Article Outline
Glossary
Definition of the Subject
Introduction
The Quantum Circuit Model
PolynomialâTime Quantum Computations
Quantum Proofs
Quantum Interactive Proof Systems
Other Selected Notions in Quantum Complexity
Future Directions
Bibliography
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Abbreviations
- Quantum circuit:
-
AÂ quantum circuit is an acyclic network of quantum gates connected by wires: the gates represent quantum operations and the wires represent the qubits on which these operations are performed. The quantum circuit model is the most commonly studied model of quantum computation.
- Quantum complexity class:
-
A quantum complexity class is a collection of computational problems that are solvable by a chosen quantum computational model that obeys certain resource constraints. For example, BQP is the quantum complexity class of all decision problems that can be solved in polynomial time by a quantum computer.
- Quantum proof:
-
A quantum proof is a quantum state that plays the role of a witness or certificate to a quantum computer that runs a verification procedure. The quantum complexity class QMA is defined by this notion: it includes all decision problems whose yesâinstances are efficiently verifiable by means of quantum proofs.
- Quantum interactive proof system:
-
A quantum interactive proof system is an interaction between a verifier and one or more provers, involving the processing and exchange of quantum information, whereby the provers attempt to convince the verifier of the answer to some computational problem.
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Watrous, J. (2012). Quantum Computational Complexity. In: Meyers, R. (eds) Computational Complexity. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1800-9_147
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