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Quantum algorithm for linear systems of equations.
This work exhibits a quantum algorithm for estimating x(-->)(dagger) Mx(-->) whose runtime is a polynomial of log(N) and kappa, and proves that any classical algorithm for this problem generically requires exponentially more time than this quantum algorithm.
Supervised learning with quantum-enhanced feature spaces
Two classification algorithms that use the quantum state space to produce feature maps are demonstrated on a superconducting processor, enabling the solution of problems when the feature space is large and the kernel functions are computationally expensive to estimate.
Local Random Quantum Circuits are Approximate Polynomial-Designs
We prove that local random quantum circuits acting on n qubits composed of O(t10n2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether
Random Quantum Circuits are Approximate 2-designs
It is shown that random circuits of only polynomial length will approximate the first and second moments of the Haar distribution, thus forming approximate 1- and 2-designs.
Hypercontractivity, sum-of-squares proofs, and their applications
Reductions between computing the 2->4 norm and computing the injective tensor norm of a tensor, a problem with connections to quantum information theory and the study of Khot's Unique Games Conjecture are shown.
Quantum Supremacy through the Quantum Approximate Optimization Algorithm
It is argued that beyond its possible computational value the QAOA can exhibit a form of Quantum Supremacy in that, based on reasonable complexity theoretic assumptions, the output distribution of even the lowest depth version cannot be efficiently simulated on any classical device.
A Resource Framework for Quantum Shannon Theory
This paper advocates a unified approach to an important class of problems in quantum Shannon theory, consisting of those that are bipartite, unidirectional, and memoryless.
A family of quantum protocols
This paper describes the family of quantum protocols, aNoiseless qubit channel, noiseless classical bit channel and pure ebit (EPR pair) that reflect their classical-quantum and dynamic-static nature.
The Quantum Reverse Shannon Theorem and Resource Tradeoffs for Simulating Quantum Channels
The amounts of communication and auxiliary resources needed in both the classical and quantum cases, the tradeoffs among them, and the loss of simulation efficiency when auxiliary resources are absent or insufficient are established.
On the capacities of bipartite Hamiltonians and unitary gates
This work investigates the capacities for interaction Hamiltonians and nonlocal unitary gates to generate entanglement and transmit classical information and shows that these quantities are additive, so that the asymptotic capacities equal the corresponding 1-shot capacities.