What is the most expensive part of quantum device characterization? Clearly, the answer is quantum process tomography. However, especially for noisy intermediate-scale quantum (NISQ) computers, a comprehensive understanding of the noisy quantum dynamics is essential in interpreting the computational output. In this work, we introduce an efficient method -- Procrustes tomography -- that outperforms established methods in a number of aspects. After a pedagogical and constructive introduction, we demonstrate the utility of the method for representative examples of noisy quantum channels.
What is the most expensive part of quantum device characterization? Clearly, the answer is quantum process tomography. However, especially for noisy intermediate-scale quantum (NISQ) computers, a comprehensive understanding of the noisy quantum dynamics is essential in interpreting the computational output. In this work, we introduce an efficient method -- Procrustes tomography -- that outperforms established methods in a number of aspects. After a pedagogical and constructive introduction, we demonstrate the utility of the method for representative examples of noisy quantum channels.
What is the most expensive part of quantum device characterization? Clearly, the answer is quantum process tomography. However, especially for noisy intermediate-scale quantum (NISQ) computers, a comprehensive understanding of the noisy quantum dynamics is essential in interpreting the computational output. In this work, we introduce an efficient method -- Procrustes tomography -- that outperforms established methods in a number of aspects. After a pedagogical and constructive introduction, we demonstrate the utility of the method for representative examples of noisy quantum channels.
Characterisation protocols have so far played a central role in the development of noisy intermediate-scale quantum (NISQ) computers capable of impressive quantum feats. This trajectory is expected to continue in building the next generation of devices: ones that can surpass classical computers for particular tasks -- but progress in characterisation must keep up with the complexities of intricate device noise. A missing piece in the zoo of characterisation procedures is tomography which can completely describe non-Markovian dynamics over a given time frame. Here, we formally introduce a generalisation of quantum process tomography, which we call process tensor tomography. We detail the experimental requirements, construct the necessary post-processing algorithms for maximum-likelihood estimation, outline the best-practice aspects for accurate results, and make the procedure efficient for low-memory processes. The characterisation is a pathway to diagnostics and informed control of correlated noise. As an example application of the hardware-agnostic technique, we show how its predictive control can be used to substantially improve multi-time circuit fidelities on superconducting quantum devices. Our methods could form the core for carefully developed software that may help hardware consistently pass the fault-tolerant noise threshold.
Quantum state tomography (QST) is a fundamental technique for characterizing quantum states, traditionally employed in research laboratories with highly controlled environments. However, the burgeoning field of quantum computing faces the significant challenge of deploying and verifying quantum hardware in the presence of noise and decoherence, characteristics inherent in current Noisy Intermediate-Scale Quantum (NISQ) devices. This paper proposes an adapted QST algorithm designed to overcome these limitations. The core idea is to systematically reconstruct the density matrix of a qubit or a small quantum system using a series of carefully designed measurements. We address the impact of noise by incorporating error mitigation strategies within the reconstruction process. The algorithm's performance is evaluated through theoretical analysis and conceptual implementation, highlighting its potential to provide a practical and efficient method for hardware verification of NISQ computers. This work establishes a novel approach for characterizing and debugging NISQ hardware, a critical step toward realizing the full potential of quantum computation.
Quantum process tomography is a powerful tool for understanding quantum channels and characterizing the properties of quantum devices. Inspired by recent advances using classical shadows in quantum state tomography [H.-Y. Huang, R. Kueng, and J. Preskill, .], we have developed ShadowQPT, a classical shadow method for quantum process tomography. We introduce two related formulations with and without ancilla qubits. ShadowQPT stochastically reconstructs the Choi matrix of the device allowing for an classical evaluation of the device on arbitrary inputs with respect to arbitrary outputs. Using shadows, we then show how to compute overlaps, generate all k -weight reduced processes, and perform reconstruction via Hamiltonian learning. These latter two tasks are efficient for large systems as the number of quantum measurements needed scales only logarithmically with the number of qubits. A number of additional approximations and improvements are developed, including the use of a pair-factorized Clifford shadow and a series of postprocessing techniques that significantly enhance the accuracy for recovering the quantum channel. We have implemented ShadowQPT using both Pauli and Clifford measurements on the IonQ trapped ion quantum computer for quantum processes up to n=4 qubits, and we achieved good performance. Published by the American Physical Society 2024
In recent years, Noisy Intermediate Scale Quantum (NISQ) computers have been widely used as a test bed for quantum dynamics. This work provides a new hardware-agnostic framework for modelling the Markovian noise and dynamics of quantum systems in benchmark procedures used to evaluate device performance. As an accessible example, the application and performance of this framework is demonstrated on IBM Quantum computers. This framework serves to extract multiple calibration parameters simultaneously through a simplified process which is more reliable than previously studied calibration experiments and tomographic procedures. Additionally, this method allows for real-time calibration of several hardware parameters of a quantum computer within a comprehensive procedure, providing quantitative insight into the performance of each device to be accounted for in future quantum circuits. The framework proposed here has the additional benefit of highlighting the consistency among qubit pairs when extracting parameters, which leads to a less computationally expensive calibration process than evaluating the entire device at once.
A significant amount of research is currently devoted to quantum technologies, i.e., technologies that harness the complex features of quantum systems for practical purposes. Remarkably, these have the potential to shape the way we will live in the future by, for example, providing new ways of breaking the current cryptographic security measures or by exponentially enhancing the computational capability of computers. This, in turn, could serve as a means for studying phenomena so complex that they render classical computers completely unusable. With these promises at hand, methods that efficiently certify the correct functioning of quantum devices and computations become of paramount importance. Specifically, it is often required to assess a characterization of the quantum states that come out from a specific computation or experiment. The traditional method of quantum state tomography relies on a rather straightforward but brute-force approach to reconstruct the full density matrix that encodes a quantum state. This method is highly demanding because of the curse of dimensionality, according to which the number of required measurements scales with the system’s dimension, and thus exponentially with the number of qubits. As the quantum protocols demand a progressively higher number of qubits, overall, a complete characterization of quantum states through tomography loses its effectiveness, thus calling for a partial but simpler reconstruction of states. Furthermore, an additional obstacle must be taken into account. In particular, the same complex features of the quantum realm that would help to navigate through the sea of potential applications hinder a growth of the current technological state of the art, which indeed is limited within the so-called NISQ (Noisy Intermediate-Scale Quantum) devices. These, as the name suggests, are characterized by inevitable noises and imperfections, and as such are not advanced enough for achieving a real quantum advantage in the near term. In this Thesis we are going to discuss new techniques for the estimation of properties of unknown quantum states in the context of quantum information science. The protocols that we will present are flexible enough to not only include state tomography within them, but to also adapt to noises and imperfections present in the computational devices. Ivan Palmisano was funded by the CITI-GENS project. This project received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Actions COFUND Action (Grant Agreement No 945231). All views expressed in this article are strictly those of the author and may under no circumstances be regarded as an official position of the European Research Executive Agency or the European Commission.