Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Quantum Information

Experimental demonstration of optimized quantum process tomography on the IBM quantum experience

Akshay Vijay Gaikwad, Krishna Shende, Kavita Dorai

Published Oct 7, 2020• 9 citations
Publisher

Abstract

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.

DOI
10.1142/s0219749920400043

Related papers

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

Akshay Vijay Gaikwad, Krishna Shende, Arvind +1 more

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.

arXiv:2107.07462•Scientific Reports•Mar 7, 2022•17 citations

Novel techniques for efficient quantum state tomography and quantum process tomography and their experimental implementation

Akshay Vijay Gaikwad

This thesis actively focuses on designing, analyzing, and experimentally implementing various QST and QPT protocols using an NMR ensemble quantum processor and superconducting qubit-based IBM cloud quantum processor. Part of the thesis also includes a study of duality quantum simulation algorithms and Sz-Nagy's dilation algorithm on NMR where several 2-qubit non-unitary quantum channels were simulated using only a single ancilla qubit. The work carried out in the thesis mainly addresses several important issues in experimental QST and QPT which include: i) dealing with invalid experimental density (process) matrices using constraint convex optimization (CCO) method, ii) scalable QST and QPT using incomplete measurements via compressed sensing (CS) algorithm and artificial neural network (ANN) technique, iii) selective and direct measurement of unknown quantum states and processes using the concept of quantum 2-design states and weak measurement (WM) approach and iv) quantum simulation and characterization of open quantum dynamics using the dilation technique.

arXiv:2401.09941•Jan 18, 2024•0 citations

Compressed sensing quantum process tomography for superconducting quantum gates

Andrey V. Rodionov, Andrzej Veitia, R. Barends +6 more

We apply the method of compressed sensing (CS) quantum process tomography (QPT) to characterize quantum gates based on superconducting Xmon and phase qubits. Using experimental data for a two-qubit controlled-Z gate, we obtain an estimate for the process matrix $\ensuremath{\chi}$ with reasonably high fidelity compared to full QPT, but using a significantly reduced set of initial states and measurement configurations. We show that the CS method still works when the amount of used data is so small that the standard QPT would have an underdetermined system of equations. We also apply the CS method to the analysis of the three-qubit Toffoli gate with numerically added noise, and similarly show that the method works well for a substantially reduced set of data. For the CS calculations, we use two different bases in which the process matrix $\ensuremath{\chi}$ is approximately sparse, and show that the resulting estimates of the process matrices match each other with reasonably high fidelity. For both two-qubit and three-qubit gates, we characterize the quantum process by not only its process matrix and fidelity, but also by the corresponding standard deviation, defined via variation of the state fidelity for different initial states.

arXiv:1407.0761•Physical Review B•Oct 9, 2014•71 citations

Complete characterization of the single-qubit quantum gates used in the IBM quantum processors

Abhishek Shukla, Mitali Sisodia, Anirban Pathak

Quantum process tomography of each single-qubit quantum gate used in the IBM quantum processors is performed to compute gate error in order to check viability of complex quantum operations in the superconductivity-based quantum computers introduced by IBM and to compare the quality of these gates with the corresponding gates implemented using other technologies. Gate fidelities for all the allowed gates for every allowed position (i.e., by placing the gates in different qubit lines) have been obtained and reported for IBM QX4 architecture. Gate fidelities are observed to be lower than the corresponding values obtained in the other technologies, like NMR. Further, gate fidelities for all the single-qubit gates are obtained for IBM QX2 architecture by placing the gates in the third qubit line ($q[2]$). It's observed that the IBM QX4 architecture yields better gate fidelity compared to IBM QX2 in all cases except the case of $\operatorname{Y}$ gate as far as the gate fidelity corresponding to the third qubit line is concerned. In general, the analysis performed here leads to a conclusion that a considerable technological improvement would be inevitable to achieve the desired scalability required for the realization of complex quantum operations.

•May 18, 2018•4 citations

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

Akshay Vijay Gaikwad, Diksha Rehal, Amandeep Singh +2 more

We present the 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 subsystem 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.

arXiv:1707.06739•Physical Review A•Feb 7, 2018•36 citations

Bootstrapping quantum process tomography via a perturbative ansatz

L. C. G. Govia, G. J. Ribeill, Diego Ristè +2 more

Quantum process tomography has become increasingly critical as the need grows for robust verification and validation of candidate quantum processors, since it plays a key role in both performance assessment and debugging. However, as these processors grow in size, standard process tomography becomes an almost impossible task. Here, we present an approach for efficient quantum process tomography that uses a physically motivated ansatz for an unknown quantum process. Our ansatz bootstraps to an effective description for an unknown process on a multi-qubit processor from pairwise two-qubit tomographic data. Further, our approach can inherit insensitivity to system preparation and measurement error from the two-qubit tomography scheme. We benchmark our approach using numerical simulation of noisy three-qubit gates, and show that it produces highly accurate characterizations of quantum processes. Further, we demonstrate our approach experimentally on a superconducting quantum processor, building three-qubit gate reconstructions from two-qubit tomographic data.

arXiv:1902.10821•Nature Communications•Feb 27, 2020•32 citations
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.
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.
This thesis actively focuses on designing, analyzing, and experimentally implementing various QST and QPT protocols using an NMR ensemble quantum processor and superconducting qubit-based IBM cloud quantum processor. Part of the thesis also includes a study of duality quantum simulation algorithms and Sz-Nagy's dilation algorithm on NMR where several 2-qubit non-unitary quantum channels were simulated using only a single ancilla qubit. The work carried out in the thesis mainly addresses several important issues in experimental QST and QPT which include: i) dealing with invalid experimental density (process) matrices using constraint convex optimization (CCO) method, ii) scalable QST and QPT using incomplete measurements via compressed sensing (CS) algorithm and artificial neural network (ANN) technique, iii) selective and direct measurement of unknown quantum states and processes using the concept of quantum 2-design states and weak measurement (WM) approach and iv) quantum simulation and characterization of open quantum dynamics using the dilation technique.
We apply the method of compressed sensing (CS) quantum process tomography (QPT) to characterize quantum gates based on superconducting Xmon and phase qubits. Using experimental data for a two-qubit controlled-Z gate, we obtain an estimate for the process matrix $\ensuremath{\chi}$ with reasonably high fidelity compared to full QPT, but using a significantly reduced set of initial states and measurement configurations. We show that the CS method still works when the amount of used data is so small that the standard QPT would have an underdetermined system of equations. We also apply the CS method to the analysis of the three-qubit Toffoli gate with numerically added noise, and similarly show that the method works well for a substantially reduced set of data. For the CS calculations, we use two different bases in which the process matrix $\ensuremath{\chi}$ is approximately sparse, and show that the resulting estimates of the process matrices match each other with reasonably high fidelity. For both two-qubit and three-qubit gates, we characterize the quantum process by not only its process matrix and fidelity, but also by the corresponding standard deviation, defined via variation of the state fidelity for different initial states.
Quantum process tomography of each single-qubit quantum gate used in the IBM quantum processors is performed to compute gate error in order to check viability of complex quantum operations in the superconductivity-based quantum computers introduced by IBM and to compare the quality of these gates with the corresponding gates implemented using other technologies. Gate fidelities for all the allowed gates for every allowed position (i.e., by placing the gates in different qubit lines) have been obtained and reported for IBM QX4 architecture. Gate fidelities are observed to be lower than the corresponding values obtained in the other technologies, like NMR. Further, gate fidelities for all the single-qubit gates are obtained for IBM QX2 architecture by placing the gates in the third qubit line (q[2]q[2]q[2]). It's observed that the IBM QX4 architecture yields better gate fidelity compared to IBM QX2 in all cases except the case of Y⁡\operatorname{Y}Y gate as far as the gate fidelity corresponding to the third qubit line is concerned. In general, the analysis performed here leads to a conclusion that a considerable technological improvement would be inevitable to achieve the desired scalability required for the realization of complex quantum operations.
We present the 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 subsystem 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.
Quantum process tomography has become increasingly critical as the need grows for robust verification and validation of candidate quantum processors, since it plays a key role in both performance assessment and debugging. However, as these processors grow in size, standard process tomography becomes an almost impossible task. Here, we present an approach for efficient quantum process tomography that uses a physically motivated ansatz for an unknown quantum process. Our ansatz bootstraps to an effective description for an unknown process on a multi-qubit processor from pairwise two-qubit tomographic data. Further, our approach can inherit insensitivity to system preparation and measurement error from the two-qubit tomography scheme. We benchmark our approach using numerical simulation of noisy three-qubit gates, and show that it produces highly accurate characterizations of quantum processes. Further, we demonstrate our approach experimentally on a superconducting quantum processor, building three-qubit gate reconstructions from two-qubit tomographic data.