Compressive gate set tomography

Brieger, Raphael; Roth, Ingo; Kliesch, Martin

doi:10.48550/arxiv.2112.05176

Cited by 4 publications

(5 citation statements)

References 75 publications

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“…This means that it can be verified to the same degree that one can characterize those measurement apparata. For single-or two-qubit measurements this is possible using tools such as gate set tomography (Blume-Kohout et al, 2017, 2013Brieger et al, 2022;Cerfontaine et al, 2020;Greenbaum, 2015;Helsen et al, 2021;Merkel et al, 2013) or the device-independent verification of quantum processes and instruments (Sekatski et al, 2018).…”

Section: Efficient Quantum Verificationmentioning

confidence: 99%

Computational advantage of quantum random sampling

Hangleiter¹,

Eisert²

2022

Preprint

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Quantum random sampling is the leading proposal for demonstrating a computational advantage of quantum computers over classical computers. Recently, first large-scale implementations of quantum random sampling have arguably surpassed the boundary of what can be simulated on existing classical hardware. In this article, we comprehensively review the theoretical underpinning of quantum random sampling in terms of computational complexity and verifiability, as well as the practical aspects of its experimental implementation using superconducting and photonic devices and its classical simulation. We discuss in detail open questions in the field and provide perspectives for the road ahead, including potential applications of quantum random sampling.

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Section: Efficient Quantum Verificationmentioning

confidence: 99%

Computational advantage of quantum random sampling

Hangleiter¹,

Eisert²

2022

Preprint

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“…In Appendix K we discuss gate set tomography from the perspective of our mathematical theory. There we argue that existing gate set tomography protocols [7,10,25,49] may be viewed as methods for predicting the extrinsic behavior of a world model. Based on this understanding, the algorithm used in the proof of Theorem 4 establishes rigorous gate set tomography learning algorithms with provable prediction guarantees under suitable conditions.…”

Section: Predicting Extrinsic Behavior Of the World Modelmentioning

confidence: 99%

“…This result may seem to contradict claims about known protocols, such as gate set tomography [7,10,25,49] and ACES [21]. To resolve the conflict, recall that gate set tomography learns an effective model that can be used to predict the extrinsic behavior.…”

Section: B Bit-flip or Phase-flip Error?mentioning

confidence: 99%

“…In order to avoid the worst-case complexity proved in the previous subsection, we need to make a stronger assumption about the true world model. We present one such assumption that is closely related to the assumption used in existing gate set tomography protocols [7,10,25,49]. Intuitively, the assumption is that we can efficiently find a complete set of states that span the set of states we can generate using the world model, and a complete set of POVM elements whose span includes the complete set of states.…”

Section: J a General Theorem For Predicting Extrinsic Behaviormentioning

confidence: 99%

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Foundations for learning from noisy quantum experiments

Huang¹,

Flammia²,

Preskill³

2022

Preprint

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Understanding what can be learned from experiments is central to scientific progress. In this work, we use a learning-theoretic perspective to study the task of learning physical operations in a quantum machine when all operations (state preparation, dynamics, and measurement) are a priori unknown. We prove that, without any prior knowledge, if one can explore the full quantum state space by composing the operations, then every operation can be learned. When one cannot explore the full state space but all operations are approximately known and noise in Clifford gates is gate-independent, we find an efficient algorithm for learning all operations up to a single unlearnable parameter characterizing the fidelity of the initial state. For learning a noise channel on Clifford gates to a fixed accuracy, our algorithm uses quadratically fewer experiments than previously known protocols. Under more general conditions, the true description of the noise can be unlearnable; for example, we prove that no benchmarking protocol can learn gate-dependent Pauli noise on Clifford+T gates even under perfect state preparation and measurement. Despite not being able to learn the noise, we show that a noisy quantum computer that performs entangled measurements on multiple copies of an unknown state can yield a large advantage in learning properties of the state compared to a noiseless device that measures individual copies and then processes the measurement data using a classical computer. Concretely, we prove that noisy quantum computers with two-qubit gate error rate 𝜖 can achieve a learning task using 𝑁 copies of the state, while 𝑁 Ω(1/𝜖) copies are required classically.

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“…However, process tomography has exponentially increasing experimental costs and suffers from state-preparation and measurement (SPAM) errors. Although its variant, the gate-set tomography [14][15][16][17][18], can handle SPAM errors, the experimental costs cannot be reduced.…”

mentioning

confidence: 99%

Benchmarking universal quantum gates via channel spectrum

Zhuang

Chai

et al. 2023

Preprint

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Noise remains the major obstacle to scalable quantum computation. Quantum benchmarking provides key information on noise properties and is an important step for developing more advanced quantum processors. However, current benchmarking methods are either limited to a specific subset of quantum gates or cannot directly describe the performance of the individual target gate. To overcome these limitations, we propose channel spectrum benchmarking (CSB), a novel method to infer the noise properties of the target gate, including process fidelity, stochastic fidelity, and some unitary parameters, from the eigenvalues of its noisy channel. Our CSB method is insensitive to state-preparation and measurement errors, and importantly, can benchmark universal gates and is scalable to many-qubit systems. Unlike standard randomized schemes, CSB can provide direct noise information for both target native gates and circuit fragments, allowing benchmarking and calibration of frequently used modules in quantum algorithms like Trotterized Hamiltonian evolution operator in quantum simulation.

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Compressive gate set tomography

Cited by 4 publications

References 75 publications

Computational advantage of quantum random sampling

Computational advantage of quantum random sampling

Foundations for learning from noisy quantum experiments

Benchmarking universal quantum gates via channel spectrum

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