# A Hierarchy for Replica Quantum Advantage

@article{Chen2021AHF, title={A Hierarchy for Replica Quantum Advantage}, author={Sitan Chen and Jordan S. Cotler and Hsin-Yuan Huang and Jerry Zheng Li}, journal={ArXiv}, year={2021}, volume={abs/2111.05874} }

Sitan Chen, 2, ∗ Jordan Cotler, 4, † Hsin-Yuan Huang, 6, ‡ and Jerry Li § Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Berkeley, CA, USA Simons Institute for the Theory of Computing, Berkeley, CA, USA Society of Fellows, Harvard University, Cambridge, MA, USA Black Hole Initiative, Harvard University, Cambridge, MA, USA Institute for Quantum Information and Matter, Caltech, Pasadena, CA, USA Department of Computing and Mathematical Sciences…

## 9 Citations

### The Complexity of NISQ

- Computer ScienceArXiv
- 2022

This work defines and study the complexity class NISQ, which is intended to encapsulate problems that can be efficiently solved by a classical computer with access to a N ISQ device, and considers the power of NISZ for three well-studied problems.

### Quantum advantage in learning from experiments

- PhysicsScience
- 2022

This research presents a probabilistic model of the black hole that combines quantum entanglement, superposition, and superposition to describe the fabric of space-time.

### Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix

- PhysicsArXiv
- 2022

Learning about physical systems from quantum-enhanced experiments, relying on a quantum memory and quantum processing, can outperform learning from experiments in which only classical memory and…

### Unitary property testing lower bounds by polynomials

- Computer ScienceITCS
- 2023

A generalized polynomial method for unitary property testing problems, leveraging connections with invariant theory, is applied to obtain lower bounds on problems such as determining recurrence times of unitaries, approximating the dimension of a marked subspace, and approximates the entanglement entropy of a marking state.

### Lower bounds for learning quantum states with single-copy measurements

- Computer ScienceArXiv
- 2022

In the case of adaptive, single-copy measurements implementable with polynomial-size circuits, this rigorously establishes the optimality of the folklore “Pauli tomography” algorithm in terms of its sample complexity.

### Information-theoretic Hardness of Out-of-time-order Correlators

- Computer Science
- 2022

The results provide a theoretical foundation for novel applications of OTOCs in quantum simulations and elucidate a general deﬁnition of time-ordered versus out-of-time-order experimental measurement protocols, which can be consid-ered as classes of adaptive quantum learning algorithms.

### Tight Bounds for State Tomography with Incoherent Measurements

- Computer ScienceArXiv
- 2022

This work fully resolves the question of whether or not this rate of coherent measurements is tight, by showing that any protocol using incoherent measurements, even if they are chosen adaptively, requires Ω(d/ε) copies, matching the upper bound of [KRT17].

### Tight Bounds for Quantum State Certification with Incoherent Measurements

- Computer Science2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)
- 2022

The copy complexity of mixedness testing with incoherent measurements is settled and it is shown that $\Omega(d^{3/2}/\varepsilon^{2})$ copies are necessary and the instance-optimal bounds for state certification to general $\sigma$ first derived in [7] for non-adaptive measurements also hold for arbitrary incoherence measurements.

### Challenges and opportunities in quantum machine learning

- Computer Science, PhysicsNature Computational Science
- 2022

Current methods and applications for quantum machine learning are reviewed, including differences between quantum and classical machine learning, with a focus on quantum neural networks and quantum deep learning.

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