Experimental Estimation of Average Fidelity of a Clifford Gate on a 7-Qubit Quantum Processor

Abstract

Quantum gates in experiment are inherently prone to errors that need to be characterized before they can be corrected. Full characterization via quantum process tomography is impractical and often unnecessary. For most practical purposes, it is enough to estimate more general quantities such as the average fidelity. Here we use a unitary 2-design and twirling protocol for efficiently estimating the average fidelity of Clifford gates, to certify a 7-qubit entangling gate in a nuclear magnetic resonance quantum processor. Compared with more than 10 8 experiments required by full process tomography, we conducted 1656 experiments to satisfy a statistical confidence level of 99%. The average fidelity of this Clifford gate in experiment is 55.1%, and rises to 87.5% if the infidelity due to decoherence is removed. The entire protocol of certifying Clifford gates is efficient and scalable, and can easily be extended to any general quantum information processor with minor modifications. . Introduction. Benchmarking protocols for characterizing the level of coherent control are fundamental in evaluating potential quantum information processing (QIP) devices. They provide an objective comparison of quantum control capabilities between diverse QIP devices, and also indicate the prospects of a given platform with respect to fault-tolerant quantum computation [1]. The traditional approach of using quantum process tomography (QPT) [2,3] is useful for completely characterizing a quantum channel, and has been applied to at most 3-qubit systems in experiment [4][5][6][7][8][9][10][11]. However, QPT requires number of measurements that scale exponentially with number of qubits n (≈ 2 4n ), making it impractical even in relatively small systems. Moreover,for many practical purposes, such as benchmarking, the full description of a particular quantum channel is not necessary and more accessible properties of the gates are sufficient. To benchmark a gate it is enough to estimate the distance between the implemented channel and the ideal gate. Several methods such as randomized benchmarking [12][13][14], twirling [15][16][17], and Monte Carlo estimations [18,19] have been proposed to evaluate a particular quantum channel in an efficient manner, each with its own restrictions and drawbacks. Here, in order to benchmark our coherent controls on a 7-qubit nuclear magnetic resonance (NMR) system, we adopted the twirling protocol [17] to estimate the average fidelity of an important Clifford gate in QIP. The gate of interest generates maximal coherence from single coherence with the aid of lo-

Quantum gate learning in qubit networks: Toffoli gate without time-dependent control

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Parallel quantum trajectories via forking for sampling without redundancy

“…The QFS procedure to construct a convex combination of unitary channels can naturally extend to quantum channel twirling. Twirling has been established as an important technique in quantum information science that appears in a variety of contexts, such as entanglement purification [20,21], characterizing quantum processes [22][23][24][25][26][27], studying the performance of quantum error correcting codes [28][29][30], and quantum error mitigation [31,32]. Twirling a quantum channel Λ with a finite set of unitaries,…”

NMR Quantum Information Processing

“…Another experiment of certifying a 7-qubit Clifford gate in NMR was carried out recently [37]. The sample was Dichlorocyclobutanone, and the seven carbons formed a 7-qubit quantum processor.…”

“…In this section, we focus on the twirling and randomized benchmarking protocols, and describe the relevant NMR experiments [29,31,34,37] briefly. We show that reliable coherent control has been achieved in NMR quantum computing up to seven qubits.…”