Exact electronic states with shallow quantum circuits through global optimisation

Abstract

Quantum computers promise to revolutionise electronic simulations by overcoming the exponential scaling of many-electron problems. While electronic wave functions can be represented using a product of fermionic unitary operators, shallow quantum circuits for exact states have not yet been achieved. We construct universal wave functions from gate-efficient, symmetry-preserving fermionic operators by introducing an algorithm that globally optimises the wave function in the discrete ansatz design and the continuous parameter spaces. Our approach maximises the accuracy that can be obtained with near-term quantum circuits. Highly accurate numerical simulations on strongly correlated molecules, including water and molecular nitrogen, and the condensed-matter Hubbard model, demonstrate that our algorithm reliably advances the state-of-the-art, defining a new paradigm for quantum simulations featuring strong electron correlation.

Variational quantum chemistry requires gate-error probabilities below the fault-tolerance threshold

“…We do not anticipate these algorithms to be feasible options to study strongly correlated systems, whose simulation using quantum algorithms provides the most benefit over classical algorithms. We also omit the DISCO-VQE [40]. Due to its large jumps in Hilbert space during the discrete optimisations of the ansatz, we expect DISCO-VQE to lack tolerance to barren plateaus.…”

Orbital expansion variational quantum eigensolver

“…Previous studies have explored various strategies to reduce the necessary quantum resources in solving quantum chemical problems, including qubit-reduction methods [27][28][29][30][31][32][33][34], heuristics ansatz construction methods [35][36][37][38], circuit depth reduction methods [39,40] and heuristics parameter training methods [41,42]. Specifically, to address the issue of limited size in current NISQ devices, [28,30,32,33] employed the quantum embedding theory to partition the molecular Hamiltonian into smaller fragments.…”

“…This approach reduces the size of operator pool meanwhile decreases the quantum circuit depth. In addition, there are other strategies available to reduce the circuit depth, for instance, the Qdrift-based quantum imaginary time evolution method [39] and the discretely optimized VQE approach [40] offer alternative ways to achieve circuit depth reduction. Finally, training the parameters within quantum circuits may be challenging due to the presence of barren plateaus phenomenon [43][44][45], and heuristics training strategies may help to alleviate this challenge, such as the layerwise training method [41], quasidynamical evolution [42], and suitable parameter initialization strategies [46].…”