Approximate unitary $t$-designs by short random quantum circuits using nearest-neighbor and long-range gates

Harrow, Aram W.; Mehraban, Saeed

doi:10.48550/arxiv.1809.06957

Cited by 63 publications

(118 citation statements)

References 39 publications

(131 reference statements)

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“…The first case in Proposition 2 corresponds to the generators of PSA layered Hardware Efficient Ansatz [64], and hence Proposition 1 indicates that this system can exhibit barren plateaus. While it is known that the layered Hardware Efficient Ansatz converges to a 2-design for sufficient depth [37,49,[84][85][86], the proof of existence of barren plateaus for this ansatz presented here is novel in that we show that the system is controllable.…”

Section: Proposition 1 (Controllable)mentioning

confidence: 87%

Diagnosing barren plateaus with tools from quantum optimal control

Larocca,

Czarnik,

Sharma

et al. 2021

Preprint

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Variational Quantum Algorithms (VQAs) have received considerable attention due to their potential for achieving near-term quantum advantage. However, more work is needed to understand their scalability. One known scaling result for VQAs is barren plateaus, where certain circumstances lead to exponentially vanishing gradients. It is common folklore that problem-inspired ansatzes avoid barren plateaus, but in fact, very little is known about their gradient scaling. In this work we employ tools from quantum optimal control to develop a framework that can diagnose the presence or absence of barren plateaus for problem-inspired ansatzes. Such ansatzes include the Quantum Alternating Operator Ansatz (QAOA), the Hamiltonian Variational Ansatz (HVA), and others. With our framework, we prove that avoiding barren plateaus for these ansatzes is not always guaranteed. Specifically, we show that the gradient scaling of the VQA depends on the controllability of the system, and hence can be diagnosed trough the dynamical Lie algebra g obtained from the generators of the ansatz. We analyze the existence of barren plateaus in QAOA and HVA ansatzes, and we highlight the role of the input state, as different initial states can lead to the presence or absence of barren plateaus. Taken together, our results provide a framework for trainability-aware ansatz design strategies that do not come at the cost of extra quantum resources. Moreover, we prove no-go results for obtaining ground states with variational ansatzes for controllable system such as spin glasses. We finally provide evidence that barren plateaus can be linked to dimension of g.

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Section: Proposition 1 (Controllable)mentioning

confidence: 87%

Diagnosing barren plateaus with tools from quantum optimal control

Larocca,

Czarnik,

Sharma

et al. 2021

Preprint

View full text Add to dashboard Cite

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“…Compared with RB variants where the analysis mainly works for Clifford gates or more general finite groups, RCS benchmarking has the advantage of being flexible with the gate set and does not rely on any group structure. This is because many special properties of random quantum circuits, such as fast scrambling and convergence to unitary t-designs, hold with generic gate sets [20][21][22][23][24]. See section II C for a more detailed discussion of the relationship between RCS and other benchmarking protocols.…”

Section: Introductionmentioning

confidence: 99%

Benchmarking near-term quantum computers via random circuit sampling

Liu¹,

Otten²,

Bassirianjahromi³

et al. 2021

Preprint

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A major challenge in the development of near-term quantum computers is to characterize the underlying quantum noise with minimal hardware requirements. We show that random circuit sampling (RCS) is a powerful benchmarking primitive that can be used to efficiently extract the total amount of quantum noise of a many qubit system by creating an exponential decay of fidelity. Compared with randomized benchmarking (RB) and its scalable variants, RCS benchmarking has the unique advantage of being flexible with the gate set, as the fidelity decay in RCS benchmarking comes from scrambling properties of random quantum circuits, which hold for generic gate sets and do not rely on any group structure. First, under a first order approximation in the noise rate, we rigorously prove the exponential decay of average fidelity of low-depth noisy random circuits, using a technique that maps random quantum circuits to a classical spin model. Second, we use the unbiased linear cross entropy as a sample efficient estimator of fidelity and numerically verify its correctness by simulating up to 20 qubits with different noise models. Third, we develop a theoretical model of the total variance of RCS benchmarking, which generalizes previous statistical analysis of cross entropy by considering the variance across different circuits. Finally, we experimentally demonstrate RCS benchmarking on IBM Quantum hardware with up to 20 superconducting qubits, which verifies our theoretical analysis. We expect RCS benchmarking to be widely applicable across different hardware platforms due to its flexibility with the gate set and architecture.

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“…10(d) for datasets of different number of qubits n. Here we can see that as the circuit depth depth increases, the purities achieve the saturation value of 2 n+1 1+2 2n , which corresponds to the Haar-averaged reduced state purity. As expected this is due to the fact that deep HWE ansatzes form unitary 2-designs [77,78].…”

Section: Entanglement Analysis Of the Depth-based Datasetmentioning

confidence: 59%

Entangled Datasets for Quantum Machine Learning

Schatzki¹,

Arrasmith²,

Coles³

et al. 2021

Preprint

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High-quality, large-scale datasets have played a crucial role in the development and success of classical machine learning. Quantum Machine Learning (QML) is a new field that aims to use quantum computers for data analysis, with the hope of obtaining a quantum advantage of some sort. While most proposed QML architectures are benchmarked using classical datasets, there is still doubt whether QML on classical datasets will achieve such an advantage. In this work, we argue that one should instead employ quantum datasets composed of quantum states. For this purpose, we introduce the NTangled dataset composed of quantum states with different amounts and types of multipartite entanglement. We first show how a quantum neural network can be trained to generate the states in the NTangled dataset. Then, we use the NTangled dataset to benchmark QML models for supervised learning classification tasks. We also consider an alternative entanglement-based dataset, which is scalable and is composed of states prepared by quantum circuits with different depths. As a byproduct of our results, we introduce a novel method for generating multipartite entangled states, providing a use-case of quantum neural networks for quantum entanglement theory.

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Approximate unitary $t$-designs by short random quantum circuits using nearest-neighbor and long-range gates

Cited by 63 publications

References 39 publications

Diagnosing barren plateaus with tools from quantum optimal control

Diagnosing barren plateaus with tools from quantum optimal control

Benchmarking near-term quantum computers via random circuit sampling

Entangled Datasets for Quantum Machine Learning

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