Unexpected CZ gate about pygsti HOT 3 CLOSED

Adriaan, thanks for the nice description. This is a confirmed bug in pyGSTi 0.9.3 and earlier, and only currently fixed on the beta branch. The error arises due to an incorrect 1-qubit phase that is included when using the CZ(pi, Q0, Q1) specification in build_gateset. A similar error occurs when creating a CNOT gate from CX(pi, Q0, Q1). The CZ(theta) gate uses a Z-rotation, whose unitary is defined as exp(i 0.5 theta Z), which for theta=pi gives an extra phase factor of "i", namely

[ -i 0 ]
[ 0  i ]

instead of

[ 1 0 ]
[ 0 -1]

as desired.

The workaround for the time being is to do exactly as Adriaan suggests, which I'll repeat here in the context of creating a GateSet:

myGateset = pygsti.construction.build_gateset(
    [4], [('Q0','Q1')],['Gix','Giy','Gxi','Gyi'],
    [ "I(Q0):X(pi/2,Q1)", "I(Q0):Y(pi/2,Q1)", "X(pi/2,Q0):I(Q1)", "Y(pi/2,Q0):I(Q1)" ],
    prepLabels=['rho0'], prepExpressions=["0"],
    effectLabels=['E0','E1','E2'], effectExpressions=["0","1","2"],
    spamdefs={'upup': ('rho0','E0'), 'updn': ('rho0','E1'),
              'dnup': ('rho0','E2'), 'dndn': ('rho0','remainder') }, basis="pp")

cphaseUnitary =  np.diag([1,1,1,-1])
cphaseSuperOp_stdbasis = pygsti.unitary_to_process_mx(cphaseUnitary)
cphaseSuperOp_ppbasis = pygsti.std_to_pp(cphaseSuperOp_stdbasis)
myGateset['Gcphase'] = mySuperOp_ppbasis

The next version of pyGSTi (hopefully pushed out soon) will include fixes for these bugs as they affect the standard gate sets in pygsti.construction. I'm not sure if we'll change the implementation of CX and CZ, but will comment again once this has been resolved.

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@enielse Thanks for the update 👍

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So... "hopefully soon" ended up being a year later, but the recently released pyGSTi version 0.9.4 now includes a proper cphase gate - so you can do:

pygsti.construction.build_gate([4],[('Q0', 'Q1')], 'CPHASE(Q0, Q1)', basis='pp')

and

pygsti.construction.build_gate([4],[('Q0', 'Q1')], 'CNOT(Q0, Q1)', basis='pp')

to obtain the standard CPhase and CNot gates. Using the CZ and CX directives still act as before, since, for instance, we want the "Z" in a "controlled-Z" operation to have a consistent phase with a rotation by 0 degrees being the identity (not i times the identity). This means, somewhat non-intuitively, that 'CPHASE(Q0,Q1)' and 'CZ(pi,Q0,Q1)' are equivalent only up to a phase on the target qubit and not exactly equal.

Finally, it's worth noting that any standard gate set in pyGSTi, as of version 0.9.4, that includes a CPhase or CNot gate uses the standard form of these gates, which should be intuitive to most users.

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