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We give a new proof for the area law for general 1D gapped systems, which exponentially improves Hastings’ famous result [1]. Specifically, we show that for a chain of d-dimensional spins, governed… (More)

- Umesh V. Vazirani, Thomas Vidick
- Philosophical transactions. Series A…
- 2012

We introduce a protocol through which a pair of quantum mechanical devices may be used to generate n random bits that are ε-close in statistical distance from n uniformly distributed bits, starting… (More)

- Erick Chastain, Adi Livnat, Christos H. Papadimitriou, Umesh V. Vazirani
- Proceedings of the National Academy of Sciences…
- 2014

Even the most seasoned students of evolution, starting with Darwin himself, have occasionally expressed amazement that the mechanism of natural selection has produced the whole of Life as we see it… (More)

We present a new proof for the 1D area law for frustration-free systems with a constant gap, which exponentially improves the entropy bound in Hastings 1D area law and which is tight to within a… (More)

Computing ground states of local Hamiltonians is a fundamen tal problem in condensed matter physics. We give the first randomized polynomial-time algorithm for fi nding ground states of gapped… (More)

One of the central challenges in the study of quantum many-body systems is the complexity of simulating them on a classical computer. A recent advance [LVV15] gave a polynomial time algorithm to… (More)

1 Abstract This paper surveys the use of thèhybrid argument' to prove to that quantum computations are insensitive to small perturbations. This property of quantum computations is used to establish… (More)

Learning Probability Distributions

Quantum computation teaches us that quantum mechanics exhibits exponential complexity. We argue that the standard scientific paradigm of “predict and verify” cannot be applied to testing quantum… (More)