Storing a Sparse Table with 0(1) Worst Case Access Time
Journal of the ACM (JACM)
Private vs. common random bits in communication complexity
Information Processing Letters
A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
Optimal bounds for the predecessor problem
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Quantum Entanglement and the Communication Complexity of the Inner Product Function
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Lower Bounds in the Quantum Cell Probe Model
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
The quantum complexity of set membership
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Lower Bounds in the Quantum Cell Probe Model
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
The Quantum Communication Complexity of the Pointer Chasing Problem: The Bit Version
FST TCS '02 Proceedings of the 22nd Conference Kanpur on Foundations of Software Technology and Theoretical Computer Science
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We introduce a new model for studying quantum data structure problems -- the quantum cell probe model. We prove a lower bound for the static predecessor problem in the address-only version of this model where, essentially, we allow quantum parallelism only over the 'address lines' of the queries. This model subsumes the classical cell probe model, and many quantum query algorithms like Grover's algorithm fall into this framework. We prove our lower bound by obtaining a round elimination lemma for quantum communication complexity. A similar lemma was proved by Miltersen, Nisan, Safra and Wigderson [9] for classical communication complexity, but their proof does not generalise to the quantum setting. We also study the static membership problem in the quantum cell probe model. Generalising a result of Yao [16], we show that if the storage scheme is implicit, that is it can only store members of the subset and 'pointers', then any quantum query scheme must make Ω(log n) probes. We also consider the one-round quantum communication complexity of set membership and show tight bounds.