Artemiy Burov

Noisy intermediate-scale quantum computers are constrained by circuit depth, while product-formula simulation of spin systems leads to narrow and deep circuits. Here we introduce a fan-out-based gadget compiler that trades circuit depth for width in simulations of Heisenberg-type nuclear magnetic resonance (NMR) Hamiltonians. Each logical spin is encoded into a small repetition-code register sized by its interaction degree, so that all pairwise interactions of a given Pauli type execute in parallel after a logarithmic-depth CNOT fan-out, and the redundant registers provide error detection for post-selection at no additional algorithmic overhead. The central result is a fixed-protocol resource comparison of the two compilations, transpiled to heavy-hex superconducting and all-to-all trapped-ion targets across a set of NMR spin systems. For interaction graphs with a high-degree hub the volume-optimal schedule halves the two-qubit depth and reduces the volume 1.7-fold for the 13-spin demonstration, which on heavy-hex also lowers the two-qubit gate count, and the depth reduction rises to 2.5-fold on all-to-all for the highest-degree molecule studied. On all-to-all the two-qubit gate count rises for every system, so the volume reduction is a benefit on depth-limited hardware. The gain grows with the degree inhomogeneity of the interaction graph and vanishes for dense uniform graphs, where the optimum is the sequential circuit. We simulate the zero-field NMR spectrum of tetramethylsilane, a 13-spin star system. Under a noise model scaled from a published present-day processor calibration, the shallower gadget circuits match or surpass the sequential compilation only after post-selection on their built-in error detection, once error rates improve by one to one and a half orders of magnitude. We verify the spectra against an independent classical computation.

With the latest advances in quantum computing technology, we are gradually moving from the noisy intermediate-scale quantum (NISQ) era characterized by hardware limited in the number of qubits and plagued with quantum noise, to the age of quantum utility where both the newest hardware and software methods allow for tackling problems which have been deemed difficult or intractable with conventional classical methods. One of these difficult problems is the simulation of one-dimensional (1D) nuclear magnetic resonance (NMR) spectra, a major tool to learn about the structure of molecules, helping the design of new materials or drugs. Using advanced error mitigation and error suppression techniques from Q-CTRL together with the latest commercially available superconducting-qubit quantum computer from IBM and trapped-ion quantum computer from IonQ, we present the quantum Hamiltonian simulation of liquid-state 1D NMR spectra in the high-field regime for spin systems up to 34 spins. Our pipeline has a major impact on the ability to execute deep quantum circuits with the reduction of quantum noise, improving mean square error by a factor of 22. It allows for the execution of deep quantum circuits and obtaining salient features of the 1D NMR spectra for both 16-spin and 22-spin systems, as well as a 34-spin system, which lies beyond the regime where unrestricted full Liouvillespace simulations are practical (32 spins, the Liouville limit). Our work is a step toward near-term quantum utility in NMR spectroscopy.