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arXiv:1106.2906 · Bulletin of the Russian Academy of Sciences Physics

Accuracy characteristics for quantum process tomography using superconductor phase qubits

Yu. I. Bogdanov, S. A. Nuyanzin

Published Feb 1, 2012• 4 citations
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Abstract

A method for the precision statistical control of quantum processes is developed on the basis of applications of superconductor phase qubits. A detailed analysis of tomographic accuracy for a 2-qubit SQiSW gate arising due to capacitive coupling between qubits is performed by means of universal quantum tomography. The presented approach can be used to solve problems of quality and efficiency in superconductor quantum information technologies.

DOI
10.3103/s1062873812020049

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The dissertation "Quantum Process Tomography: High Fidelity Methods" focuses on quantum tomographic methods using repeated (multi-pass) applications of quantum processes, which allows for the amplification of very small errors to measurable levels. The thesis is based on three studies that illustrate this approach. The first study introduces the Multi-pass Quantum Process Tomography (MQPT) method, which mitigates the measurement errors caused by state preparation and measurement (SPAM), readout errors, and statistical (shot noise) errors. The method employs some standard tomographic techniques applied to a multi-pass quantum gate or process, after which the single process is determined with significantly higher accuracy and precision through post-processing. The effectiveness of MQPT has been demonstrated through simulations and experiments on IBM Quantum processors, achieving substantial enhancement on accuracy and precision. The second study investigates the dynamics of quantum multi-level systems interacting with pulse sequences that exhibit Wigner-Majorana and Morris-Shore symmetries. Exact analytical formulas have been derived to describe these processes, revealing important characteristics of these interactions. The third study focuses on precision methods for characterization of high fidelity Raman qubit gates with Morris-Shore dynamic symmetry. By repeatedly applying the same gate, coherent errors are amplified to measurable levels, enabling more precise...

•Sep 17, 2024•0 citations
A method for the precision statistical control of quantum processes is developed on the basis of applications of superconductor phase qubits. A detailed analysis of tomographic accuracy for a 2-qubit SQiSW gate arising due to capacitive coupling between qubits is performed by means of universal quantum tomography. The presented approach can be used to solve problems of quality and efficiency in superconductor quantum information technologies.
A general approach to the provision of the quality and efficiency of quantum information technologies is proposed. The approach is based on the analysis of quantum noise generated on the implementation of quantum operations. The method of precision quantum measurements of logic quantum gates based on superconducting phase qubits is developed. The universal method of quantum state and process tomography is used to carry out a comprehensive analysis of the fidelity of the tomography of two-qubit SQiSW, CNOT, and CZ gates arising from the capacitive coupling between qubits. The method of optimization of quantum process tomography is proposed to provide a substantially higher degree of adequacy and fidelity compared to those attained by previously known methods. The examples of simulation of depolarizing quantum noise and amplitude- and phase-relaxation processes on the implementation of quantum operations in registers are considered.
We experimentally demonstrate quantum process tomography of controlled-Z and controlled-NOT gates using capacitively coupled superconducting phase qubits. These gates are realized by using the ∣2⟩|2⟩∣2⟩ state of the phase qubit. We obtain a process fidelity of 0.70 for the controlled phase and 0.56 for the controlled-NOT gate, with the loss of fidelity mostly due to single-qubit decoherence. The controlled-Z gate is also used to demonstrate a two-qubit Deutsch-Jozsa algorithm with a single function query.
In quantum information transformation and quantum computation, the most critical issues are security and accuracy. These features, therefore, stimulate research on quantum state characterization. A characterization tool, Quantum state tomography, reconstructs the density matrix of an unknown quantum state. Theoretically, reconstructing an unknown state using this method can be arbitrarily accurate. However, this is less practical owing to the huge burden of measurements and data processing for large numbers of qubits. Even comprising an efficient estimator and a precise algorithm, an optimal tomographic framework can also be overburdened owing to the exponential growth of the measurements. Moreover, the consequential postprocessing of huge amounts of data challenges the capacity of computers. Thus, it is crucial to build an efficient framework that requires fewer measurements but yields an expected accuracy. To this end, we built a tomography schema by which only a few Pauli measurements enable an accurate tomographic reconstruction. Subsequently, this schema was verified as efficient and accurate through numerical simulations on the tomography of multi-qubit quantum states. Furthermore, this schema was proven to be robust through numerical simulations on a noisy superconducting qubit system. Therefore, the tomography schema paves an alternatively effective way to reconstruct the density matrix of a quantum state owing to its efficiency and accuracy, which are essential for quantum state tomography.
Quantum tomography is a widely applicable tool for complete characterization of quantum states and processes. We develop a method for precision-guaranteed quantum process tomography. With the use of the Choi–Jamiołkowski isomorphism, we generalize the recently suggested extended norm minimization estimator for the case of quantum processes. Our estimator is based on the Hilbert–Schmidt distance for quantum processes. Specifically, we discuss the application of our method for characterizing quantum gates of a superconducting quantum processor in the framework of the IBM Q Experience.
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.
The dissertation "Quantum Process Tomography: High Fidelity Methods" focuses on quantum tomographic methods using repeated (multi-pass) applications of quantum processes, which allows for the amplification of very small errors to measurable levels. The thesis is based on three studies that illustrate this approach. The first study introduces the Multi-pass Quantum Process Tomography (MQPT) method, which mitigates the measurement errors caused by state preparation and measurement (SPAM), readout errors, and statistical (shot noise) errors. The method employs some standard tomographic techniques applied to a multi-pass quantum gate or process, after which the single process is determined with significantly higher accuracy and precision through post-processing. The effectiveness of MQPT has been demonstrated through simulations and experiments on IBM Quantum processors, achieving substantial enhancement on accuracy and precision. The second study investigates the dynamics of quantum multi-level systems interacting with pulse sequences that exhibit Wigner-Majorana and Morris-Shore symmetries. Exact analytical formulas have been derived to describe these processes, revealing important characteristics of these interactions. The third study focuses on precision methods for characterization of high fidelity Raman qubit gates with Morris-Shore dynamic symmetry. By repeatedly applying the same gate, coherent errors are amplified to measurable levels, enabling more precise...