Quantum Circuits in the Dirac, Quayle and Bayes Conventions

Consider the following quantum state (expressed in Dirac notation):

where 0,1,2 label qubits. Suppose you wanted to portray this state graphically, as a “quantum circuit diagram”.

In my papers, I always draw quantum circuit diagrams with time pointing from right to left. I call this the Dirac convention. Thus, I would portray the state of Eq.(1) as

Fig.1

Most scientists in the field of quantum computing draw their diagrams with time pointing from left to right, in proper Christian order. I call this the Quayle convention (in honor of Dan Quayle, U.S. Vice President from 1989 to 1993). Thus, Dan Quayle would portray the state of Eq.(1) as

Fig.2

To go from Eq.(1) to Fig.2 requires an ugly, totally pointless reversal (akin to holding a grenade launcher backwards) of the operator ordering chosen by none other than Dirac himself in his 1930 book, and used by almost every physicist ever since.

Be forewarned that users of the Quayle convention consider the Dirac convention uncouth and un-Christian (used by sinful Jews and Muslims in their uncivilized Hebrew and Arabic languages).

It’s also interesting to ponder how Reverend Bayes would have portrayed this state. He would, no doubt, have done so as follows, in what I like to call the Bayes convention (i.e., as a quantum Bayesian network):

Fig.3

Dan Quayle Holding Grenade Launcher
(c)Bill Gentile/CORBIS
Date Photographed: June 13, 1989
Location: El Salvador
Photographer: Bill Gentile
(higher resolution available at Corbis)

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