Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic resonance experiments.

We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from time-resolved measurements of spin-spin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challenging to classically simulate in some contexts. We demonstrate the ability to directly estimate the Jacobian and Hessian of the corresponding learning problem on a quantum computer, allowing us to learn the Hamiltonian parameters.

Nearly Optimal Quantum Algorithm for Estimating Multiple Expectation Values.

Many quantum algorithms involve the evaluation of expectation values. Optimal strategies for estimating a single expectation value are known, requiring a number of state preparations that scales with the target error ϵ as O(1/ϵ). In this Letter, we address the task of estimating the expectation values of M different observables, each to within additive error ϵ, with the same 1/ϵ dependence.

Observing ground-state properties of the Fermi-Hubbard model using a scalable algorithm on a quantum computer.

The famous, yet unsolved, Fermi-Hubbard model for strongly-correlated electronic systems is a prominent target for quantum computers. However, accurately representing the Fermi-Hubbard ground state for large instances may be beyond the reach of near-term quantum hardware. Here we show experimentally that an efficient, low-depth variational quantum algorithm with few parameters can reproduce important qualitative features of medium-size instances of the Fermi-Hubbard model.

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer.

The phenomena of quantum criticality underlie many novel collective phenomena found in condensed matter systems. They present a challenge for classical and quantum simulation, in part because of diverging correlation lengths and consequently strong finite-size effects. Tensor network techniques that work directly in the thermodynamic limit can negotiate some of these difficulties.

Time-crystalline eigenstate order on a quantum processor.

Quantum many-body systems display rich phase structure in their low-temperature equilibrium states. However, much of nature is not in thermal equilibrium. Remarkably, it was recently predicted that out-of-equilibrium systems can exhibit novel dynamical phases that may otherwise be forbidden by equilibrium thermodynamics, a paradigmatic example being the discrete time crystal (DTC).

What the foundations of quantum computer science teach us about chemistry.

With the rapid development of quantum technology, one of the leading applications that has been identified is the simulation of chemistry. Interestingly, even before full scale quantum computers are available, quantum computer science has exhibited a remarkable string of results that directly impact what is possible in a chemical simulation with any computer. Some of these results even impact our understanding of chemistry in the real world.