00> + |01> + |10> + |11>]      
|+-> = [+ |00> - |01> + |10> - |11>]       
|-+> = [+ |00> + |01> - |10> - |11>]     
|—-> = [+ |00> - |01> - |10> + |11>]

|00> = + |++> + |+-> + |-+> + |—->   
|01> = + |++> - |+-> + |-+> - |—->   
|10> = + |++> + |+-> - |-+> - |—->   
|11> = + |++> - |+-> - |-+> + |—->

 

1 Control Qubit:

|10> to |11>   
|11> to |10>

|++> = [+ |00> + |01> + |10> + |11>] to [+ |00> + |01> + |10> + |11>] = |++>   
|+-> = [+ |00> - |01> + |10> - |11>] to [+ |00> - |01> - |10> + |11>] = |-->   
|-+> = [+ |00> + |01> - |10> - |11>] to [+ |00> + |01> - |10> - |11>] = |-+>   
|--> = [+ |00> - |01> - |10> + |11>] to [+ |00> - |01> + |10> - |11>] = |+->

 

2 Control Qubits:

|110> to |111>   
|111> to |110>

|+++> = [+ |000> + |010> + |100> + |110> + |001> + |011> + |101> + |111>] to [+ |000> + |010> + |100> + |111> + |001> + |011> + |101> + |110>] = |+++>   
|+-+> = [+ |000> - |010> + |100> - |110> + |001> - |011> + |101> - |111>] to [+ |000> - |010> + |100> - |111> + |001> - |011> + |101> - |110>] = |+-+>    
|-++> = [+ |000> + |010> - |100> - |110> + |001> + |011> - |101> - |111>] to [+ |000> + |010> - |100> - |111> + |001> + |011> - |101> - |110>] = |-++>   
|—-+> = [+ |000> - |010> - |100> + |110> + |001> - |011> - |101> + |111>] to [+ |000> - |010> - |100> + |111> + |001> - |011> - |101> + |110>] = |--+>    
|++-> = [+ |000> + |010> + |100> + |110> - |001> - |011> - |101> - |111>] to [+ |000> + |010> + |100> - |110> - |001> - |011> - |101> + |111>] = (+ |++-> + |+--> + |-+-> - |—-->)   
|+--> = [+ |000> - |010> + |100> - |110> - |001> + |011> - |101> + |111>] to [+ |000> - |010> + |100> + |110> - |001> + |011> - |101> - |111>] = (+ |++-> + |+--> - |-+-> + |—-->)   
|-+-> = [+ |000> + |010> - |100> - |110> - |001> - |011> + |101> + |111>] to [+ |000> + |010> - |100> + |110> - |001> - |011> + |101> - |111>] = (+ |++-> - |+--> + |-+-> + |—-->)   
|—--> = [+ |000> - |010> - |100> + |110> - |001> + |011> + |101> - |111>] to [+ |000> - |010> - |100> - |110> - |001> + |011> + |101> + |111>] = (- |++-> + |+--> + |-+-> + |—-->)

#notetoself #rocketscience #quantumcomputing

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