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

2003
*
arXiv
*
pre-print

We show that if a language is recognized within certain error

arXiv:quant-ph/0312209v2
fatcat:xyrqsatl7jhevfjlhfd7akpxqy
*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. ...##
###
Bounds on the Power of Constant-Depth Quantum Circuits
[chapter]

2005
*
Lecture Notes in Computer Science
*

In particular, our results imply where EQNC 0 is

doi:10.1007/11537311_5
fatcat:yeirll7shrfrtaipzpm5q5pnjy
*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. ...##
###
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]

1996
*
arXiv
*
pre-print

This establishes that noisy reversible computation has

arXiv:quant-ph/9611028v1
fatcat:eehjdujtuffk3n4bj4khaxxjwu
*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. ...##
###
Quantum Advantage with Shallow Circuits under Arbitrary Corruption
[article]

2021
*
arXiv
*
pre-print

This gives another compelling evidence

arXiv:2105.00603v2
fatcat:75p5lqp5cfhcxn5dckjt24356i
*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. ...##
###
Quantum Lower Bounds for Fanout
[article]

2003
*
arXiv
*
pre-print

We prove several new lower

arXiv:quant-ph/0312208v1
fatcat:ikmw6hbxpfeq3kfyuzecvyu3lm
*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. ...##
###
Low depth algorithms for quantum amplitude estimation
[article]

2022
*
arXiv
*
pre-print

We design and analyze two new low

arXiv:2012.03348v2
fatcat:us4jatejajebdnz2nzi7pntc7a
*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. ...##
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Computational Depth Complexity of Measurement-Based Quantum Computation
[chapter]

2011
*
Lecture Notes in Computer Science
*

Since

doi:10.1007/978-3-642-18073-6_4
fatcat:uqyledk2o5c4voltzyfddkpok4
*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. ...##
###
Computational depth complexity of measurement-based quantum computation
[article]

2009
*
arXiv
*
pre-print

Since

arXiv:0909.4673v1
fatcat:k57w5ddj7vdovbny234bj2bbpm
*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. ...##
###
Possibilistic simulation of quantum circuits by classical circuits
[article]

2021
*
arXiv
*
pre-print

Their result is equivalent to saying that a particular family

arXiv:1904.05282v3
fatcat:5fzzvt3qejdk3gd5jla2dh3rva
*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*...##
###
Universal Quantum Circuits
[article]

2008
*
arXiv
*
pre-print

Such

arXiv:0804.2429v1
fatcat:w3vj25oeereadn7j6htvdkd7ie
*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. ...##
###
Quantum Circuits with Unbounded Fan-out
[article]

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. ...

##
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Efficient Universal Quantum Circuits
[chapter]

2009
*
Lecture Notes in Computer Science
*

Such

doi:10.1007/978-3-642-02882-3_42
fatcat:6bmilsgiqfelnpccdgezu4r7le
*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. ...##
###
Implementing a Fast Unbounded Quantum Fanout Gate Using Power-Law Interactions
[article]

2020
*
arXiv
*
pre-print

We leverage

arXiv:2007.00662v1
fatcat:r7bs2vdkczdvjlfmknrifossmm
*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. ...##
###
Fast parallel circuits for the quantum Fourier transform
[article]

2000
*
arXiv
*
pre-print

We give new

arXiv:quant-ph/0006004v1
fatcat:z6eks6foirdzji7eiir5au47ne
*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 ...
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