Quantum Oracle Interrogation: Getting all information for almost half the price
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In this paper, it was shown that N/2+sqrt(N) calls to the oracle are sufficient to guess the whole content of the binary oracle (being an N bit string) with probability greater than 95%.Abstract:
Consider a quantum computer in combination with a binary oracle of domain size N. It is shown how N/2+sqrt(N) calls to the oracle are sufficient to guess the whole content of the oracle (being an N bit string) with probability greater than 95%. This contrasts the power of classical computers which would require N calls to achieve the same task. From this result it follows that any function with the N bits of the oracle as input can be calculated using N/2+sqrt(N) queries if we allow a small probability of error. It is also shown that this error probability can be made arbitrary small by using N/2+O(sqrt(N)) oracle queries.
In the second part of the article `approximate interrogation' is considered. This is when only a certain fraction of the N oracle bits are requested. Also for this scenario does the quantum algorithm outperform the classical protocols. An example is given where a quantum procedure with N/10 queries returns a string of which 80% of the bits are correct. Any classical protocol would need 6N/10 queries to establish such a correctness ratio.read more
Citations
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Complexity measures and decision tree complexity: a survey
Harry Buhrman,Ronald de Wolf +1 more
TL;DR: Several complexity measures for Boolean functions are discussed: certificate complexity, sensitivity, block sensitivity, and the degree of a representing or approximating polynomial, and how they give bounds for the decision tree complexity of Boolean functions on deterministic, randomized, and quantum computers.
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Quantum lower bounds by polynomials
TL;DR: This work examines the number of queries to input variables that a quantum algorithm requires to compute Boolean functions on {0,1}N in the black-box model and gives asymptotically tight characterizations of T for all symmetric f in the exact, zero-error, and bounded-error settings.
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Quantum Lower Bounds by Polynomials
TL;DR: In this article, it was shown that the exponential quantum speed-up obtained for partial functions (i.e., problems involving a promise on the input) by Deutsch and Jozsa and by Simon cannot be obtained for any total function, and that there is a classical deterministic algorithm that computes some total Boolean function f with bounded-error using T black-box queries.
Proceedings ArticleDOI
Quantum lower bounds by polynomials
TL;DR: This work examines the number T of queries that a quantum network requires to compute several Boolean functions on {0,1}/sup N/ in the black-box model and gives asymptotically tight characterizations of T for all symmetric f in the exact, zero-error, and bounded-error settings.
Proceedings ArticleDOI
Exponential lower bound for 2-query locally decodable codes via a quantum argument
TL;DR: Recently, Goldreich et al. as mentioned in this paper showed that a 2-query LDC can be decoded with only 1 quantum query, and then proved an exponential lower bound for such 1-query locally quantum-decodable codes.
References
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Journal ArticleDOI
Communication via One- and Two-Particle Operators on Einstein-Podolsky-Rosen States
TL;DR: The set of states accessible from an initial EPR state by one-particle operations are characterized and it is shown that in a sense they allow two bits to be encoded reliably in one spin-1/2 particle.
Journal ArticleDOI
Quantum Complexity Theory
Ethan Bernstein,Umesh Vazirani +1 more
TL;DR: This paper gives the first formal evidence that quantum Turing machines violate the modern (complexity theoretic) formulation of the Church--Turing thesis, and proves that bits of precision suffice to support a step computation.
Journal ArticleDOI
Quantum algorithms revisited
TL;DR: In this article, a common pattern underpinning quantum algorithms can be identified when quantum computation is viewed as multiparticle interference, and an explicit algorithm for generating any prescribed interference pattern with an arbitrary precision is provided.
Posted Content
Quantum Lower Bounds by Polynomials
TL;DR: In this article, it was shown that the exponential quantum speed-up obtained for partial functions (i.e., problems involving a promise on the input) by Deutsch and Jozsa and by Simon cannot be obtained for any total function, and that there is a classical deterministic algorithm that computes some total Boolean function f with bounded-error using T black-box queries.
Journal ArticleDOI
Quantum Computers Can Search Arbitrarily Large Databases by a Single Query
TL;DR: This paper shows that a quantum mechanical algorithm that can query information relating to multiple items of the database can search a database for a unique item satisfying a given condition, in a single query.