Fig. 5 | npj Quantum Information

Fig. 5

From: Variational quantum state diagonalization

Fig. 5

Diagonalization test circuits used in VQSD. (a) The Destructive Swap Test computes Tr(στ) via a depth-two circuit. (b) The Diagonalized Inner Product (DIP) Test computes \({\mathrm{Tr}}({\cal{Z}}(\sigma ){\cal{Z}}(\tau ))\) via a depth-one circuit. (c) The Partially Diagonalized Inner Product (PDIP) Test computes \({\mathrm{Tr}}({\cal{Z}}_{\boldsymbol{j}}(\sigma ){\cal{Z}}_{\boldsymbol{j}}(\tau ))\) via a depth-two circuit, for a particular set of qubits j. While the DIP test requires no postprocessing, the postprocessing for the Destructive Swap Test and the Partial DIP Test scales linearly in n

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