David G. Tempel's research while affiliated with Harvard University and other places

... While for universal gate-based quantum computers, the challenge to implement time evolution is determining efficient quantum circuits and mappings that can be executed on available devices, the challenge for D-Wave's QAs is in finding a viable QUBO matrix that can be implemented. First formalized for scientific applications in the context of quantum chemistry [76,103], Feynman clock states [104,105] provide a way to timeevolve quantum systems in a single run of a QA (its first implementation on quantum hardware can be found in Ref. [106]). The constraint of real entries in the QUBO matrix can be circumvented by an appropriate change of basis that transforms the Hamiltonian into a purely imaginary form, renderingÛ t = e −itĤ real, for example, as used in Ref. [75]. ...

... We call the task of constructing such a K-S potential when given the timeevolution of the on-site probability density, the K-S potential inversion problem. In article [18], a scheme of solving the K-S potential inversion problem utilizing a quantum computer was proposed. We have recently returned to this proposal with improved numerical methods for inverting the potential [19]. ...

... We treat the strong coupling by using a polaron transformation [22]. Energy transfer in the polaron frame has been studied before [22][23][24][25][26][27], but not in the context of dark state protection. We will show that strong coupling has a profound effect on quantum interference processes such that it no longer necessarily improves the efficiency of devices. ...

... In fact, the interest on it arises because, regardless of the intrinsic nonlinearity given by the logarithmic term, it preserves the norm of the wavefunction. To give an example of its usefulness from a practical side, we mention that it has been recently considered in the context of dissipative time-dependent density functional theory [6] as a way to construct dissipative functionals. Moreover, a very recent and different example of the applicability of non-linear Schrödinger equations can be found in [7,8], where the authors combine two different non-linearites, one of them being Kostin-like and the other incorporating continuous measurements, which can be understood as an energy dissipation operator in an effective Hamiltonian. ...

... These pairs of operators can be expressed as strings of Pauli matrices, which are directly measurable on the quantum computer [34]. The resulting 2-RDMs, according to Rosina's theorem, completely characterize the ground-state energy and order parameters of a system with only pairwise interactions [58,59], circumventing the need for a full wave-function description of the system, which could require significantly more measurements on a NISQ device [60] increasing error and computational time. Discontinuities in the individual order parameters obtained from the 2-RDM as the system's Hamiltonian is manipulated, can be used to find critical points [40,55]. ...

... 66 A computational procedure integrating relaxation of electrons as an open system with time-dependent density functional theory (TDDFT) treatment of excited states was recently offered. 75,76 Historically, in the limit of long time dynamics, low couplings, and multiple electronic states, one considers multilevel Redfield theory as a common approach for electronic relaxation. 77−84 Redfield theory of electron relaxation can be combined with onthe-fly coupling of electrons-to-lattice through a molecular dynamics trajectory in the basis of DFT. ...

... Placing a quantum system driven by a Hamiltonian H and weakly-coupled to a reservoir with an effective temperature T = 1 β , the system will asymptotically reach a thermal equilibrium state, given by the quantum Gibbs distribution where Z = Tr[e −βH ] is the partition function 5 . Efficiently preparing a thermal state on a quantum computer is a problem of broad practical importance, with applications ranging from quantum chemistry and many-body physics simulations in an open environment [6][7][8] to semi-definite programming 9,10 and quantum machine learning 11,12 . However, sampling from a general Gibbs distribution is a computationally hard task for classical computers, due to the complexity of calculating the partition function 13 . ...

... In the limit of Q bath → 0 (i.e., vanishing coupling with the bath) the equation above reduces to the von Neumann equation of the isolated OQS and, if we assume linear response, to the Casida equations. 5,6 If Q bath 0, then Eq. (1) leads to the following Dyson equation for the OQS density-density response function (which we label with Roman numeral I as there can be more than one OQS), in a short-hand notation for the traced variables, in the limit of Markovian system-bath dynamics easily implemented in real-time time-dependent DFT (TDDFT) algorithms. The Markovian limit is perhaps the most common and useful limit to approach. ...

... where, in general, 2 < 1 [1,11,25,39,54]. Larger values of , 1 , and 2 correspond to a quantum memory with a longer memory lifetime. ...

... These are common objectives for quantum optics [49] and open quantum-system dynamics but are rarely even considered in state-of-the-art ab initio calculations. Existing opensystem extensions of density-functional theory [50] are thus far limited in their applicability due to physically less motivated [51] or much more involved constructions [41,52,53]. The TDDFT codes Salmon [54] and Octopus [53,55] allow the self-consistent propagation of Maxwell and Kohn-Sham equations but the complexity of the implementation and its computational cost limit their widespread use. ...