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- Amod J. G. Anandkumar, Dean P. Foster, Daniel J. Hsu, Sham M. Kakade, Yi-Kai Liu
- Algorithmica
- 2012

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)

- David Gross, Yi-Kai Liu, Steven T. Flammia, Stephen P Becker, Jens Eisert
- Physical review letters
- 2010

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)

- Yi-Kai Liu
- NIPS
- 2011

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)

- Alberto Blanc, Yi-Kai Liu, Amin Vahdat
- Proceedings IEEE 24th Annual Joint Conference of…
- 2005

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)

- Yi-Kai Liu, Matthias Christandl, Frank Verstraete
- Physical review letters
- 2007

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)

- Yi-Kai Liu
- APPROX-RANDOM
- 2006

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)

- Yi-Kai Liu
- ArXiv
- 2013

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)

- Yi-Kai Liu
- IACR Cryptology ePrint Archive
- 2014

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)