We present the first NMR implementation of a scheme for selective and efficient quantum process tomography without ancilla. We generalize this scheme such that it can be implemented efficiently using only a set of measurements involving product operators. The method allows us to estimate any element of the quantum process matrix to a desired precision, provided a set of quantum states can be prepared efficiently. Our modified technique requires fewer experimental resources as compared to the standard implementation of selective and efficient quantum process tomography, as it exploits the special nature of NMR measurements to allow us to compute specific elements of the process matrix by a restrictive set of sub-system measurements. To demonstrate the efficacy of our scheme, we experimentally tomograph the processes corresponding to 'no operation', a controlled-NOT (CNOT), and a controlled-Hadamard gate on a two-qubit NMR quantum information processor, with high fidelities.
The experimental implementation of selective quantum process tomography (SQPT) involves computing individual elements of the process matrix with the help of a special set of states called quantum 2-design states. However, the number of experimental settings required to prepare input states from quantum 2-design states to selectively and precisely compute a desired element of the process matrix is still high, and hence constructing the corresponding unitary operations in the lab is a daunting task. In order to reduce the experimental complexity, we mathematically reformulated the standard SQPT problem, which we term the modified SQPT (MSQPT) method. We designed the generalized quantum circuit to prepare the required set of input states and formulated an efficient measurement strategy aimed at minimizing the experimental cost of SQPT. We experimentally demonstrated the MSQPT protocol on the IBM QX2 cloud quantum processor and selectively characterized various two- and three-qubit quantum gates.
We experimentally performed complete and optimized quantum process tomography of quantum gates implemented on superconducting qubit-based IBM QX2 quantum processor via two constrained convex optimization (CCO) techniques: least squares optimization and compressed sensing optimization. We studied the performance of these methods by comparing the experimental complexity involved and the experimental fidelities obtained. We experimentally characterized several two-qubit quantum gates: identity gate, a controlled-NOT gate, and a SWAP gate. The general quantum circuit is efficient in the sense that the data needed to perform CCO-based process tomography can be directly acquired by measuring only a single qubit. The quantum circuit can be extended to higher dimensions and is also valid for other experimental platforms.
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