Abstract
We present an efficient algorithm for simulating the time evolution due to a sparse Hamiltonian. In terms of the maximum degree d and dimension N of the space on which the Hamiltonian H acts for time t, this algorithm uses (d 2(d + log* N) ∥ Ht ∥ )1 + o(1) queries. This improves the complexity of the sparse Hamiltonian simulation algorithm of Berry, Ahokas, Cleve, and Sanders, which scales like (d 4(log* N) ∥ Ht ∥ )1 + o(1). To achieve this, we decompose a general sparse Hamiltonian into a small sum of Hamiltonians whose graphs of non-zero entries have the property that every connected component is a star, and efficiently simulate each of these pieces.
Work supported by MITACS, NSERC, QuantumWorks, and the US ARO/DTO.
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Childs, A.M., Kothari, R. (2011). Simulating Sparse Hamiltonians with Star Decompositions. In: van Dam, W., Kendon, V.M., Severini, S. (eds) Theory of Quantum Computation, Communication, and Cryptography. TQC 2010. Lecture Notes in Computer Science, vol 6519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18073-6_8
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DOI: https://doi.org/10.1007/978-3-642-18073-6_8
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