Asymmetry of CNOT gate operation in superconducting transmon quantum
  processors using cross-resonance entangling
Controlled-NOT (CNOT) gates are commonly included in the standard gate set of
quantum processors and provide an important way to entangle qubits. For
fixed-frequency qubits using the cross-resonance entangling technique, using
the higher-frequency qubit to control the lower-frequency qubit enables much
shorter entangling times than using the lower-frequency qubit as the control.
Consequently, when implementing a CNOT gate where logical control by the
lower-frequency qubit is needed, compilers may implement this functionality by
using an equivalent circuit such as placing Hadamard gates on both qubits
before and after a CNOT gate controlled by the higher-frequency qubit. However,
since the implementation is different depending on which qubit is the control,
a natural question arises regarding the relative performance of the
implementations. We have explored this using quantum processors on the IBM Q
network. The basic circuit used consisted of operations to create a Bell State,
followed by the inverse operations so as to return the qubits to their initial
state in the absence of errors (Hadamard + CNOT + barrier + CNOT + Hadamard).
The circuit depth was varied using multiples of this basic circuit. An
asymmetry in the error of the final state was observed that increased with the
circuit depth. The strength and direction of the asymmetry was unique but
repeatable for each pair of coupled qubits tested. This observation suggests
that the asymmetry in CNOT implementation should be characterized for the
qubits of interest and incorporated into circuit transpilation to obtain the
best accuracy for a particular computation.
Travis Hurant Daniel D. Stancil