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Topic modeling is a generalization of clustering that posits that observations (words in a document) are generated by multiple latent factors (topics), as opposed to just one. The increased representational power comes at the cost of a more challenging unsupervised learning problem for estimating the topic-word distributions when only words are observed,(More)
We establish methods for quantum state tomography based on compressed sensing. These methods are specialized for quantum states that are fairly pure, and they offer a significant performance improvement on large quantum systems. In particular, they are able to reconstruct an unknown density matrix of dimension d and rank r using O(rdlog²d) measurement(More)
In a peer-to-peer network, nodes are typically required to route packets for each other. This leads to a problem of "free-loaders", nodes that use the network but refuse to route other nodes' packets. In this paper we study ways of designing incentives to discourage free-loading. We model the interactions between nodes as a "random matching game", and(More)
We study the problem of reconstructing an unknown matrix M of rank r and dimension d using O(rd poly log d) Pauli measurements. This has applications in quantum state tomography, and is a non-commutative analogue of a well-known problem in compressed sensing: recovering a sparse vector from a few of its Fourier coefficients. We show that almost all sets of(More)
Suppose we have an n-qubit system, and we are given a collection of local density matrices ρ 1 ,. .. , ρ m , where each ρ i describes a subset C i of the qubits. We say that the ρ i are " consistent " if there exists some global state σ (on all n qubits) that matches each of the ρ i on the subsets C i. This generalizes the classical notion of the(More)
We study the computational complexity of the N-representability problem in quantum chemistry. We show that this problem is quantum Merlin-Arthur complete, which is the quantum generalization of nondeterministic polynomial time complete. Our proof uses a simple mapping from spin systems to fermionic systems, as well as a convex optimization technique that(More)
A central problem in the algorithmic study of lattices is the closest vector problem: given a lattice v represented by some basis, and a target point y, nd the lattice point closest to y. Bounded Distance Decoding is a variant of this problem in which the target is guaranteed to be close to the lattice, relative to the minimum distance 1(v) of the lattice.(More)
One-time memories (OTM's) are a simple type of tamper-resistant cryptographic hardware, which can be used to implement many forms of secure computation, such as one-time programs. Here we investigate the possibility of building OTM's using isolated qubits — qubits that can only be accessed using local operations and classical communication (LOCC). Isolated(More)