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Quantum NP - A Survey
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We describe Kitaev's result from 1999, in which he defines the complexity class QMA, the quantum analog of the class NP, and shows that a natural extension of 3-SAT, namely local Hamiltonians, is QMA complete. The result builds upon the classical Cook-Levin proof of the NP completeness of SAT, but differs from it in several fundamental ways, which we highlight. This result raises a rich array of open problems related to quantum complexity, algorithms and entanglement, which we state at the end of this survey. This survey is the extension of lecture notes taken by Naveh for Aharonov's quantum computation course, held in Tel Aviv University, 2001.
Forward citations
Cited by 4 Pith papers
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Quantum SAT Problems with Finite Sets of Projectors are Complete for a Plethora of Classes
New QSAT variants on qubits and qudits are complete for BQP_1, coRP, QCMA and six PI/SoPU classes, implying any classification of strong quantum CSPs must contain at least 13 classes unless some collapse.
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On the complexity of estimating ground state entanglement and free energy
Detecting high-entanglement ground states is claimed qq-QAM-complete and free-energy approximation in qq-QAM, but the main containment proofs mishandle the number of Hamiltonian terms.
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Quantum Differential Equation Solvers with Low State Preparation Cost: Eliminating the Time Dependence in Dissipative Equations
For strictly dissipative linear ODEs, quantum solvers based on time-marching or LCHS achieve query complexity O(polylog(1/ε)) that is independent of the evolution time T.
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Deciding Whether a C-Q Channel Preserves a Bit is QCMA-Complete
Deciding if a classical-quantum channel can exactly preserve a single bit is QCMA-complete, with optimal witnesses characterized as computational basis states (minimum) and |+>, |-> states (maximum).
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