Fast and feasible periodic sorting networks of constant depth

2002 ◽  
Author(s):  
M. Kutylowski ◽  
K. Lorys ◽  
B. Oesterdiekhoff ◽  
R. Wanka
Keyword(s):  
Constant Depth ◽  
Sorting Networks

Periodic constant depth sorting networks

1994 ◽  
pp. 199-212 ◽  
Author(s):  
Marcin Kik ◽  
Mirosław Kutyłowski ◽  
Grzegorz Stachowiak
Keyword(s):  
Constant Depth ◽  
Sorting Networks ◽  
Periodic Constant

scholarly journals Some Subsystems of Constant-Depth Frege with Parity

2018 ◽  
Vol 19 (4) ◽  
pp. 1-34 ◽  
Author(s):  
Michal Garlík ◽  
Leszek Aleksander Kołodziejczyk
Keyword(s):  
Constant Depth

scholarly journals Reproducible Biofilm Cultivation of Chemostat-Grown Escherichia coli and Investigation of Bacterial Adhesion on Biomaterials Using a Non-Constant-Depth Film Fermenter

PLoS ONE ◽  
2014 ◽  
Vol 9 (1) ◽  
pp. e84837 ◽  
Author(s):  
Claudia Lüdecke ◽  
Klaus D. Jandt ◽  
Daniel Siegismund ◽  
Marian J. Kujau ◽  
Emerson Zang ◽  
...  
Keyword(s):  
Escherichia Coli ◽  
Bacterial Adhesion ◽  
Constant Depth

scholarly journals Trading Locality for Time: Certifiable Randomness from Low-Depth Circuits

2021 ◽  
Author(s):  
Matthew Coudron ◽  
Jalex Stark ◽  
Thomas Vidick
Keyword(s):  
Linear Time ◽  
Bell Inequality ◽  
Quantum Circuit ◽  
Constant Depth ◽  
Information Theoretic ◽  
Small Constant ◽  
Fundamental Information ◽  
Simple Quantum ◽  
Variation Distance ◽  
Noise Tolerant

AbstractThe generation of certifiable randomness is the most fundamental information-theoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified randomness expansion using a single quantum device. The protocol calls for the device to implement a simple quantum circuit of constant depth on a 2D lattice of qubits. The output of the circuit can be verified classically in linear time, and is guaranteed to contain a polynomial number of certified random bits assuming that the device used to generate the output operated using a (classical or quantum) circuit of sub-logarithmic depth. This assumption contrasts with the locality assumption used for randomness certification based on Bell inequality violation and more recent proposals for randomness certification based on computational assumptions. Furthermore, to demonstrate randomness generation it is sufficient for a device to sample from the ideal output distribution within constant statistical distance. Our procedure is inspired by recent work of Bravyi et al. (Science 362(6412):308–311, 2018), who introduced a relational problem that can be solved by a constant-depth quantum circuit, but provably cannot be solved by any classical circuit of sub-logarithmic depth. We develop the discovery of Bravyi et al. into a framework for robust randomness expansion. Our results lead to a new proposal for a demonstrated quantum advantage that has some advantages compared to existing proposals. First, our proposal does not rest on any complexity-theoretic conjectures, but relies on the physical assumption that the adversarial device being tested implements a circuit of sub-logarithmic depth. Second, success on our task can be easily verified in classical linear time. Finally, our task is more noise-tolerant than most other existing proposals that can only tolerate multiplicative error, or require additional conjectures from complexity theory; in contrast, we are able to allow a small constant additive error in total variation distance between the sampled and ideal distributions.

Sign in / Sign up

Export Citation Format

Share Document