Mathias Weiden

Mathias Weiden, Ed Younis, Justin Kalloor et al.

In the Noisy Intermediate Scale Quantum (NISQ) era, finding implementations of quantum algorithms that minimize the number of expensive and error prone multi-qubit gates is vital to ensure computations produce meaningful outputs. Unitary synthesis, the process of finding a quantum circuit that implements some target unitary matrix, is able to solve this problem optimally in many cases. However, current bottom-up unitary synthesis algorithms are limited by their exponentially growing run times. We show how applying machine learning to unitary datasets permits drastic speedups for synthesis algorithms. This paper presents QSeed, a seeded synthesis algorithm that employs a learned model to quickly propose resource efficient circuit implementations of unitaries. QSeed maintains low gate counts and offers a speedup of $3.7\times$ in synthesis time over the state of the art for a 64 qubit modular exponentiation circuit, a core component in Shor's factoring algorithm. QSeed's performance improvements also generalize to families of circuits not seen during the training process.

Marc Grau Davis, Ed Younis, Mathias Weiden et al.

We present a formulation of the problem of finding the smallest T -Count circuit that implements a given unitary as a binary search over a sequence of continuous minimization problems, and demonstrate that these problems are numerically solvable in practice. We reproduce best-known results for synthesis of circuits with a small number of qubits, and push the bounds of the largest circuits that can be solved for in this way. Additionally, we show that circuit partitioning can be used to adapt this technique to be used to optimize the T -Count of circuits with large numbers of qubits by breaking the circuit into a series of smaller sub-circuits that can be optimized independently.