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Error mitigation for universal gates on encoded qubits [article]

Christophe Piveteau, David Sutter, Sergey Bravyi, Jay M. Gambetta, Kristan Temme
2021 arXiv   pre-print
As 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.  ... 
arXiv:2103.04915v2 fatcat:g23quvamnze4rbtitqhn7sfori

New algorithms and lower bounds for circuits with linear threshold gates [article]

Ryan Williams
2014 arXiv   pre-print
Let ACC ∘ THR be the class 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.  ... 
arXiv:1401.2444v1 fatcat:ienft6r5evacrozmwkbbseuktu

Computing Majority by Constant Depth Majority Circuits with Low Fan-in Gates [article]

Alexander S. Kulikov, Vladimir V. Podolskii
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.  ... 
arXiv:1610.02686v1 fatcat:74xhlc3drncynhzp4v7nnitiry

Efficient decomposition of single-qubit gates intoVbasis circuits

Alex Bocharov, Yuri Gurevich, Krysta M. Svore
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.  ... 
doi:10.1103/physreva.88.012313 fatcat:26na6doulbbjrci2nsfji2qxvu

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

Pablo A. M. Casares, Roberto Campos, M. A. Martin-Delgado
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.  ... 
arXiv:2110.05899v2 fatcat:7jowtrgszfb6xgsdhpj545uufi

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

Pablo A. M. Casares, Roberto Campos, M. A. Martin-Delgado
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.  ... 
doi:10.22331/q-2022-07-20-768 fatcat:smzkvbboqja2xdl7ektfnqd7au

Secure Multi-Party Computation in Large Networks [article]

Varsha Dani, Valerie King, Mahnush Movahedi, Jared Saia, Mahdi Zamani
2015 arXiv   pre-print
For any deterministic function that 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).  ... 
arXiv:1203.0289v3 fatcat:3tleszkgtba7dcd7fmwsdnivka

Some Notes on Parallel Quantum Computation [article]

Cristopher Moore, Martin Nilsson
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.  ... 
arXiv:quant-ph/9804034v2 fatcat:p4vqta2a45clxibhoqsoz4fnma

Optimal Sorting Circuits for Short Keys [article]

Wei-Kai Lin, Elaine Shi
2021 arXiv   pre-print
Our result 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.  ... 
arXiv:2102.11489v2 fatcat:ui3fp5tiibeodorpujo2djxari

Separating OR, SUM, and XOR circuits

Magnus Find, Mika Göös, Matti Järvisalo, Petteri Kaski, Mikko Koivisto, Janne H. Korhonen
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.  ... 
doi:10.1016/j.jcss.2016.01.001 pmid:28529379 pmcid:PMC5432968 fatcat:rzb7c4kwafchxposnbep2hudtu

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

Joshua Brody, Kasper Green Larsen
2012 arXiv   pre-print
Building on lower bound proofs for data structures 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.  ... 
arXiv:1208.2846v2 fatcat:anf3tz53aneqdnquxok6pmnwsy

Internal Diffusion-Limited Aggregation: Parallel Algorithms and Complexity [article]

Cristopher Moore, Jonathan Machta
1999 arXiv   pre-print
The numerical results are compatible 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.  ... 
arXiv:cond-mat/9909233v1 fatcat:7x43mvxwvza6rmo4ntgrhx63ia

Deterministic Preparation of Dicke States [article]

Andreas Bärtschi, Stephan Eidenbenz
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  ... 
arXiv:1904.07358v1 fatcat:emlse2msqfapnn4nzobikvq3py

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

Ivan Damgård, Yuval Ishai, Mikkel Krøigaard
2010 Lecture Notes in Computer Science  
Thus, for typical largescale computations whose circuit width is much bigger than their 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.  ... 
doi:10.1007/978-3-642-13190-5_23 fatcat:fwuhrsowirfmdli5726lvixrqi

Good approximate quantum LDPC codes from spacetime circuit Hamiltonians

Thomas C. Bohdanowicz, Elizabeth Crosson, Chinmay Nirkhe, Henry Yuen
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 .  ... 
doi:10.1145/3313276.3316384 dblp:conf/stoc/BohdanowiczCNY19 fatcat:cum2dlxhdvht5cgyonf4vf4pmq
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