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Register a new userMatchgate benchmarking: Scalable benchmarking of a continuous family of many-qubit gates
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We propose a method to reliably and efficiently extract the fidelity of many-qubit quantum circuits composed of continuously parametrized two-qubit gates called matchgates. This method, which we call matchgate benchmarking, relies on advanced techniques from randomized benchmarking as well as insights from the representation theory of matchgate circuits. We argue the formal correctness and scalability of the protocol, and moreover deploy it to estimate the performance of matchgate circuits generated by two-qubit XY spin interactions on a quantum processor.
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A key requirement for scalable quantum computing is that elementary quantum gates can be implemented with sufficiently low error. One method for determining the error behavior of a gate implementation is to perform process tomography. However, standard process tomography is limited by errors in state preparation, measurement and one-qubit gates. It suffers from inefficient scaling with number of qubits and does not detect adverse error-compounding when gates are composed in long sequences. An additional problem is due to the fact that desirable error probabilities for scalable quantum computing are of the order of 0.0001 or lower. Experimentally proving such low errors is challenging. We describe a randomized benchmarking method that yields estimates of the computationally relevant errors without relying on accurate state preparation and measurement. Since it involves long sequences of randomly chosen gates, it also verifies that error behavior is stable when used in long computations. We implemented randomized benchmarking on trapped atomic ion qubits, establishing a one-qubit error probability per randomized pi/2 pulse of 0.00482(17) in a particular experiment. We expect this error probability to be readily improved with straightforward technical modifications.
As quantum circuits increase in size, it is critical to establish scalable multiqubit fidelity metrics. Here we investigate three-qubit randomized benchmarking (RB) with fixed-frequency transmon qubits coupled to a common bus with pairwise microwave-activated interactions (cross-resonance). We measure, for the first time, a three-qubit error per Clifford of 0.106 for all-to-all gate connectivity and 0.207 for linear gate connectivity. Furthermore, by introducing mixed dimensionality simultaneous RB --- simultaneous one- and two-qubit RB --- we show that the three-qubit errors can be predicted from the one- and two-qubit errors. However, by introducing certain coherent errors to the gates we can increase the three-qubit error to 0.302, an increase that is not predicted by a proportionate increase in the one- and two-qubit errors from simultaneous RB. This demonstrates three-qubit RB as a unique multiqubit metric.
Any technology requires precise benchmarking of its components, and the quantum technologies are no exception. Randomized benchmarking allows for the relatively resource economical estimation of the average gate fidelity of quantum gates from the Clifford group, assuming identical noise levels for all gates, making use of suitable sequences of randomly chosen Clifford gates. In this work, we report significant progress on randomized benchmarking, by showing that it can be done for individual quantum gates outside the Clifford group, even for varying noise levels per quantum gate. This is possible at little overhead of quantum resources, but at the expense of a significant classical computational cost. At the heart of our analysis is a representation-theoretic framework that we develop here which is brought into contact with classical estimation techniques based on bootstrapping and matrix pencils. We demonstrate the functioning of the scheme at hand of benchmarking tensor powers of T-gates. Apart from its practical relevance, we expect this insight to be relevant as it highlights the role of assumptions made on unknown noise processes when characterizing quantum gates at high precision.
Targeting at the realization of scalable photonic quantum technologies, the generation of many photons, their propagation in large optical networks, and a subsequent detection and analysis of sophisticated quantum correlations are essential for the understanding of macroscopic quantum systems. In this experimental contribution, we explore the joint operation of all mentioned ingredients. We benchmark our time-multiplexing framework that includes a high-performance source of multiphoton states and a large multiplexing network, together with unique detectors with high photon-number resolution, readily available for distributing quantum light and measuring complex quantum correlations. Using an adaptive approach that employs flexible time bins, rather than static ones, we successfully verify high-order nonclassical correlations of many photons distributed over many modes. By exploiting the symmetry of our system and using powerful analysis tools, we can analyze correlations that would be inaccessible by classical means otherwise. In particular, we produce on the order of ten photons and distribute them over 64 modes. Nonclassicality is verified with correlation functions up to the 128th order and statistical significances of up to 20 standard deviations.
The possibility to utilize different types of two-qubit gates on a single quantum computing platform adds flexibility in the decomposition of quantum algorithms. A larger hardware-native gate set may decrease the number of required gates, provided that all gates are realized with high fidelity. Here, we benchmark both controlled-Z (CZ) and exchange-type (iSWAP) gates using a parametrically driven tunable coupler that mediates the interaction between two superconducting qubits. Using randomized benchmarking protocols we estimate an error per gate of $0.9pm0.03%$ and $1.3pm0.4%$ fidelity for the CZ and the iSWAP gate, respectively. We argue that spurious $ZZ$-type couplings are the dominant error source for the iSWAP gate, and that phase stability of all microwave drives is of utmost importance. Such differences in the achievable fidelities for different two-qubit gates have to be taken into account when mapping quantum algorithms to real hardware.
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