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Quantum Zero-Error Algorithms Cannot be Composed [article]

Harry Buhrman, Ronald de Wolf
2003 arXiv   pre-print
This shows that quantum zero-error algorithms cannot be composed. In oracle terms, we give a relativized world where ZQP^ZQPZ̄QP, while classically we always have ZPP^ZPP=ZPP.  ...  We exhibit two black-box problems, both of which have an efficient quantum algorithm with zero-error, yet whose composition does not have an efficient quantum algorithm with zero-error.  ...  This result is somewhat surprising, because exact quantum algorithms can easily be composed, and so can bounded-error quantum algorithms.  ... 
arXiv:quant-ph/0211029v2 fatcat:45ukmtw4dja7rd57p54h5hli5m

Quantum zero-error algorithms cannot be composed

Harry Buhrman, Ronald de Wolf
2003 Information Processing Letters  
This shows that quantum zero-error algorithms cannot be composed. In oracle terms, we give a relativized world where ZQP ZQP = ZQP, while classically we always have ZPP ZPP = ZPP.  ...  We exhibit two black-box problems, both of which have an efficient quantum algorithm with zero-error, yet whose composition does not have an efficient quantum algorithm with zero-error.  ...  This result is somewhat surprising, because exact quantum algorithms can easily be composed, and so can bounded-error quantum algorithms.  ... 
doi:10.1016/s0020-0190(03)00254-0 fatcat:jrwfs2tfy5atllqezujkt2nsqe

Quantum Proofs of Knowledge [chapter]

Dominique Unruh
2012 Lecture Notes in Computer Science  
Combining our results with Watrous' results on quantum zeroknowledge, we show that there are zero-knowledge quantum proofs of knowledge for all languages in NP (assuming quantum one-way permutations).  ...  We motivate, define and construct quantum proofs of knowledge, proofs of knowledge secure against quantum adversaries.  ...  Two features unique to the quantum setting prohibit (naive) rewinding: The no-cloning theorem [WZ82] states that quantum-information cannot be copied, so we cannot make snapshots.  ... 
doi:10.1007/978-3-642-29011-4_10 fatcat:cs3mb3dnknhjpam4ex7pcrdeva

Page 3298 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
zero-error algorithms cannot be composed.  ...  This shows that quantum zero-error algorithms cannot be composed. In oracle terms, we give a relativized world where ZQPZ2" 4 ZQP, while classically we always have ZPP2??  ... 

Separations in query complexity using cheat sheets

Scott Aaronson, Shalev Ben-David, Robin Kothari
2016 Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2016  
be quadratic (from Grover's algorithm).  ...  We show a power 2.5 separation between bounded-error randomized and quantum query complexity for a total Boolean function, refuting the widely believed conjecture that the best such separation could only  ...  We also thank Hardik Bansal for spotting an error in an earlier version of the proof of Theorem 5.  ... 
doi:10.1145/2897518.2897644 dblp:conf/stoc/AaronsonBK16 fatcat:x77uykivsvhfle3icc2ocbqcai

Quantum Distinguishing Complexity, Zero-Error Algorithms, and Statistical Zero Knowledge

Shalev Ben-David, Robin Kothari, Michael Wagner
2019 Theory of Quantum Computation, Communication, and Cryptography  
We show that a general lifting theorem for either zero-error quantum query complexity or for QSZK would imply a general lifting theorem for bounded-error quantum query complexity.  ...  Using this measure, we establish a new relationship in query complexity: For all total functions f , Q 0 (f ) = O(Q(f ) 5 ), where Q 0 (f ) and Q(f ) denote the zero-error and bounded-error quantum query  ...  However, this is not known to be true for zero-error quantum algorithms, and zero-error quantum algorithms that also output a certificate when they output a non-?  ... 
doi:10.4230/lipics.tqc.2019.2 dblp:conf/tqc/Ben-DavidK19 fatcat:7m7noj75jnhz7ao5hop6pyzgyu

Quantum distinguishing complexity, zero-error algorithms, and statistical zero knowledge [article]

Shalev Ben-David, Robin Kothari
2019 arXiv   pre-print
We show that a general lifting theorem for either zero-error quantum query complexity or for QSZK would imply a general lifting theorem for bounded-error quantum query complexity.  ...  Using this measure, we establish a new relationship in query complexity: For all total functions f, Q_0(f)=O~(Q(f)^5), where Q_0(f) and Q(f) denote the zero-error and bounded-error quantum query complexity  ...  However, this is not known to be true for zero-error quantum algorithms, and zero-error quantum algorithms that also output a certificate when they output a non-?  ... 
arXiv:1902.03660v1 fatcat:ax7hxx6xe5hsffxhnshsrxepyy

Bounds for Small-Error and Zero-Error Quantum Algorithms [article]

H. Buhrman, R. de Wolf (CWI and U.Amsterdam), Ch. Zalka
1999 arXiv   pre-print
We present a number of results related to quantum algorithms with small error probability and quantum algorithms that are zero-error.  ...  Next, we establish nearly optimal quantum-classical separations for the query complexity of monotone functions in the zero-error model (where our quantum zero-error model is defined so as to be robust  ...  quantum search, and Mosca and Yevgeniy Dodis for helpful discussions about graph properties.  ... 
arXiv:cs/9904019v2 fatcat:6xj5kxpbifg37fezhfyril3s7e

Classical algorithms for quantum mean values [article]

Sergey Bravyi, David Gosset, Ramis Movassagh
2019 arXiv   pre-print
We also prove a technical lemma characterizing a zero-free region for certain polynomials associated with a quantum circuit, which may be of independent interest.  ...  This task is a cornerstone of variational quantum algorithms for optimization, machine learning, and the simulation of quantum many-body systems.  ...  Our results suggest that achieving a quantum advantage with variational quantum algorithms requires either a superconstant circuit depth (e.g., d ∼ log n) or qubit connectivity graphs that cannot be locally  ... 
arXiv:1909.11485v1 fatcat:u5uxit3xrvepfbnfdc5zel3hme

Interference versus success probability in quantum algorithms with imperfections

Daniel Braun, Bertrand Georgeot
2008 Physical Review A. Atomic, Molecular, and Optical Physics  
We study the influence of errors and decoherence on both the performance of Shor's factoring algorithm and Grover's search algorithm, and on the amount of interference in these algorithms using a recently  ...  We consider systematic unitary errors, random unitary errors, and decoherence processes. We show that unitary errors which destroy the interference destroy the efficiency of the algorithm, too.  ...  According to Jozsa and Linden's result [10] this algorithm cannot provide any speed-up over its classical counterpart (as it creates zero entanglement), and indeed, it can evidently be efficiently simulated  ... 
doi:10.1103/physreva.77.022318 fatcat:whtord4isbezreao7mg36chc5q

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  ...  (Gate errors, on the other hand, will not be improved by parallelization, and may even get worse if the parallel algorithm involves more gates. ) We define quantum operators and quantum circuits as follows  ... 
arXiv:quant-ph/9804034v2 fatcat:p4vqta2a45clxibhoqsoz4fnma

On the Quantum Black-Box Complexity of Majority [article]

Thomas Hayes, Samuel Kutin, Dieter van Melkebeek
2002 arXiv   pre-print
We describe a quantum black-box network computing the majority of N bits with zero-sided error eps using only 2N/3 + O(sqrtN (log log N + log 1/eps)) queries: the algorithm returns the correct answer with  ...  Any classical randomized decision tree computing the majority on N bits with zero-sided error 1/2 has cost N.  ...  It is also known that we can efficiently compose quantum algorithms.  ... 
arXiv:quant-ph/0109101v3 fatcat:iyy6fwqkvnhf5iubi4yudjs65u

Resemblance Coefficient and a Quantum Genetic Algorithm for Feature Selection [chapter]

Gexiang Zhang, Laizhao Hu, Weidong Jin
2004 Lecture Notes in Computer Science  
Feature selection algorithm using RC criterion and a quantum genetic algorithm is described in detail.  ...  are used respectively to select the optimal feature subset from original feature set (OFS) composed of 16 features of radar emitter signals.  ...  done. (2) An efficient optimization algorithm called quantum genetic algorithm is introduced to select the best feature subset from the original feature set composed of a large number of features.  ... 
doi:10.1007/978-3-540-30214-8_12 fatcat:fpkvyaxr7fb3lo4ncnzs4bp22u

Designing quantum repeater networks

Rodney Meter, Joe Touch
2013 IEEE Communications Magazine  
Quantum information cannot be copied, a restriction known as the no-cloning theorem [3] .  ...  Quantum Error Correction -QEC may be based on classical codes or purely quantum concepts.  ... 
doi:10.1109/mcom.2013.6576340 fatcat:akseehucfvf6bj45itdyfhnyzq

Efficient classical simulation of the Deutsch-Jozsa algorithm [article]

Niklas Johansson, Jan-Åke Larsson
2015 arXiv   pre-print
While this is thought to be true in general, there is usually no way of knowing that the corresponding classical algorithms are the best possible solutions.  ...  Our conclusion is that the Deutsch-Jozsa quantum algorithm owes its speed-up to resources that are not necessarily quantum-mechanical, and when compared with the classical simulation offers no speed-up  ...  Given such an oracle, a quantum computer can solve the problem with a single query by using the Deutsch-Jozsa algorithm [2, 6] , in the ideal case with zero error probability.  ... 
arXiv:1506.04627v3 fatcat:vdtln5knvbcthhfinex2r2ug6q
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