All reports by Author Adam Bouland:

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TR16-140
| 9th September 2016
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Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, Prashant Nalini Vasudevan#### On SZK and PP

Revisions: 3

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TR16-039
| 15th March 2016
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Adam Bouland, Laura Mancinska, Xue Zhang#### Complexity Classification of Two-Qubit Commuting Hamiltonians

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TR14-181
| 19th December 2014
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Scott Aaronson, Adam Bouland, Joseph Fitzsimons, Mitchell Lee#### The space "just above" BQP

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TR13-147
| 25th October 2013
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Adam Bouland, Scott Aaronson#### Any Beamsplitter Generates Universal Quantum Linear Optics

Revisions: 3

Adam Bouland, Lijie Chen, Dhiraj Holden, Justin Thaler, Prashant Nalini Vasudevan

In both query and communication complexity, we give separations between the class NISZK, containing those problems with non-interactive statistical zero knowledge proof systems, and the class UPP, containing those problems with randomized algorithms with unbounded error. These results significantly improve on earlier query separations of Vereschagin [Ver95] and Aaronson [Aar12] ... more >>>

Adam Bouland, Laura Mancinska, Xue Zhang

We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian $H$ which one can apply to any pair of qubits, starting in a computational basis state. We prove a dichotomy theorem: either this model is efficiently classically simulable or it allows one ... more >>>

Scott Aaronson, Adam Bouland, Joseph Fitzsimons, Mitchell Lee

We explore the space "just above" BQP by defining a complexity class PDQP (Product Dynamical Quantum Polynomial time) which is larger than BQP but does not contain NP relative to an oracle. The class is defined by imagining that quantum computers can perform measurements that do not collapse the ... more >>>

Adam Bouland, Scott Aaronson

In 1994, Reck et al. showed how to realize any linear-optical unitary transformation using a product of beamsplitters and phaseshifters. Here we show that any single beamsplitter that nontrivially mixes two modes, also densely generates the set of m by m unitary transformations (or orthogonal transformations, in the real case) ... more >>>