## Project Details

### Description

Simulation of quantum physical systems on a quantum computer is one of the most important potential applications of quantum computers. This simulation typically requires solving the Schrodinger equation, and PI Berry developed many of the key techniques in quantum algorithms for that task. Moreover, Hamiltonian simulation can be used as a basis to solve many other problems, particularly optimization.

In the area of quantum simulation a major application is that of FeMoco. That is because industrial nitrogen fixing it an inefficient process, and understanding of the FeMoco cofactor in biological nitrogen fixing could lead to an efficient industrial process. Initial efforts in quantum algorithms for FeMoco gave estimates of 10

In optimization, quantum algorithms can typically provide a square root speedup in complexity, though there is the extra overhead of providing error correction in quantum computing. It is therefore of paramount importance to quantify the complexity of the quantum algorithms in order to determine what improvement over classical computing is possible. We have already provided explicit techniques for a number of optimization approaches for an initial Google award. In this project we will focus on the adiabatic approaches with phase randomization from. We will further optimize these approaches, and provide explicit circuits with gate counts so that it is possible to compare these methods with classical optimization.

In the area of quantum simulation a major application is that of FeMoco. That is because industrial nitrogen fixing it an inefficient process, and understanding of the FeMoco cofactor in biological nitrogen fixing could lead to an efficient industrial process. Initial efforts in quantum algorithms for FeMoco gave estimates of 10

^{14}T gates, which would be extremely impractical. PI Berry and Ryan Babbush have been very successful at reducing the gate counts for this problem, giving three orders of magnitude reduction in the complexity. That method could potentially be implemented in 12 days with 20 million qubits. We have also developed highly efficient methods with the plane wave basis that could potentially be used for FeMoco. Part of this project is to provide explicit gate estimates for this approach, and optimize for minimum gate count.In optimization, quantum algorithms can typically provide a square root speedup in complexity, though there is the extra overhead of providing error correction in quantum computing. It is therefore of paramount importance to quantify the complexity of the quantum algorithms in order to determine what improvement over classical computing is possible. We have already provided explicit techniques for a number of optimization approaches for an initial Google award. In this project we will focus on the adiabatic approaches with phase randomization from. We will further optimize these approaches, and provide explicit circuits with gate counts so that it is possible to compare these methods with classical optimization.

Short title | OOA |
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Status | Finished |

Effective start/end date | 1/01/20 → 31/12/20 |