A survey on the complexity of learning quantum states

A Anshu, S Arunachalam - Nature Reviews Physics, 2024 - nature.com
Quantum learning theory is a new and very active area of research at the intersection of
quantum computing and machine learning. Important breakthroughs in the past two years …

Quantum advantage in learning from experiments

HY Huang, M Broughton, J Cotler, S Chen, J Li… - Science, 2022 - science.org
Quantum technology promises to revolutionize how we learn about the physical world. An
experiment that processes quantum data with a quantum computer could have substantial …

On quantum backpropagation, information reuse, and cheating measurement collapse

A Abbas, R King, HY Huang… - Advances in …, 2023 - proceedings.neurips.cc
The success of modern deep learning hinges on the ability to train neural networks at scale.
Through clever reuse of intermediate information, backpropagation facilitates training …

Cryptography from pseudorandom quantum states

P Ananth, L Qian, H Yuen - Annual International Cryptology Conference, 2022 - Springer
Pseudorandom states, introduced by Ji, Liu and Song (Crypto'18), are efficiently-computable
quantum states that are computationally indistinguishable from Haar-random states. One …

Random unitaries in extremely low depth

T Schuster, J Haferkamp, HY Huang - arxiv preprint arxiv:2407.07754, 2024 - arxiv.org
We prove that random quantum circuits on any geometry, including a 1D line, can form
approximate unitary designs over $ n $ qubits in $\log n $ depth. In a similar manner, we …

Learning quantum states and unitaries of bounded gate complexity

H Zhao, L Lewis, I Kannan, Y Quek, HY Huang… - PRX Quantum, 2024 - APS
While quantum state tomography is notoriously hard, most states hold little interest to
practically minded tomographers. Given that states and unitaries appearing in nature are of …

Quantum commitments and signatures without one-way functions

T Morimae, T Yamakawa - Annual International Cryptology Conference, 2022 - Springer
In the classical world, the existence of commitments is equivalent to the existence of one-
way functions. In the quantum setting, on the other hand, commitments are not known to …

Quantum cryptography in algorithmica

W Kretschmer, L Qian, M Sinha, A Tal - Proceedings of the 55th Annual …, 2023 - dl.acm.org
We construct a classical oracle relative to which P= NP yet single-copy secure
pseudorandom quantum states exist. In the language of Impagliazzo's five worlds, this is a …

Certifying almost all quantum states with few single-qubit measurements

HY Huang, J Preskill… - 2024 IEEE 65th Annual …, 2024 - ieeexplore.ieee.org
A fundamental challenge in quantum information science is certifying that an n-qubit state ρ
prepared in the lab closely matches a target state |ψ⟩. Previous approaches to this problem …

On the computational hardness needed for quantum cryptography

Z Brakerski, R Canetti, L Qian - arxiv preprint arxiv:2209.04101, 2022 - arxiv.org
In the classical model of computation, it is well established that one-way functions (OWF) are
minimal for computational cryptography: They are essential for almost any cryptographic …