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Bounds on the Power of Constant-Depth Quantum Circuits [article]

Stephen Fenner, Frederic Green, Steven Homer, Yong Zhang
2003 arXiv   pre-print
We show that if a language is recognized within certain error bounds by constant-depth quantum circuits over a finite family of gates, then it is computable in (classical) polynomial time.  ...  In particular, our results imply EQNC^0 is contained in P, where EQNC^0 is the constant-depth analog of the class EQP.  ...  Acknowledgments We would like to thank David DiVincenzo and Mark Heiligman for helpful conversations on this topic.  ... 
arXiv:quant-ph/0312209v2 fatcat:xyrqsatl7jhevfjlhfd7akpxqy

Bounds on the Power of Constant-Depth Quantum Circuits [chapter]

Stephen Fenner, Frederic Green, Steven Homer, Yong Zhang
2005 Lecture Notes in Computer Science  
In particular, our results imply where EQNC 0 is the constant-depth analog of the class EQP.  ...  On the other hand, we adapt and extend ideas of Terhal & DiVincenzo [TD02] to show that, for any family F of quantum gates including Hadamard and CNOT gates, computing the acceptance probabilities of depth-five  ...  Acknowledgments We would like to thank David DiVincenzo and Mark Heiligman for helpful conversations on this topic.  ... 
doi:10.1007/11537311_5 fatcat:yeirll7shrfrtaipzpm5q5pnjy

Page 3765 of Mathematical Reviews Vol. , Issue 2003e [page]

2003 Mathematical Reviews  
; Prague) Communication complexity towards lower bounds on circuit depth.  ...  to prove circuit depth bounds.”  ... 

Limitations of Noisy Reversible Computation [article]

D. Aharonov and M. Ben-Or(CS,Hebrew univ.) and R. Impagliazzo
1996 arXiv   pre-print
This establishes that noisy reversible computation has the power of the complexity class NC^1. We extend this to quantum circuits(QC).  ...  For the lower bound, we show that quasi-polynomial noisy QC are at least powerful as logarithmic depth QC, (or QNC^1). Making these bounds tight is left open in the quantum case.  ...  We next give a lower bound on the power of noisy quantum circuits: We show that noisy quantum circuits can simulate general quantum circuits, with an exponential cost.  ... 
arXiv:quant-ph/9611028v1 fatcat:eehjdujtuffk3n4bj4khaxxjwu

Quantum Advantage with Shallow Circuits under Arbitrary Corruption [article]

Atsuya Hasegawa, François Le Gall
2021 arXiv   pre-print
This gives another compelling evidence of the computational power of quantum shallow circuits.  ...  We show that even in this model, quantum circuits can still solve in constant depth computational problems that require logarithmic depth to solve with bounded fan-in classical circuits.  ...  JP16H01705, JP19H04066, JP20H00579, JP20H04139 and by the MEXT Quantum Leap Flagship Program (MEXT Q-LEAP) grant No. JPMXS0120319794.  ... 
arXiv:2105.00603v2 fatcat:75p5lqp5cfhcxn5dckjt24356i

Quantum Lower Bounds for Fanout [article]

Maosen Fang, Stephen Fenner, Frederic Green, Steven Homer, Yong Zhang
2003 arXiv   pre-print
We prove several new lower bounds for constant depth quantum circuits.  ...  In the case of a non-constant number a of ancillae, we give a tradeoff between a and the required depth, that results in a non-trivial lower bound for fanout when a = n^1-o(1).  ...  Acknowledgements We thank Luc Longpré for helpful discussions and comments on this paper.  ... 
arXiv:quant-ph/0312208v1 fatcat:ikmw6hbxpfeq3kfyuzecvyu3lm

Low depth algorithms for quantum amplitude estimation [article]

Tudor Giurgica-Tiron, Iordanis Kerenidis, Farrokh Labib, Anupam Prakash, William Zeng
2022 arXiv   pre-print
We design and analyze two new low depth algorithms for amplitude estimation (AE) achieving an optimal tradeoff between the quantum speedup and circuit depth.  ...  The first algorithm (Power law AE) uses power law schedules in the framework introduced by Suzuki et al .  ...  We thank an anonymous reviewer for helpful comments and for pointing out errors in a previous version of the QoPrime algorithm.  ... 
arXiv:2012.03348v2 fatcat:us4jatejajebdnz2nzi7pntc7a

Computational Depth Complexity of Measurement-Based Quantum Computation [chapter]

Dan Browne, Elham Kashefi, Simon Perdrix
2011 Lecture Notes in Computer Science  
Since one-way model has the same computational power as unbounded quantum fanout circuits, the quantum Fourier transform can be approximated in constant depth in the one-way model, and thus the factorisation  ...  The extra power of the one-way model, comparing with the quantum circuit model, comes from its classical-quantum hybrid nature.  ...  Section 3 is dedicated to the comparison of the computational power of the one-way model and the quantum circuit model.  ... 
doi:10.1007/978-3-642-18073-6_4 fatcat:uqyledk2o5c4voltzyfddkpok4

Computational depth complexity of measurement-based quantum computation [article]

Dan E. Browne, Elham Kashefi, Simon Perdrix
2009 arXiv   pre-print
Since one-way model has the same computational power as unbounded quantum fan-out circuits, the quantum Fourier transform can be approximated in constant depth in the one-way model, and thus the factorisation  ...  The extra power of the one-way model, comparing with the quantum circuit model, comes from its classical-quantum hybrid nature.  ...  Section 3 is dedicated to the comparison of the computational power of the one-way model and the quantum circuit model.  ... 
arXiv:0909.4673v1 fatcat:k57w5ddj7vdovbny234bj2bbpm

Possibilistic simulation of quantum circuits by classical circuits [article]

Daochen Wang
2021 arXiv   pre-print
Their result is equivalent to saying that a particular family of constant depth quantum circuits takes classical circuits at least Ω(log n) depth to "simulate", in a certain sense.  ...  In a recent breakthrough, Bravyi, Gosset, and König (BGK) [Science, 2018] unconditionally proved that constant depth quantum circuits are more powerful than their classical counterparts.  ...  ACKNOWLEDGEMENTS I'm indebted to Luke Schaeffer for finding a critical error in my costing the total depth of Stage 3 of the construction in v1 as O(log t) (cf. footnote [29]), sharing an early draft of  ... 
arXiv:1904.05282v3 fatcat:5fzzvt3qejdk3gd5jla2dh3rva

Universal Quantum Circuits [article]

Debajyoti Bera, Stephen Fenner, Frederic Green, Steve Homer
2008 arXiv   pre-print
Such circuits can be viewed as general-purpose simulators for central classes of quantum circuits and can be used to capture the computational power of the circuit class being simulated.  ...  We define and construct efficient depth-universal and almost-size-universal quantum circuits.  ...  The second author is grateful to Richard Cleve and IQC (Waterloo) and to Harry Buhrman and CWI (Amsterdam) for their hospitality.  ... 
arXiv:0804.2429v1 fatcat:w3vj25oeereadn7j6htvdkd7ie

Quantum Circuits with Unbounded Fan-out [article]

Peter Hoyer
2004 arXiv   pre-print
Constant-depth polynomial-size quantum circuits with bounded fan-in and unbounded fan-out over a fixed basis (denoted by QNCf^0) can approximate with polynomially small error the following gates: parity  ...  If we allow arbitrary one-qubit gates instead of a fixed basis, then these circuits can also be made exact in log-star depth.  ...  Introduction Classically, Threshold gates are strictly more powerful than polynomial-size constant-depth circuits with AND/OR/NOT/PARITY gates.  ... 
arXiv:quant-ph/0208043v3 fatcat:j3b7tuwqnzaarn63bfnfnorpxy

Efficient Universal Quantum Circuits [chapter]

Debajyoti Bera, Stephen Fenner, Frederic Green, Steve Homer
2009 Lecture Notes in Computer Science  
Such circuits can be viewed as generalpurpose simulators for central quantum circuit classes and used to capture the computational power of the simulated class.  ...  For depth we construct universal circuits whose depth is the same order as the circuits being simulated.  ...  The second author is grateful to Richard Cleve and IQC (Waterloo) and to Harry Buhrman and CWI (Amsterdam) for their hospitality.  ... 
doi:10.1007/978-3-642-02882-3_42 fatcat:6bmilsgiqfelnpccdgezu4r7le

Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions [article]

Andrew Y. Guo, Abhinav Deshpande, Su-Kuan Chu, Zachary Eldredge, Przemyslaw Bienias, Dhruv Devulapalli, Yuan Su, Andrew M. Childs, Alexey V. Gorshkov
2020 arXiv   pre-print
We leverage the power of these interactions to implement a fast quantum fanout gate with an arbitrary number of targets.  ...  The standard circuit model for quantum computation presumes the ability to directly perform gates between arbitrary pairs of qubits, which is unlikely to be practical for large-scale experiments.  ...  In the standard circuit model for quantum computation, the size of a quantum circuit is measured in terms of the number of gates it contains.  ... 
arXiv:2007.00662v1 fatcat:r7bs2vdkczdvjlfmknrifossmm

Fast parallel circuits for the quantum Fourier transform [article]

Richard Cleve, John Watrous
2000 arXiv   pre-print
We give new bounds on the circuit complexity of the quantum Fourier transform (QFT).  ...  Finally, we prove an Omega(log n) lower bound on the depth complexity of approximations of the QFT with constant error.  ...  Acknowledgments We thank Wayne Eberly for helpful discussions on classical circuit complexity, and Chris Fuchs and Patrick Hayden for an informative discussion regarding quantum state distance measures  ... 
arXiv:quant-ph/0006004v1 fatcat:z6eks6foirdzji7eiir5au47ne
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