Robust quantum compilation and circuit optimisation via energy minimisation

Abstract

We explore a method for automatically recompiling a quantum circuit A into a target circuit B, with the goal that both circuits have the same action on a specific input i.e. B∣in⟩=A∣in⟩. This is of particular relevance to hybrid, NISQ-era algorithms for dynamical simulation or eigensolving. The user initially specifies 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 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.

Characterization and Verification of Trotterized Digital Quantum Simulation via Hamiltonian and Liouvillian Learning

“…A natural extension of our approach for tailoring N -body interactions in DQS is the integration of the protocol into a variational feedback-loop scheme for quantum gate design. In contrast to traditional approaches to quantum compiling [74,[80][81][82][83], which optimize the fidelity with respect to some target unitary, here one exploits Hamiltonian learning to directly minimize the Hamiltonian distance to design a desired target Hamiltonian.…”

Training variational quantum circuits with CoVaR: covariance root finding with classical shadows

“…Here we wish to transform a given gate sequence V into a native gate sequence U with an optimal circuit depth, as well as make it resilient to noise. Both in the case of Full Unitary Matrix Compilation (FUMC) [26] and Fixed Input State Compilation (FISC) [29] the problem can be stated as applying U † after V onto our reference state |0 (see section IV A for details) which at the solution V = U would correspond to the identity operation U † V = Id and the resulting state |0 is then the ground state of the Hamiltonian − N j=1 Z j . While one ultimately aims to find the ground state of this Hamiltonian, note that we can also accept any computational basis state |n which are simultaneous eigenstates of the mutually commuting terms {Z j }.…”

“…In variational recompilation, we want to find a parametrised unitary circuit U (θ) that approximates a target unitary V either in the entire Hilbert space in case of recompiling a Full Unitary using a Hilbert-Schmidt test [26] or just to approximate the action on a specific input state. After applying the circuits V and U (θ) † consecutively (see figure 5 for example circuits corresponding to Full Unitary and fixed input state respectively), the goal is to find circuit parameters θ such that the state of the registers is in the ground state |0 of the Hamiltonian H = − N j=1 Z j [29]. However, the problem would be equally solved by finding ansatz parameters to produce any computational basis state, (i.e.…”

“…techniques [29,55] can be difficult because we need to discover the parameters for and project out every state from the ground state up to the energy of the state we wish to find. CoVaR is agnostic to the energy of the state and acts to find states close to the one it is initialised into.…”

Evolving Quantum Error Correction Codes

“…At present, our artificial selection algorithm can be compared to the evolution of simple bacteria in controlled laboratory conditions where the fitness landscape is simple and well understood [48]. With more complex fitness functions and the addition of quantum hardware we anticipate improvements and systematic means of devising complex quantum circuits in various applications beyond stabilizer circuits and QECCs including but not limited to learning unitaries [49], quantum compiling [50][51][52], and hardware specific tailor-made circuits [32,47]. We highlight that while evolution may be complementary to known circuit optimization schemes [51], its main strength relies on the possibility of creating novel and creative quantum circuits.…”