The complexity of analog computation
Mathematics and Computers in Simulation
Structural complexity 1
Time/space trade-offs for reversible computation
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Reversible space equals deterministic space
Journal of Computer and System Sciences - Eleventh annual conference on computational learning theory&slash;Twelfth Annual IEEE conference on computational complexity
Quantum computation and quantum information
Quantum computation and quantum information
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Adiabatic quantum state generation and statistical zero knowledge
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Classical and Quantum Computation
Classical and Quantum Computation
Quantum Information Processing
The Complexity of the Local Hamiltonian Problem
SIAM Journal on Computing
On the power of multiplication in random access machines
SWAT '74 Proceedings of the 15th Annual Symposium on Switching and Automata Theory (swat 1974)
Quantum algorithm for measuring the energy of n qubits with unknown pair-interactions
Quantum Information & Computation
3-local Hamitonian is QMA-complete
Quantum Information & Computation
The complexity of stoquastic local Hamiltonian problems
Quantum Information & Computation
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We consider a hypothetical apparatus that implements measurements for arbitrary 4- local quantum observables A on n qubits. The apparatus implements the "measurement algorithm" after receiving a classical description of A. We show that a few precise measurements applied to a basis state would provide a probabilistic solution of PSPACE problems. The error probability decreases exponentially with the number of runs, if the measurement accuracy is of the order of the spectral gaps of the operator A. Moreover, every decision problem that can be solved by a deterministic quantum algorithm in T time steps can be encoded into a 4-local observable such that the solution requires only measurements of accuracy O(1/T). Provided that BQP ≠ PSPACE, our result shows that efficient algorithms for precise measurements of general 4-local observables cannot exist. We conjecture that the class of physically existing interactions is large enough to allow the conclusion that precise energy measurements for general many-particle systems require control algorithms with high complexity.