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Abstract We experimentally study the heating of trapped atomic ions during measurement of their internal qubit states. During measurement, ions are projected into one of two basis states and discriminated by their state-dependent fluorescence. We observe that ions in the fluorescing state rapidly scatter photons and heat at a rate of $\dot{\overline{n}}\gtrsim 2\times {10}^4$quanta s⁻¹, which is orders of magnitude faster than typical anomalous ion heating rates. We introduce a quantum trajectory-based framework that accurately reproduces the experimental results and provides a unified description of ion heating for both continuous and discrete sources. 

Abstract Trapped-ion quantum simulators have demonstrated a long history of studying the physics of interacting spin-lattice systems using globally addressed entangling operations. Yet despite the multitude of studies so far, most have been limited to studying variants of the same spin interaction model, namely an Ising model with power-law decay in the couplings. Here, we demonstrate that much broader classes of effective spin–spin interactions are achievable using exclusively global driving fields. Specifically, we find that these new categories of interaction graphs become achievable with perfect or near-perfect theoretical fidelity by tailoring the coupling of the driving fields to each vibrational mode of the ion crystal. Given the relation between the ion crystal vibrational modes and the accessible interaction graphs, we show how the accessible interaction graph set can be further expanded by shaping the trapping potential to include specific anharmonic terms. Finally, we derive a rigorous test to determine whether a desired interaction graph is accessible using only globally driven fields. These tools broaden the reach of trapped-ion quantum simulators so that they may more easily address open questions in materials science and quantum chemistry. 

The accurate computational study of wavepacketnuclear dynamics is considered to be a classically intractableproblem, particularly with increasing dimensions. Here, we presenttwo algorithms that, in conjunction with other methods developedby us, may result in one set of contributions for performingquantum nuclear dynamics in arbitrary dimensions. For one of thetwo algorithms discussed here, we present a direct map betweenthe Born−Oppenheimer Hamiltonian describing the nuclearwavepacket time evolution and the control parameters of a spin−lattice Hamiltonian that describes the dynamics of qubit states in anion-trap quantum computer. This map is exact for three qubits, andwhen implemented, the dynamics of the spin states emulates thoseof the nuclear wavepacket in a continuous representation. However, this map becomes approximate as the number of qubits grows.In a second algorithm, we present a general quantum circuit decomposition formalism for such problems using a method called theQuantum Shannon Decomposition. This algorithm is more robust and is exact for any number of qubits at the cost of increasedcircuit complexity. The resultant circuit is implemented on IBM’s quantum simulator (QASM) for 3−7 qubits, without using a noisemodel so as to test the intrinsic accuracy of the method. In both cases, the wavepacket dynamics is found to be in good agreementwith the classical propagation result and the corresponding vibrational frequencies obtained from the wavepacket density timeevolution are in agreement to within a few tenths of a wavenumber.