Efficient Quantum Algorithms for Simulating Sparse Hamiltonians

We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a constant number of nonzero entries in each row...

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Bibliographic Details
Published in:Communications in mathematical physics Vol. 270; no. 2; pp. 359 - 371
Main Authors: Berry, Dominic W., Ahokas, Graeme, Cleve, Richard, Sanders, Barry C.
Format: Journal Article
Language:English
Published: Heidelberg Springer 01.03.2007
Springer Nature B.V
Subjects:
Algorithmics. Computability. Computer arithmetics
Algorithms
Applied sciences
Classical and quantum physics: mechanics and fields
Computer science; control theory; systems
Exact sciences and technology
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Physics
Quantum computation
Quantum information
Qubits (quantum computing)
Sciences and techniques of general use
Simulation
Theoretical computing
Quantum algorithm
Qubit
Hamiltonians
Mathematical physics
ISSN:0010-3616, 1432-0916
Online Access:Get full text
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Summary:We present an efficient quantum algorithm for simulating the evolution of a quantum state for a sparse Hamiltonian H over a given time t in terms of a procedure for computing the matrix entries of H. In particular, when H acts on n qubits, has at most a constant number of nonzero entries in each row/column, and ||H|| is bounded by a constant, we may select any positive integer k such that the simulation requires O((log*n)t1+1/2k) accesses to matrix entries of H. We also show that the temporal scaling cannot be significantly improved beyond this, because sublinear time scaling is not possible.
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content type line 14
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-006-0150-x