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Abstract: Since Jordan Lee and Preskill's seminal work that showed an exponential advantage for quantum simulations of scalar Phi^4 theory, applications of quantum computing to field theory has become a major emphasis for quantum algorithms development. Despite this, understanding the memory, speed and energy required for a quantum computer would need to solve such problems remain open and back of the envelope calculations have left us for this problem with prohibitively bad scaling. In this work we address this by providing a new approach to estimate certain low-lying elements of the scattering matrix using phase estimation, rather than the costly algorithms of Jordan Lee and Preskill. We find then by optimizing these algorithms explicit gate counts on the algorithm and further estimates of the number of physical qubits needed to perform the simulation using the surface code for near-future quantum computers. This work shows that, while out of reach of existing quantum computers, that quantum advantage could be seen for future fault tolerant quantum computers on a time scale on the order of months with a million or fewer physical qubits. It is our hope that, like was seen for chemistry, these estimates will simply be the jumping off point for this field and that through optimizations both on the physics side as well as the algorithmic side that these initial estimates can be further slashed just as happened with chemistry after the first concrete gate count estimates were provided.
https://bnl.zoomgov.com/j/1600951401?pwd=bjU0ak50RjRBUDFMc1NMZ1Y5NjJKQT09
Meeting ID: 160 095 1401
Passcode: 782407