Finding resource states of measurement-based quantum computing is harder than quantum computing
Abstract
Measurement-based quantum computing enables universal quantum computing with only adaptive single-qubit measurements on certain many-qubit states, such as the graph state, the Affleck-Kennedy-Lieb-Tasaki (AKLT) state, and several tensor-network states. Finding new resource states of measurement-based quantum computing is a hard task, since for a given state there are exponentially many possible measurement patterns on the state. In this paper, we consider the problem of deciding, for a given state and a set of unitary operators, whether there exists a way of measurement-based quantum computing on the state that can realize all unitaries in the set, or not. We show that the decision problem is QCMA-hard (where QCMA stands for quantum classical Merlin Arthur), which means that finding new resource states of measurement-based quantum computing is harder than quantum computing itself [unless BQP (bounded-error quantum polynomial time) is equal to QCMA]. We also derive an upper bound of the decision problem: the problem is in a quantum version of the second level of the polynomial hierarchy.
- Publication:
-
Physical Review A
- Pub Date:
- November 2017
- DOI:
- 10.1103/PhysRevA.96.052308
- arXiv:
- arXiv:1609.00457
- Bibcode:
- 2017PhRvA..96e2308M
- Keywords:
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- Quantum Physics;
- Condensed Matter - Statistical Mechanics;
- Condensed Matter - Strongly Correlated Electrons;
- Computer Science - Computational Complexity
- E-Print:
- 5 pages, 1 figure