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A survey on the complexity of learning quantum states
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 computing and machine learning. Important breakthroughs in the past two years …
Quantum advantage in learning from experiments
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 …
experiment that processes quantum data with a quantum computer could have substantial …
On quantum backpropagation, information reuse, and cheating measurement collapse
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 …
Through clever reuse of intermediate information, backpropagation facilitates training …
Cryptography from pseudorandom quantum states
Pseudorandom states, introduced by Ji, Liu and Song (Crypto'18), are efficiently-computable
quantum states that are computationally indistinguishable from Haar-random states. One …
quantum states that are computationally indistinguishable from Haar-random states. One …
Random unitaries in extremely low depth
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 …
approximate unitary designs over $ n $ qubits in $\log n $ depth. In a similar manner, we …
Learning quantum states and unitaries of bounded gate complexity
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 …
practically minded tomographers. Given that states and unitaries appearing in nature are of …
Quantum commitments and signatures without one-way functions
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 …
way functions. In the quantum setting, on the other hand, commitments are not known to …
Quantum cryptography in algorithmica
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 …
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
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 …
prepared in the lab closely matches a target state |ψ⟩. Previous approaches to this problem …
On the computational hardness needed for quantum cryptography
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 …
minimal for computational cryptography: They are essential for almost any cryptographic …