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Displaying 1 - 22 of 22

Quantum algorithm for simulating the wave equation

January 15, 2019
Author(s)
Pedro C. Costa, Stephen P. Jordan, Aaron Ostrander
We present a quantum algorithm for simulating the wave equation under Dirichlet and Neumann boundary conditions. The algorithm uses Hamiltonian simulation and quantum linear system algorithms as subroutines. It relies on factorizations of discretized

Faster quantum algorithm to simulate Fermionic quantum field theory

July 1, 2018
Author(s)
Ali Hamed Moosavian, Stephen P. Jordan
In quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states to use in simulation of Fermionic Quantum Field Theory

Experimentally Generated Random Numbers Certified by the Impossibility of Superluminal Signaling

April 11, 2018
Author(s)
Peter L. Bierhorst, Emanuel H. Knill, Scott C. Glancy, Yanbao Zhang, Alan Mink, Stephen P. Jordan, Andrea Rommal, Yi-Kai Liu, Bradley Christensen, Sae Woo Nam, Martin J. Stevens, Lynden K. Shalm
From dice to modern complex circuits, there have been many attempts to build increasingly better devices to generate random numbers. Today, randomness is fundamental to security and cryptographic systems, as well as safeguarding privacy. A key challenge

Diffusion Monte Carlo versus adiabatic computation for local Hamiltonians

February 15, 2018
Author(s)
Stephen P. Jordan, Jacob Bringewatt, Alan Mink, William Dorland
Most research regarding quantum adiabatic optimization has focused on stoquastic Hamiltonians, whose ground states can be expressed with only real, nonnegative amplitudes. This raises the question of whether classical Monte Carlo algorithms can efficiently

Fast optimization algorithms and the cosmological constant

November 1, 2017
Author(s)
Stephen P. Jordan, Ning Bao, Brad Lackey, Raphael Bousso
Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of an NP-hard problem. The number of elementary operations (quantum gates) needed to solve this problem by

Arbitrarily fast quantum computation with bounded energy

March 6, 2017
Author(s)
Stephen P. Jordan
One version of the energy-time uncertainty principle states that the minimum time for a quantum system to evolve from a given state to any orthogonal state is h/(4 Δ E) where Δ E is the energy uncertainty. Many subsequent works have interpreted this as

Adiabatic Optimization versus Diffusion Monte Carlo

October 13, 2016
Author(s)
Stephen P. Jordan, Michael Jarret, Brad Lackey
Most experimental and theoretical studies of adiabatic optimization use stoquastic Hamiltonians, whose ground states are expressible using only real nonnegative amplitudes. This raises a question as to whether classical Monte Carlo methods can simulate

Grover search and the no-signaling principle

September 14, 2016
Author(s)
Ning Bao, Bouland Adam, Stephen P. Jordan
From an information processing point of view, two of the key properties of quantum physics are the no-signaling principle and the Grover search lower bound. That is, despite admitting stronger-than-classical correlations, quantum mechanics does not imply

Report on Post-Quantum Cryptography

April 28, 2016
Author(s)
Lidong Chen, Stephen P. Jordan, Yi-Kai Liu, Dustin Moody, Rene C. Peralta, Ray A. Perlner, Daniel C. Smith-Tone
In recent years, there has been a substantial amount of research on quantum computers - machines that exploit quantum mechanical phenomena to solve mathematical problems that are difficult or intractable for conventional computers. If large-scale quantum

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