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

Advanced Quantum Technologies

Direct Quantum Process Tomography for Arbitrary Qubit Systems Without Auxiliary States

Zhiyuan Wang, Zijing Zhang

Published Mar 24, 2025• 1 citation
Publisher

Abstract

Abstract Quantum process tomography is an effective method for measuring the quantum channel parameters in the field of quantum information. However, standard quantum process tomography (SQPT) cannot obtain arbitrarily specific process–matrix elements because it requires a global reconstruction algorithm. Direct quantum tomography can be used to obtain specific matrix elements of interest without the need for a global reconstruction algorithm. Therefore, direct process quantum tomography (DQPT) has attracted widespread attention. DQPT based on weak measurements has been recently proposed. However, additional auxiliary states and post‐selection processes are necessary in these schemes, which increases the complexity of practical experiments and reduces the utilization of measurement resources. In this study, a DQPT protocol without the assistance of pointer states is proposed, which reduces the complexity of practical experiments. Subsequently, the scheme is generalized to arbitrary qubit systems and experimentally perform the protocol on a nuclear magnetic resonance (NMR) system provided by a quantum cloud platform. Finally, considering that when the qubit resources are insufficient, a superimposed coherent state is used as the pointer state to complete the direct characterization of a quantum process. The measurement protocol is easily scalable and integrated, laying the foundation for direct tomography on a chip.

DOI
10.1002/qute.202500002

Related papers

Efficient non-destructive direct characterization of arbitrary many-body quantum channels

Zhiyuan Wang, Qing He, Zijing Zhang

Quantum process tomography (QPT) is a crucial technique for characterizing unknown quantum channels. However, traditional QPT methods encounter scalability problems as the particle numbers increase, requiring exponentially more state preparations and measurement operators. The characteristics of sparse target channels (e.g., multiqubit phase-shift gates) can be obtained by measuring only a few specific matrix elements without requiring global QPT. Therefore, direct quantum channel characterization is vital. This paper proposes a direct protocol for both qubit and qudit systems that extracts specific process matrix elements without full reconstruction. The measurement operator requirements remain independent of system size and dimensionality. Notably, the proposed protocol uses nondestructive measurements and preserves qubits after evolution through unknown processes for potential reuse, making it uniquely promising for applications such as real-time monitoring of noise processes in quantum error correction and real-time feedback control requiring quantum state preservation. To validate the theoretical correctness of our approach, we conducted experimental demonstrations of both the unitary and non-unitary processes of single qubits using a nuclear magnetic resonance system on the SpinQ quantum cloud platform. The experimental results confirmed the correctness and effectiveness of the proposed method.

npj Quantum Information•Dec 14, 2025•1 citation

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

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

Direct measurement for general quantum states using parametric quantum circuits

Zhiyuan Wang, Zijing Zhang, Yuan Zhe Zhao

Abstract In the field of quantum information, the acquisition of information for unknown quantum states is very important. When we only need to obtain specific elements of a state density matrix, the traditional quantum state tomography will become very complicated, because it requires a global quantum state reconstruction. Direct measurement of the quantum state allows us to obtain arbitrary specific matrix elements of the quantum state without state reconstruction, so direct measurement schemes have obtained extensive attention. Recently, some direct measurement schemes based on weak values have been proposed, but extra auxiliary states in these schemes are necessary and it will increase the complexity of the practical experiment. Meanwhile, the post-selection process in the scheme will reduce the utilization of resources. In order to avoid these disadvantages, a direct measurement scheme without auxiliary states is proposed in this paper. In this scheme, we achieve the direct measurement of quantum states by using quantum circuits, then we extend it to the measurement of general multi-particle states and complete the error analysis. Finally, when we take into account the dephasing of the quantum states, we modify the circuits and the modified circuits still work for the dephasing case.

Communications in Theoretical Physics•Nov 1, 2022•2 citations

Pauli transfer matrix direct reconstruction: channel characterization without full process tomography

Simone Roncallo, Lorenzo Maccone, Chiara Macchiavello

Abstract We present a tomographic protocol for the characterization of multiqubit quantum channels. We discuss a specific class of input states, for which the set of Pauli measurements at the output of the channel directly relates to its Pauli transfer matrix components. We compare our results to those of standard quantum process tomography, showing an exponential reduction in the number of different experimental configurations required by a single matrix element extraction, while keeping the same number of shots. This paves the way for more efficient experimental implementations, whenever a selective knowledge of the Pauli transfer matrix is needed. We provide several examples and simulations.

arXiv:2212.11968•Quantum Science and Technology•Oct 19, 2023•4 citations

Single-qubit reaped quantum state tomography

Mahn‐Soo Choi

Quantum state tomography is the experimental procedure of determining an unknown state. It is not only essential for the verification of resources and processors of quantum information but is also important in its own right with regard to the foundation of quantum mechanics. Standard methods have been elusive for large systems because of the enormous number of observables to be measured and the exponential complexity of data post-processing. Here, we propose a new scheme of quantum state tomography that requires the measurement of only three observables (acting jointly on the system and pointer) regardless of the size of the system. The system is coupled to a "pointer" of single qubit, and the wavefunction of the system is "reaped" onto the pointer upon the measurement of the system. Subsequently, standard two-state tomography on the pointer and classical post-processing are used to reconstruct the quantum state of the system. We also developed an efficient and scalable iterative maximum likelihood algorithm to estimate states from statistically incomplete data.

arXiv:2206.09562•Scientific Reports•Jun 29, 2022•4 citations
Abstract Quantum process tomography is an effective method for measuring the quantum channel parameters in the field of quantum information. However, standard quantum process tomography (SQPT) cannot obtain arbitrarily specific process–matrix elements because it requires a global reconstruction algorithm. Direct quantum tomography can be used to obtain specific matrix elements of interest without the need for a global reconstruction algorithm. Therefore, direct process quantum tomography (DQPT) has attracted widespread attention. DQPT based on weak measurements has been recently proposed. However, additional auxiliary states and post‐selection processes are necessary in these schemes, which increases the complexity of practical experiments and reduces the utilization of measurement resources. In this study, a DQPT protocol without the assistance of pointer states is proposed, which reduces the complexity of practical experiments. Subsequently, the scheme is generalized to arbitrary qubit systems and experimentally perform the protocol on a nuclear magnetic resonance (NMR) system provided by a quantum cloud platform. Finally, considering that when the qubit resources are insufficient, a superimposed coherent state is used as the pointer state to complete the direct characterization of a quantum process. The measurement protocol is easily scalable and integrated, laying the foundation for direct tomography on a chip.
Quantum process tomography (QPT) is a crucial technique for characterizing unknown quantum channels. However, traditional QPT methods encounter scalability problems as the particle numbers increase, requiring exponentially more state preparations and measurement operators. The characteristics of sparse target channels (e.g., multiqubit phase-shift gates) can be obtained by measuring only a few specific matrix elements without requiring global QPT. Therefore, direct quantum channel characterization is vital. This paper proposes a direct protocol for both qubit and qudit systems that extracts specific process matrix elements without full reconstruction. The measurement operator requirements remain independent of system size and dimensionality. Notably, the proposed protocol uses nondestructive measurements and preserves qubits after evolution through unknown processes for potential reuse, making it uniquely promising for applications such as real-time monitoring of noise processes in quantum error correction and real-time feedback control requiring quantum state preservation. To validate the theoretical correctness of our approach, we conducted experimental demonstrations of both the unitary and non-unitary processes of single qubits using a nuclear magnetic resonance system on the SpinQ quantum cloud platform. The experimental results confirmed the correctness and effectiveness of the proposed method.
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 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.
Abstract In the field of quantum information, the acquisition of information for unknown quantum states is very important. When we only need to obtain specific elements of a state density matrix, the traditional quantum state tomography will become very complicated, because it requires a global quantum state reconstruction. Direct measurement of the quantum state allows us to obtain arbitrary specific matrix elements of the quantum state without state reconstruction, so direct measurement schemes have obtained extensive attention. Recently, some direct measurement schemes based on weak values have been proposed, but extra auxiliary states in these schemes are necessary and it will increase the complexity of the practical experiment. Meanwhile, the post-selection process in the scheme will reduce the utilization of resources. In order to avoid these disadvantages, a direct measurement scheme without auxiliary states is proposed in this paper. In this scheme, we achieve the direct measurement of quantum states by using quantum circuits, then we extend it to the measurement of general multi-particle states and complete the error analysis. Finally, when we take into account the dephasing of the quantum states, we modify the circuits and the modified circuits still work for the dephasing case.
Abstract We present a tomographic protocol for the characterization of multiqubit quantum channels. We discuss a specific class of input states, for which the set of Pauli measurements at the output of the channel directly relates to its Pauli transfer matrix components. We compare our results to those of standard quantum process tomography, showing an exponential reduction in the number of different experimental configurations required by a single matrix element extraction, while keeping the same number of shots. This paves the way for more efficient experimental implementations, whenever a selective knowledge of the Pauli transfer matrix is needed. We provide several examples and simulations.
Quantum state tomography is the experimental procedure of determining an unknown state. It is not only essential for the verification of resources and processors of quantum information but is also important in its own right with regard to the foundation of quantum mechanics. Standard methods have been elusive for large systems because of the enormous number of observables to be measured and the exponential complexity of data post-processing. Here, we propose a new scheme of quantum state tomography that requires the measurement of only three observables (acting jointly on the system and pointer) regardless of the size of the system. The system is coupled to a "pointer" of single qubit, and the wavefunction of the system is "reaped" onto the pointer upon the measurement of the system. Subsequently, standard two-state tomography on the pointer and classical post-processing are used to reconstruct the quantum state of the system. We also developed an efficient and scalable iterative maximum likelihood algorithm to estimate states from statistically incomplete data.