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Bounds on the Power of Constant-Depth Quantum Circuits
[article]
2003
arXiv
pre-print
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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]
2005
Lecture Notes in Computer Science
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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
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Communication complexity towards lower bounds on circuit depth. ...
to prove circuit depth bounds.” ...
Limitations of Noisy Reversible Computation
[article]
1996
arXiv
pre-print
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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]
2021
arXiv
pre-print
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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]
2003
arXiv
pre-print
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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]
2022
arXiv
pre-print
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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]
2011
Lecture Notes in Computer Science
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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]
2009
arXiv
pre-print
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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]
2021
arXiv
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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]
2008
arXiv
pre-print
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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]
2004
arXiv
pre-print
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2002 pre-print arXiv:quant-ph/0208043v1 fatcat:hgaqvmggvjh3rokkd34g276hceOther Versions
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]
2009
Lecture Notes in Computer Science
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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]
2020
arXiv
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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]
2000
arXiv
pre-print
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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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