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Quantum Zero-Error Algorithms Cannot be Composed
[article]

2003
*
arXiv
*
pre-print

This shows that

arXiv:quant-ph/0211029v2
fatcat:45ukmtw4dja7rd57p54h5hli5m
*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*. ...##
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Quantum zero-error algorithms cannot be composed

2003
*
Information Processing Letters
*

This shows that

doi:10.1016/s0020-0190(03)00254-0
fatcat:jrwfs2tfy5atllqezujkt2nsqe
*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*. ...##
###
Quantum Proofs of Knowledge
[chapter]

2012
*
Lecture Notes in Computer Science
*

Combining our results with Watrous' results on

doi:10.1007/978-3-642-29011-4_10
fatcat:cs3mb3dnknhjpam4ex7pcrdeva
*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. ...##
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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?? ...

##
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Separations in query complexity using cheat sheets

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. ...

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

2019
*
Theory of Quantum Computation, Communication, and Cryptography
*

We show that a general lifting theorem for either

doi:10.4230/lipics.tqc.2019.2
dblp:conf/tqc/Ben-DavidK19
fatcat:7m7noj75jnhz7ao5hop6pyzgyu
*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-? ...##
###
Quantum distinguishing complexity, zero-error algorithms, and statistical zero knowledge
[article]

2019
*
arXiv
*
pre-print

We show that a general lifting theorem for either

arXiv:1902.03660v1
fatcat:ax7hxx6xe5hsffxhnshsrxepyy
*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-? ...##
###
Bounds for Small-Error and Zero-Error Quantum Algorithms
[article]

1999
*
arXiv
*
pre-print

We present a number of results related to

arXiv:cs/9904019v2
fatcat:6xj5kxpbifg37fezhfyril3s7e
*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. ...##
###
Classical algorithms for quantum mean values
[article]

2019
*
arXiv
*
pre-print

We also prove a technical lemma characterizing a

arXiv:1909.11485v1
fatcat:u5uxit3xrvepfbnfdc5zel3hme
*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 ...##
###
Interference versus success probability in quantum algorithms with imperfections

2008
*
Physical Review A. Atomic, Molecular, and Optical Physics
*

We study the influence of

doi:10.1103/physreva.77.022318
fatcat:whtord4isbezreao7mg36chc5q
*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 ...##
###
Some Notes on Parallel Quantum Computation
[article]

1998
*
arXiv
*
pre-print

We prove that any

arXiv:quant-ph/9804034v2
fatcat:p4vqta2a45clxibhoqsoz4fnma
*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 ...##
###
On the Quantum Black-Box Complexity of Majority
[article]

2002
*
arXiv
*
pre-print

We describe a

arXiv:quant-ph/0109101v3
fatcat:iyy6fwqkvnhf5iubi4yudjs65u
*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*. ...##
###
Resemblance Coefficient and a Quantum Genetic Algorithm for Feature Selection
[chapter]

2004
*
Lecture Notes in Computer Science
*

Feature selection

doi:10.1007/978-3-540-30214-8_12
fatcat:fpkvyaxr7fb3lo4ncnzs4bp22u
*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. ...##
###
Designing quantum repeater networks

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. ...

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

2015
*
arXiv
*
pre-print

While this is thought to

arXiv:1506.04627v3
fatcat:vdtln5knvbcthhfinex2r2ug6q
*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. ...
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