Abstract
We propose a modification to Nielsen's circuit complexity for Hamiltonian simulation using the Suzuki-Trotter (ST) method, which provides a network like structure for the quantum circuit. This leads to an optimized gate counting linear in the geodesic distance and spatial volume, unlike in the original proposal. The optimized ST iteration order is correlated with the error tolerance and plays the role of an anti-de Sitter radial coordinate. The density of gates is shown to be monotonic with the tolerance and a holographic interpretation using path-integral optimization is given.
Highlights
Introduction.âOne of the key questions in quantum computing is to find efficient quantum circuits which can simulate Hamiltonian evolution
One writes down a cost function which is minimized to obtain a geodesic in circuit space which tells us how the gates should be arranged in an optimum manner
The corresponding projected unitary Up provides a good approximation to the target U up to some error
Summary
We propose a modification to Nielsenâs circuit complexity for Hamiltonian simulation using the SuzukiTrotter (ST) method, which provides a network like structure for the quantum circuit This leads to an optimized gate counting linear in the geodesic distance and spatial volume, unlike in the original proposal. Î2 and approximate the average unitary by quantum gates using the Lie-Trotter formula [14] Putting all these results together and assuming all penalty factors to be identical (without loss of generality), one obtains [1] the total number of gates required to synthesize the unitary as Ngates 1â4 OĂ°m3d3=ÎŽ2Ă [1] where m is the number of easy terms in the Hamiltonian and ÎŽ is the specified tolerance.
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