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We explore a method for automatically recompiling a quantum circuit $\mathcal{A}$ into a target circuit $\mathcal{B}$, with the goal that both circuits have the same action on a specific input i.e. $\mathcal{B}{\mid{in}\rangle}=\mathcal{A}{\mid{in}\rangle}$. This is of particular relevance to hybrid, NISQ-era algorithms for dynamical simulation or eigensolving. The user initially specifies $\mathcal{B}$ as a blank template: a layout of parameterised unitary gates configured to the identity. The compilation then proceeds using quantum hardware to perform an isomorphic energy-minimisation task, and an optional gate elimination phase to compress the circuit. If $\mathcal{B}$ is insufficient for perfect recompilation then the method will result in an approximate solution. We optimise using imaginary time evolution, and a recent extension of quantum natural gradient for noisy settings. We successfully recompile a $7$-qubit circuit involving $186$ gates of multiple types into an alternative form with a different topology, far fewer two-qubit gates, and a smaller family of gate types. Moreover we verify that the process is $robust$, finding that per-gate noise of up to $1\%$ can still yield near-perfect recompilation. We test the scaling of our algorithm on up to $20$ qubits, recompiling into circuits with up to $400$ parameterized gates, and incorporate a custom adaptive timestep technique. We note that a classical simulation of the process can be useful to optimise circuits for today's prototypes, and more generally the method may enable `blind' compilation i.e. harnessing a device whose response to control parameters is deterministic but unknown. The code and resources used to generate our results are openly available online \cite{githubLink} \cite{mmaGithubLink}. A simple Mathematica demonstration of our algorithm can be found at questlink.qtechtheory.org.

Quantum technologies exploit entanglement to enhance various tasks beyond their classical limits including computation, communication and measurements. Quantum metrology aims to increase the precision of a measured quantity that is estimated in the presence of statistical errors using entangled quantum states. We present a novel approach for finding (near) optimal states for metrology in the presence of noise, using variational techniques as a tool for efficiently searching the high-dimensional space of quantum states, which would be classically intractable. We comprehensively explore systems consisting of up to 9 qubits and find new highly entangled states that are not symmetric under permutations and non-trivially outperform previously known states up to a constant factor 2. We consider a range of environmental noise models; while passive quantum states cannot achieve a fundamentally superior scaling (as established by prior asymptotic results) we do observe a significant absolute quantum advantage. We finally outline a possible experimental setup for variational quantum metrology which can be implemented in near-term hardware.