Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision

Guoming Wang1, Daniel Stilck França2, Ruizhe Zhang1,3, Shuchen Zhu1,4, and Peter D. Johnson5

1Zapata Computing Canada Inc., Toronto, ON M5V 2Y1, Canada
2Univ Lyon, ENS Lyon, UCBL, CNRS, Inria, LIP, F-69342, Lyon Cedex 07, France
3Department of Computer Science, University of Texas at Austin, Austin, TX 78712, USA
4Department of Computer Science, Georgetown University, Washington, DC 20057, USA
5Zapata Computing Inc., Boston, MA 02110 USA

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A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will require some degree of fault tolerance. While hardware is improving towards this milestone, optimizing quantum algorithms also brings it closer to the present. Existing methods for ground state energy estimation are costly in that they require a number of gates per circuit that grows exponentially with the desired number of bits in precision. We reduce this cost exponentially, by developing a ground state energy estimation algorithm for which this cost grows linearly in the number of bits of precision. Relative to recent resource estimates of ground state energy estimation for the industrially-relevant molecules of ethylene-carbonate and PF$_6^-$, the estimated gate count and circuit depth is reduced by a factor of 43 and 78, respectively. Furthermore, the algorithm can use additional circuit depth to reduce the total runtime. These features make our algorithm a promising candidate for realizing quantum advantage in the era of early fault-tolerant quantum computing.

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