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Displaying 26 - 44 of 44

Yang-Baxter operators need quantum entanglement to distinguish knots

January 12, 2016
Author(s)
Stephen P. Jordan, Gorjan Alagic, Michael Jarret
Solutions to the Yang-Baxter equation yield representations of braid groups. Under certain conditions, identified by Turaev, traces of these representations yield link invariants. The matrices satisfying the Yang-Baxter equation, if unitary, can be

Adiabatic optimization without local minima

March 1, 2015
Author(s)
Stephen P. Jordan, Michael Jarret
Several previous works have investigated the circumstances under which quantum adiabatic optimization algorithms can tunnel out of local energy minima that trap simulated annealing or other classical local search algorithms. Here we investigate the even

Classical simulation of Yang-Baxter gates

November 3, 2014
Author(s)
Stephen P. Jordan, Gorjan Alagic, Aniruddha Bapat
A unitary operator that satisfies the constant Yang-Baxter equation immediately yields a unitary representation of the braid group Bn for every n ≥ 2. If we view such an operator as a quantum-computational gate, then topological braiding corresponds to a

BQP-completeness of Scattering in Scalar Quantum Field Theory

September 1, 2014
Author(s)
Stephen P. Jordan, Keith S. Lee, John Preskill
Recent work has shown that quantum computers can in polynomial time compute scattering probabilities in massive quantum field theories. One can translate this task into a corresponding formal problem in computational complexity theory. Here, we establish

Quantum Algorithms for Fermionic Quantum Field Theories

April 28, 2014
Author(s)
Stephen P. Jordan, Keith S. Lee, John Preskill
Extending previous work on scalar field theories, we develop a quantum algorithm to compute relativistic scattering amplitudes in fermionic field theories, exemplified by the massive Gross-Neveu model. The algorithm introduces new techniques to meet the

Strong equivalence of reversible circuits is coNP-complete

July 2, 2013
Author(s)
Stephen P. Jordan
It is well-known that deciding equivalence of logic circuits is a coNP-complete problem. As a corollary, the problem of deciding weak equivalence of reversible circuits, i.e. ignoring the ancilla bits, is also coNP-complete. The complexity of deciding

Testing quantum expanders is co-QMA-complete

May 31, 2013
Author(s)
Yi-Kai Liu, Stephen P. Jordan, Pawel Wocjan, Adam Bookatz
A quantum expander is a unital quantum channel that is rapidly mixing, has only a few Kraus operators, and can be implemented efficiently on a quantum computer. We consider the problem of estimating the mixing time (i.e., the spectral gap) of a quantum

Quantum Algorithms for Quantum Field Theories

June 1, 2012
Author(s)
Stephen P. Jordan, Keith S. Lee, John Preskill
Quantum field theory reconciles quantum mechanics and special relativity, and plays a central role in many areas of physics. We develop a quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self

QCMA with One-sided Error Equals QCMA with Two-sided Error

November 30, 2011
Author(s)
Stephen P. Jordan, Daniel Nagaj
QCMA is the set of decision problems such that if the answer is yes, there exists a classical bitstring, or proof, that can be efficiently verified by a quantum computer. The verifier is allowed a small probability of rejecting a valid proof or accepting