Quantum algorithmic measurement

Aharonov, Dorit; Cotler, Jordan; Qi, Xiao-Liang

doi:10.1038/s41467-021-27922-0

Cited by 59 publications

(62 citation statements)

References 41 publications

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“…where 𝑠 𝑖𝑗 = ±1 is an unknown phase. If 𝑠 12 = 1, we define 𝑈 (2) = 𝑈 (1) . If 𝑠 12 = −1, we define 𝑈 (2) = 𝑈 (1) 𝐾, where 𝐾 is the complex conjugation operation.…”

Section: D5 Learning Descriptions Of a Special Set Of Statesmentioning

confidence: 99%

“…If 𝑠 12 = 1, we define 𝑈 (2) = 𝑈 (1) . If 𝑠 12 = −1, we define 𝑈 (2) = 𝑈 (1) 𝐾, where 𝐾 is the complex conjugation operation. We have 𝑈 (2) is either a unitary or anti-unitary transformation.…”

Section: D5 Learning Descriptions Of a Special Set Of Statesmentioning

confidence: 99%

“…If 𝑠 12 = −1, we define 𝑈 (2) = 𝑈 (1) 𝐾, where 𝐾 is the complex conjugation operation. We have 𝑈 (2) is either a unitary or anti-unitary transformation. Using the newly defined 𝑈 (2) , we have…”

Section: D5 Learning Descriptions Of a Special Set Of Statesmentioning

confidence: 99%

“…We have 𝑈 (2) is either a unitary or anti-unitary transformation. Using the newly defined 𝑈 (2) , we have…”

Section: D5 Learning Descriptions Of a Special Set Of Statesmentioning

confidence: 99%

See 3 more Smart Citations

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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Section: D5 Learning Descriptions Of a Special Set Of Statesmentioning

confidence: 99%

Section: D5 Learning Descriptions Of a Special Set Of Statesmentioning

confidence: 99%

Section: D5 Learning Descriptions Of a Special Set Of Statesmentioning

confidence: 99%

“…We have 𝑈 (2) is either a unitary or anti-unitary transformation. Using the newly defined 𝑈 (2) , we have…”

Section: D5 Learning Descriptions Of a Special Set Of Statesmentioning

confidence: 99%

See 2 more Smart Citations

Foundations for learning from noisy quantum experiments

Huang¹,

Flammia²,

Preskill³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Recent experimental progress on quantum hardware and algorithms has generated great excitement in trying to identify applications that can lead to a quantum advantage over classical devices [9][10][11][12]. One such application is quantum machine learning (QML) which employs parameterized quantum circuits to analyze either classical or quantum data [13][14][15].…”

mentioning

confidence: 99%

An analytic theory for the dynamics of wide quantum neural networks

Liu¹,

Najafi²,

Sharma³

et al. 2022

Preprint

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Parametrized quantum circuits can be used as quantum neural networks and have the potential to outperform their classical counterparts when trained for addressing learning problems. To date, much of the results on their performance on practical problems are heuristic in nature. In particular, the convergence rate for the training of quantum neural networks is not fully understood. Here, we analyze the dynamics of gradient descent for the training error of a class of variational quantum machine learning models. We define wide quantum neural networks as parameterized quantum circuits in the limit of a large number of qubits and variational parameters. We then find a simple analytic formula that captures the average behavior of their loss function and discuss the consequences of our findings. For example, for random quantum circuits, we predict and characterize an exponential decay of the residual training error as a function of the parameters of the system. We finally validate our analytic results with numerical experiments.

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Statistical Methods for Quantum State Verification and Fidelity Estimation

Shang

Gühne

2022

Adv Quantum Tech

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The efficient and reliable certification of quantum states is essential for various quantum information processing tasks as well as for the general progress on the implementation of quantum technologies. In the last few years several methods have been introduced which use advanced statistical methods to certify quantum states in a resource‐efficient manner. In this article, a review of the recent progress in this field is presented. How the verification and fidelity estimation of a quantum state can be discussed in the language of hypothesis testing is explained first. Then, various strategies for the verification of entangled states with local measurements or measurements assisted by local operations and classical communication are explained in detail. Finally, several extensions of the problem, such as the certification of quantum channels and the verification of entanglement are discussed.

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Quantum algorithmic measurement

Cited by 59 publications

References 41 publications

Foundations for learning from noisy quantum experiments

Foundations for learning from noisy quantum experiments

An analytic theory for the dynamics of wide quantum neural networks

Statistical Methods for Quantum State Verification and Fidelity Estimation

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