Experimental demonstration of selective quantum process tomography on an NMR quantum information processor

Abstract

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.

Experimental demonstration of fully contextual quantum correlations on an NMR quantum information processor

“…7 and Table VI for details of the experimental parameters). The Hamiltonian for a two-qubit system is given by [30] with the flip angle θ = 180 • and state fidelity 0.99 is depicted in Fig. 9.…”

“…Let π i be the observables (projectors) whose expectation value is to be measured in a state ρ = |ψ ψ|. Instead of measuring π , the state ρ can be mapped to ρ i by using ρ i = U i .ρ.U † i followed by a z-magnetization measurement of one of the qubits [30]. Table V The quantum circuit to achieve the required states to test the inequality C on a four-dimensional quantum system is shown in Fig.…”

Implementing efficient selective quantum process tomography of superconducting quantum gates on IBM quantum experience

“…The first implementation of SQPT was reported using optics 28 , which involved the preparation of special quantum states called quantum 2-design states. Further developments in SQPT include the generalization of the SQPT protocol for arbitrary dimensions 29 and an efficient protocol using an NMR quantum processor 30 . However, the experimental complexity involved in performing SQPT is still high, and better strategies to implement SQPT need to be designed.…”

Objective compressive quantum process tomography

“…The quality of computed results hinges on the reliability of tomographic certifications of these gates, each of which is a quantum process Φ represented by a positive Choi-Jamiołkowski operator ρ Φ [9,10], naively requiring O(d 4 ) informationally complete (IC) measurements [11][12][13][14] that are too resource-intensive to be implemented for large d. Ancilla- [15][16][17][18] and error-correction-based [19][20][21][22] quantum process tomography (QPT) were introduced to circumvent this problem. For highly-specific property prediction tasks, probing selected elements of ρ Φ is another option [23][24][25][26][27][28]. One attempt to directly reduce the measurement cost of QPT with non-IC measurements and entropy methods was reported [29].…”