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

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## Publications (15)

We show that Kitaevs construction of Feynmans clock, in which the time-evolution of a closed quantum system is encoded as a ground state problem, can be extended to open quantum systems. In our formalism, the ground states of an ensemble of non-Hermitian Kitaev–Feynman clock Hamiltonians yield stochastic trajectories, which unravel the evolution of...

Time-dependent density functional theory (TDDFT) is rapidly emerging as a
premier method for solving dynamical many-body problems in physics and
chemistry. The mathematical foundations of TDDFT are established through the
formal existence of a fictitious non-interacting system (known as the Kohn-Sham
system), which can reproduce the one-electron re...

We show that Feynman's Clock construction, in which the time-evolution of a
closed quantum system is encoded as a ground state problem, can be extended to
open quantum systems. In our formalism, the ground states of an ensemble of
non-Hermitian Feynman Clock Hamiltonians yield stochastic trajectories, which
unravel the evolution of a Lindblad maste...

In this work, we develop an approach to treat correlated many-electron dynamics, dressed by the presence of a finite-temperature harmonic bath. Our theory combines a small polaron transformation with the second-order time-convolutionless master equation and includes both electronic and system-bath correlations on equal footing. Our theory is based...

We prove that the theorems of TDDFT can be extended to a class of qubit Hamiltonians that are universal for quantum computation. The theorems of TDDFT applied to universal Hamiltonians imply that single-qubit expectation values can be used as the basic variables in quantum computation and information theory, rather than wavefunctions. From a practi...

We model the coherent energy transfer of an electronic excitation within covalently linked aromatic homodimers from first-principles. Our results shed light on whether commonly used models of the bath calculated via detailed electronic structure calculations can reproduce the key dynamics. For the systems we model, the time scales of coherent trans...

This chapter introduces the basic concepts of digital quantum simulation. The study of the computational complexity of problems in quantum simulation helps us better understand how quantum computers can surpass classical computers. The chapter briefly summarizes a few important examples of complexity classes of decision problems. Quantum algorithms...

In its original formulation, TDDFT addresses the isolated dynamics of
electronic systems evolving unitarily (Runge and Gross 1984). However,
there exist many situations in which the electronic degrees of freedom
are not isolated, but must be treated as a subsystem imbedded in a much
larger thermal bath.

Time-dependent density functional theory (TDDFT) has recently been extended to describe many-body open quantum systems evolving under nonunitary dynamics according to a quantum master equation. In the master equation approach, electronic excitation spectra are broadened and shifted due to relaxation and dephasing of the electronic degrees of freedo...

The dissipative dynamics of many-electron systems interacting with a thermal
environment has remained a long-standing challenge within time-dependent
density functional theory (TDDFT). Recently, the formal foundations of open
quantum systems time-dependent density functional theory (OQS-TDDFT) within the
master equation approach were established. I...

The Casida equations of linear response TDDFT are extended to calculate linear spectra of open quantum systems evolving according to a Markovian master equation. By mapping a many-body open quantum system onto an open, non-interacting Kohn-Sham system, extrinsic line broadening due to electron-bath coupling can be described exactly within TDDFT. Th...

We extend the Runge-Gross theorem for a very general class of open quantum systems under weak assumptions about the nature of the bath and its coupling to the system. We show that for Kohn-Sham (KS) time-dependent density functional theory, it is possible to rigorously include the effects of the environment within a bath functional in the KS potent...

A two-electron one-dimensional model of a heteroatomic molecule composed of two open-shell atoms is considered. Including only two electrons isolates and examines the effect that the highest occupied molecular orbital has on the Kohn-Sham potential as the molecule dissociates. We reproduce the characteristic step and peak that previous high-level w...

Adiabatic time-dependent density functional theory fails for excitations of a heteroatomic molecule composed of two open-shell fragments at large separation. Strong frequency dependence of the exchange-correlation kernel is necessary for both local and charge-transfer excitations. The root of this is the static correlation created by the step in th...

## Citations

... 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. ...