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Quantum algorithm for linear systems of equations.
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b(-->), find a vector x(-->) such thatExpand
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Supervised learning with quantum-enhanced feature spaces
TLDR
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. Expand
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Random Quantum Circuits are Approximate 2-designs
Given a universal gate set on two qubits, it is well known that applying random gates from the set to random pairs of qubits will eventually yield an approximately Haar-distributed unitary. However,Expand
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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 whetherExpand
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A Resource Framework for Quantum Shannon Theory
TLDR
We advocate a unified approach to an important class of problems in quantum Shannon theory, consisting of those that are bipartite, unidirectional, and memoryless. Expand
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A family of quantum protocols
This paper describes the family of quantum protocols. The basic protocols are naturally organized into mutually dual hierarchies. A noiseless qubit channel, noiseless classical bit channel and pureExpand
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Hypercontractivity, sum-of-squares proofs, and their applications
TLDR
We study the computational complexity of approximating the 2-to-q norm of linear operators (defined as |A|2->q = maxv≠ 0|Av|q/|v|2) for q > 2, as well as connections between this question and issues arising in quantum information theory and the study of Khot's Unique Games Conjecture (UGC). Expand
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The Quantum Reverse Shannon Theorem and Resource Tradeoffs for Simulating Quantum Channels
TLDR
We establish 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. Expand
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Efficient quantum circuits for Schur and Clebsch-Gordan transforms.
The Schur basis on n d-dimensional quantum systems is a generalization of the total angular momentum basis that is useful for exploiting symmetry under permutations or collective unitary rotations.Expand
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Quantum dynamics as a physical resource
How useful is a quantum dynamical operation for quantum information processing? Motivated by this question, we investigate several strength measures quantifying the resources intrinsic to a quantumExpand
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