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

Abhishek Shukla, Mitali Sisodia, Anirban Pathak

Published May 18, 2018• 4 citations
OpenAlex

Abstract

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.

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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.
In circuit-based quantum computing the available gate set typically consists of single-qubit gates acting on each individual qubit and at least one entangling gate between pairs of qubits.In certain physical architectures, however, some qubits may be "hidden" and lacking direct addressability through dedicated control and readout lines, for instance, because of limited on-chip routing capabilities, or because the number of control lines becomes a limiting factor for many-qubit systems.In this case, no single-qubit operations can be applied to the hidden qubits and their state cannot be measured directly.Instead, they may be controlled and read out only via single-qubit operations on connected "control" qubits and a suitable set of two-qubit gates.We first discuss the impact of such restricted control capabilities on the performance of specific qubit coupling networks.We then experimentally demonstrate full control and measurement capabilities in a superconducting two-qubit device with local single-qubit control and iSWAP and controlledphase two-qubit interactions enabled by a tunable coupler.We further introduce an iterative tune-up process required to completely characterize the gate set used for quantum process tomography and evaluate the resulting gate fidelities.
Quantum computers are becoming a reality today due to the rapid progress made by researchers in the last years. In the process of building quantum computers, IBM has developed several versions-starting from 5-qubit architectures like IBM QX2 and IBM QX4 to larger 16- or 20-qubit architectures. These architectures support arbitrary rotations of a single qubit and a controlled negation (CNOT) involving two qubits. The two qubit operations come with added coupling-map restrictions that only allow specific physical qubits to be the control and target qubits of the operation. In order to execute a quantum circuit on the IBM QX architecture, CNOT gates must satisfy the so-called coupling constraints of the architecture. Previous works addressed this issue with the objective of reducing the number of gates and the circuit depth. However, in this article, we show that further improvements are possible. To this end, we present a general approach for further improving the number of gate operations and depth of the mapped circuit. The proposed approach encompasses the selection of physical qubits, determining initial and local permutations efficiently to obtain the final circuit mapped to the given IBM QX architecture. Through experiments, improvements are observed over existing methods in terms of the number of gates and circuit depth.
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.
Abstract The potential of achieving computational hardware with quantum advantage depends heavily on the quality of quantum gate operations. However, the presence of imperfect two-qubit gates poses a significant challenge and acts as a major obstacle in developing scalable quantum information processors. Google’s Quantum AI and collaborators claimed to have conducted a supremacy regime experiment. In this experiment, a new two-qubit universal gate called theSycamoregate is constructed and employed to generate random quantum circuits (RQCs), using a programmable quantum processor with 53 qubits. These computations were carried out in a computational state space of size 9×10159 \times 10^{15}9×1015 9×1015 . Nevertheless, even in strictly-controlled laboratory settings, quantum information on quantum processors is susceptible to various disturbances, including undesired interaction with the surroundings and imperfections in the quantum state. To address this issue, we conduct both quantum state tomography (QST) and quantum process tomography (QPT) experiments on Google’sSycamoregate using different artificial architectural superconducting quantum computer. Furthermore, to demonstrate how errors affect gate fidelity at the level of quantum circuits, we design and conduct full QST experiments for the five-qubit eight-cycle circuit, which was introduced as an example of the programability of Google’sSycamorequantum processor. These quantum tomography experiments are conducted in three distinct environments: noise-free, noisy simulation, and on IBM Quantum’s genuine quantum computer. Our results offer valuable insights into the performance of IBM Quantum’s hardware and the robustness ofSycamoregates within this experimental setup. These findings contribute to our understanding of quantum hardware performance and provide valuable information for optimizing quantum algorithms for practical applications.
Abstract The emergence of noisy intermediate-scale quantum processors marked a pivotal stage in quantum computing, enabling the first demonstrations of quantum computational advantage despite limitations in qubit count, connectivity, and gate fidelity. Among the earliest and most accessible NISQ platforms were the IBM Quantum TM^\texttt {TM}TM TM computers, which provided an open testbed for algorithm development, benchmarking, and error mitigation. Crucially, many of these pioneering quantum computers have since been retired, rendering their performance records fragmented and at risk of permanent loss. This work presents a comprehensive benchmarking study of these early IBM quantum computers, documenting their architectural layouts, qubit connectivity, native gate sets, coherence properties, effective Hamiltonians, control mechanisms, error rates, and operational performance. We reconstruct the operational profiles of these quantum computers and highlight the trends, trade-offs, and limitations that characterized superconducting quantum hardware in the NISQ era. This study establishes a historical baseline for assessing progress in quantum hardware development, offering essential guidance on error scaling, coherence limitations, and architectural trade-offs for designing next-generation quantum hardware. These insights directly inform superconducting quantum architecture design, compilation strategies, and error-resilient algorithms on the path toward fault-tolerant quantum computation.
Abstract A single-shot entangling gate plays a crucial role in quantum information processing due to its high fidelity. This operation gate is fast to create a maximally entangled state and forms a universal gate set for quantum computing. Currently, the preparation and demonstration of multi-qubit entanglement are achieved based on sequences of single- and two-qubit operations, yielding lower fidelity and requiring longer execution time. Here, we demonstrate by numerically simulating the use of quantum process tomography to fully characterize the performance of a single-shot three-qubit entangling gate. This gate is used to create a Greenberger–Horne–Zeilinger entangled state in Sakhouf et al (2021 J. Phys. B: At. Mol. Opt. Phys. 54 175501), directly generated by three transmon-type superconducting qubits which are mediated by a resonator with the assistance of a microwave field. Comparing ideal and simulated quantum process tomography, we characterize the entangling gate performance by calculating the mean fidelity achieving a high value ≻ 0.93 .