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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)
We study the problem of reconstructing an unknown matrix M of rank r and dimension d using O(rdpoly 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)
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)
Intuitively, if a density operator has small rank, then it should be easier to estimate from experimental data, since in this case only a few eigenvectors need to be learned. We prove two complementary results that confirm this intuition. Firstly, we show that a low-rank density matrix can be estimated using fewer copies of the state, i.e. the sample(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)
Suppose we have an n-qubit system, and we are given a collection of local density matrices ρ1, . . . , ρm, where each ρi describes a subset Ci of the qubits. We say that the ρi are “consistent” if there exists some global state σ (on all n qubits) that matches each of the ρi on the subsets Ci. This generalizes the classical notion of the consistency of(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)
One-time memories (OTM’s) are simple, tamper-resistant cryptographic devices, which can be used to implement sophisticated functionalities such as one-time programs. Can one construct OTM’s whose security follows from some physical principle? This is not possible in a fully-classical world, or in a fully-quantum world, but there is evidence that OTM’s can(More)