Exploring ab initio machine synthesis of quantum circuits

Abstract

Gate-level quantum circuits are often derived manually from higher level algorithms. While this suffices for small implementations and demonstrations, ultimately automatic circuit design will be required to realise complex algorithms using hardware-specific operations and connectivity. Therefore, ab initio creation of circuits within a machine, either a classical computer or a hybrid quantum-classical device, is of key importance. We explore a range of established and novel techniques for the synthesis of new circuit structures, the optimisation of parameterised circuits, and the efficient removal of low-value gates via the quantum geometric tensor. Using these techniques we tackle the tasks of automatic encoding of unitary processes and translation (recompilation) of a circuit from one form to another. Using emulated quantum computers with various noise-free gate sets we provide simple examples involving up to 10 qubits, corresponding to 20 qubits in the augmented space we use. Further applications of specific relevance to chemistry modelling are considered in a sister paper, 'Exploiting subspace constraints and ab initio variational methods for quantum chemistry'.

Exploiting subspace constraints and ab initio variational methods for quantum chemistry

“…The performance of a VQA scheme crucially depends on the setup of the optimiser. We outline the core aspects of our optimization techniques below, which are elaborated in greater detail in our sister paper [33], to which we refer the interested reader.…”

“…We take advantage of the block diagonal structure of propagators to synthesise very shallow circuits (⩽18 gates) constrained to a subspace, with a target error of less than 0.001 for various ∆t. Our sister paper [33] shows that circuit synthesis in a subspace is more efficient than in the entire space, given that the unitary has a block diagonal form. In the following, we summarise the idea of the subspace compilation technique; we refer to our sister paper [33] for further details.…”

“…Our sister paper [33] shows that circuit synthesis in a subspace is more efficient than in the entire space, given that the unitary has a block diagonal form. In the following, we summarise the idea of the subspace compilation technique; we refer to our sister paper [33] for further details.…”

“…We only consider noise-free gates, and we performed our algorithms on an emulated quantum computer with up to 14 qubits. This work is accompanied by our study on various existing and new optimisation technicalities in the sister paper [33]; here, we apply techniques we found to perform well.…”

“…For the latter, we consider both full Hilbert space dynamics, as well as circuits created under the more permissive condition that dynamics should be correct in a specific subspace; specifically, this is a in a subspace that preserves the occupation number. The subspace constrained time-evolution operator (propagator) is obtained via the subspace compilation technique that is introduced in our sister paper [33]. Our interest in the subspace-restricted propagators stems from the fact that most chemical reactions preserve the total number of particles, making processes outside of this subspace irrelevant.…”