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## Filters

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Error mitigation for universal gates on encoded qubits
[article]

2021
*
arXiv
*
pre-print

As

arXiv:2103.04915v2
fatcat:g23quvamnze4rbtitqhn7sfori
*a*result, Clifford+T circuits*with**a**number**of*T-*gates*inversely proportional to the physical noise rate*can*be implemented on small error-corrected devices without magic state distillation. ...*We*argue that such circuits*can*be out*of*reach for state-*of*-the-art classical simulation algorithms. ... Indeed, the*constant**depth*condition implies that*a*single fault*in*the circuit*can*affect only*a**constant**number**of*output qubits. ...##
###
New algorithms and lower bounds for circuits with linear threshold gates
[article]

2014
*
arXiv
*
pre-print

Let ACC ∘ THR be the class

arXiv:1401.2444v1
fatcat:ienft6r5evacrozmwkbbseuktu
*of**constant*-*depth*circuits comprised*of*AND, OR, and MODm*gates*(for some*constant*m > 1),*with**a*bottom layer*of**gates*computing arbitrary linear threshold functions. ... Several consequences are derived: ∙ The*number**of*satisfying assignments to an ACC ∘ THR circuit*of*subexponential size*can*be computed*in*2^n-n^ε time (where ε > 0 depends on the*depth*and modulus*of*... I thank Igor Carboni Olivera for sending*a*preliminary version*of*his survey, which helped the ideas*in*the proof*of*Theorem 2.5 to congeal. ...##
###
Computing Majority by Constant Depth Majority Circuits with Low Fan-in Gates
[article]

2016
*
arXiv
*
pre-print

*We*study the following computational problem: for which values

*of*k, the majority

*of*n bits MAJ_n

*can*be computed

*with*

*a*

*depth*two formula whose each

*gate*computes

*a*majority function

*of*at most k bits ... For

*depth*3 circuits

*we*show that

*a*circuit

*with*k= O(n^2/3)

*can*compute MAJ_n correctly on all inputs. ... Acknowledgments

*We*would like to thank the participants

*of*Low-

*Depth*Complexity Workshop (St. Petersburg, Russia, May 21-25, 2016) for many helpful discussions. ...

##
###
Efficient decomposition of single-qubit gates intoVbasis circuits

2013
*
Physical Review A. Atomic, Molecular, and Optical Physics
*

*We*propose two classical algorithms for quantum circuit compilation: the first algorithm has expected polynomial time (

*in*precision (1/ϵ)) and offers

*a*

*depth*/precision guarantee that improves upon state-

*of*-the-art ... The second algorithm is analogous to direct search and yields circuits

*a*factor

*of*3 to 4 times shorter than our first algorithm, and requires time exponential

*in*(1/ϵ); however,

*we*show that

*in*practice ... For the majority

*of*unitary

*gates*,

*we*

*can*significantly reduce the

*depth*

*of*the output circuit

*with*

*a*corresponding increase

*in*compilation time. ...

##
###
TFermion: A non-Clifford gate cost assessment library of quantum phase estimation algorithms for quantum chemistry
[article]

2022
*
arXiv
*
pre-print

*In*this article,

*we*introduce TFermion,

*a*library designed to estimate the T-

*gate*cost

*of*such algorithms, for an arbitrary molecule. ... As examples

*of*usage,

*we*estimate the T-

*gate*cost

*of*

*a*few simple molecules and compare the same Taylorization algorithms using Gaussian and plane-wave basis. ... Acknowledgements 11 Acknowledgements

*We*want to thank the very kind explanations

*of*Emiel Koridon

*of*some calculations

*in*one

*of*his articles and beyond. ...

##
###
TFermion: A non-Clifford gate cost assessment library of quantum phase estimation algorithms for quantum chemistry

2022
*
Quantum
*

*In*this article,

*we*introduce TFermion,

*a*library designed to estimate the T-

*gate*cost

*of*such algorithms, for an arbitrary molecule. ... As examples

*of*usage,

*we*estimate the T-

*gate*cost

*of*

*a*few simple molecules and compare the same Taylorization algorithms using Gaussian and plane-wave basis. ... Acknowledgements 11 Acknowledgements

*We*want to thank the very kind explanations

*of*Emiel Koridon

*of*some calculations

*in*one

*of*his articles and beyond. ...

##
###
Secure Multi-Party Computation in Large Networks
[article]

2015
*
arXiv
*
pre-print

For any deterministic function that

arXiv:1203.0289v3
fatcat:3tleszkgtba7dcd7fmwsdnivka
*can*be computed by an arithmetic circuit*with*$m$*gates*, both*of*our protocols require each party to send*a**number**of*field elements and perform an amount*of*computation ...*We*describe scalable protocols for solving the secure multi-party computation (MPC) problem among*a*large*number**of*parties. ...*We*are also grateful for valuable comments from Ran Canetti (Boston University), Shafi Goldwasser (MIT), Aniket Kate (Saarland), Yehuda Lindell (Bar-Ilan), and Seth Pettie (UMich). ...##
###
Some Notes on Parallel Quantum Computation
[article]

1998
*
arXiv
*
pre-print

*We*prove that any quantum circuit composed entirely

*of*controlled-not

*gates*or

*of*diagonal

*gates*

*can*be parallelized to logarithmic

*depth*, while circuits composed

*of*both cannot. ... Finally, while

*we*note the Quantum Fourier Transform

*can*be parallelized to linear

*depth*,

*we*exhibit

*a*simple quantum circuit related to it that

*we*believe cannot be parallelized to less than linear

*depth*... Equivalently, NC problems are those solvable by Boolean circuits

*with*

*a*polynomial

*number*

*of*

*gates*and

*polylogarithmic*

*depth*. ...

##
###
Optimal Sorting Circuits for Short Keys
[article]

2021
*
arXiv
*
pre-print

Our result

arXiv:2102.11489v2
fatcat:ui3fp5tiibeodorpujo2djxari
*can*be viewed as*a*generalization*of*the landmark result by Ajtai, Komlós, and Szemerédi (STOC'83), simultaneously*in*terms*of*size and*depth*. ... Asharov et al. phrase it as an open question*how*to achieve optimality both*in*size and*depth*.*In*this paper,*we*close this important gap*in*our understanding. ...*We*would like to thank Silei Ren for discussions and help*in*an early stage*of*the project. ...##
###
Separating OR, SUM, and XOR circuits

2016
*
Journal of computer and system sciences (Print)
*

*We*show

*how*to obtain matrices that admit OR-circuits

*of*size O(n), but require SUMcircuits

*of*size Ω(n 3/2 /log 2 n). 2. ...

*We*consider the task

*of*rewriting

*a*given OR-circuit as

*a*XOR-circuit and prove that any subquadratic-time algorithm for this task violates the strong exponential time hypothesis. ... Furthermore,

*we*thank Jukka Suomela for discussions, and the anonymous referee for comments. ...

##
###
Adapt or Die: Polynomial Lower Bounds for Non-Adaptive Dynamic Data Structures
[article]

2012
*
arXiv
*
pre-print

Building on lower bound proofs for data structures

arXiv:1208.2846v2
fatcat:anf3tz53aneqdnquxok6pmnwsy
*in*slightly more restrictive models,*we*also present*a**number**of*properties*of*linear operators which*we*believe are worth investigating*in*the realm ... To shed more light on the seemingly inherent*polylogarithmic*lower bound barrier,*we*study several different notions*of*non-adaptivity and identify key properties that must be dealt*with*if*we*are to prove ... Instead,*we*define the size s(C)*of**a**depth*-2 ciruit C as the total*number**of*wires*in*it; i.e., the*number**of*edges*in*the graph. ...##
###
Internal Diffusion-Limited Aggregation: Parallel Algorithms and Complexity
[article]

1999
*
arXiv
*
pre-print

The numerical results are compatible

arXiv:cond-mat/9909233v1
fatcat:7x43mvxwvza6rmo4ntgrhx63ia
*with**a*running time that is either*polylogarithmic**in*n or*a*small power*of*n. ... For*a*parallel machine*with*k processors,*we*show that random clusters*in*d dimensions*can*be generated*in*O((n/k + log k) n^2/d) steps. ... Two primary complexity measures for*a*Boolean circuits are width and*depth*. Width is the largest*number**of**gates**in**a*level and*depth*is the*number**of*levels. ...##
###
Deterministic Preparation of Dicke States
[article]

2019
*
arXiv
*
pre-print

*We*present

*a*deterministic quantum algorithm for the preparation

*of*Dicke states. Implemented as

*a*quantum circuit, our scheme uses O(kn)

*gates*, has

*depth*O(n) and needs no ancilla qubits. ... The inductive nature

*of*our approach allows for linear-

*depth*preparation

*of*arbitrary symmetric pure states and -- used

*in*reverse -- yields

*a*quasilinear-

*depth*circuit for efficient compression

*of*quantum ... Research presented

*in*this article was supported by the Center for Nonlinear Studies CNLS and the Laboratory Directed Research and Development program

*of*Los Alamos National Laboratory under project

*number*...

##
###
Perfectly Secure Multiparty Computation and the Computational Overhead of Cryptography
[chapter]

2010
*
Lecture Notes in Computer Science
*

Thus, for typical largescale computations whose circuit width is much bigger than their

doi:10.1007/978-3-642-13190-5_23
fatcat:fwuhrsowirfmdli5726lvixrqi
*depth*and the*number**of*players, the amortized overhead is just*polylogarithmic**in*n and s. ... The protocol provides perfect security*with*guaranteed output delivery*in*the presence*of*an active, adaptive adversary corrupting*a*(1/3 − ε) fraction*of*the players, for an arbitrary*constant*ε > 0 and ... This protocol*can*be realized*with**a**constant**number**of*rounds under standard cryptographic assumptions. ...##
###
Good approximate quantum LDPC codes from spacetime circuit Hamiltonians

2019
*
Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing - STOC 2019
*

*We*also show that arbitrary Pauli errors

*can*be locally detected by circuits

*of*

*polylogarithmic*

*depth*. ... Then,

*in*order to obtain

*a*code

*with*sparse checks and strong detection

*of*local errors,

*we*use

*a*spacetime circuit-to-Hamiltonian construction

*in*order to take advantage

*of*the parallelism

*of*the Brown-Fawzi ... An arbitrary circuit consisting

*of*2-local

*gates*

*can*be transformed into

*a*sequence

*of*consecutive bitonic blocks,

*with*at most

*a*

*polylogarithmic*factor

*of*blow up

*in*the

*depth*6 . ...

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