Quantum Simulator Based on the Paraxial Wave Equation

We propose a paraxial quantum simulator that requires only widely available optical fibers or metamaterials. Such a simulator would facilitate cost-effective quantum simulation without specialized techniques. We show theoretically that the method accurately simulates quantum dynamics and quantum effects for an example system, which invites extension of the method to many-body systems using nonlinear optical elements and implementation of the paraxial quantum simulator to extend access to quantum computation and prototype quantum parity-time reversal ($\mathcal{PT}$) symmetric technologies

Experimentally-realizable PT\mathcal{PT} phase transitions in reflectionless quantum scattering

A class of above-barrier quantum-scattering problems is shown to provide an experimentally-accessible platform for studying $\mathcal{PT}$-symmetric Schr\"odinger equations that exhibit spontaneous $\mathcal{PT}$ symmetry breaking despite having purely real potentials. These potentials are one-dimensional, inverted, and unstable and have the form $V(x) = - \lvert x\rvert^p$ ($p>0$), terminated at a finite length or energy to a constant value as $x\to \pm\infty$. The signature of unbroken $\mathcal{PT}$ symmetry is the existence of reflectionless propagating states at discrete real energies up to arbitrarily high energy. In the $\mathcal{PT}$-broken phase, there are no such solutions. In addition, there exists an intermediate mixed phase, where reflectionless states exist at low energy but disappear at a fixed finite energy, independent of termination length. In the mixed phase exceptional points (EPs) occur at specific $p$ and energy values, with a quartic dip in the reflectivity in contrast to the quadratic behavior away from EPs. $\mathcal{PT}$-symmetry-breaking phenomena have not been previously predicted in a quantum system with a real potential and no reservoir coupling. The effects predicted here are measurable in standard cold-atom experiments with programmable optical traps. The physical origin of the symmetry-breaking transition is elucidated using a WKB force analysis that identifies the spatial location of the above-barrier scattering

Leveraging Hamiltonian Simulation Techniques to Compile Operations on Bosonic Devices

Circuit QED enables the combined use of qubits and oscillator modes. Despite a variety of available gate sets, many hybrid qubit-boson (i.e., oscillator) operations are realizable only through optimal control theory (OCT) which is oftentimes intractable and uninterpretable. We introduce an analytic approach with rigorously proven error bounds for realizing specific classes of operations via two matrix product formulas commonly used in Hamiltonian simulation, the Lie--Trotter and Baker--Campbell--Hausdorff product formulas. We show how this technique can be used to realize a number of operations of interest, including polynomials of annihilation and creation operators, i.e., $a^p {a^\dagger}^q$ for integer $p, q$. We show examples of this paradigm including: obtaining universal control within a subspace of the entire Fock space of an oscillator, state preparation of a fixed photon number in the cavity, simulation of the Jaynes--Cummings Hamiltonian, simulation of the Hong-Ou-Mandel effect and more. This work demonstrates how techniques from Hamiltonian simulation can be applied to better control hybrid boson-qubit devices.Comment: 48 pages, 5 figure

Vibronic Dynamics of Photodissociating ICN from Simulations of Ultrafast X-Ray Absorption Spectroscopy

Ultrafast UV-pump/soft-X-ray-probe spectroscopy is a subject of great interest since it can provide detailed information about dynamical photochemical processes with ultrafast resolution and atomic specificity. Here, we focus on the photodissociation of ICN in the 1Π1 excited state, with emphasis on the transient response in the soft-X-ray spectral region as described by the ab initio spectral lineshape averaged over the nuclear wavepacket probability density. We find that the carbon K-edge spectral region reveals a rich transient response that provides direct insights into the dynamics of frontier orbitals during the I−CN bond cleavage process. The simulated UV-pump/soft-X-ray-probe spectra exhibit detailed dynamical information, including a time-domain signature for coherent vibration associated with the photogenerated CN fragment. © 2020 The Authors. Published by Wiley-VCH Gmb

Variational quantum iterative power algorithms for global optimization

We introduce a family of variational quantum algorithms called quantum iterative power algorithms (QIPA) that outperform existing hybrid near-term quantum algorithms of the same kind. We demonstrate the capabilities of QIPA as applied to three different global-optimization numerical experiments: the ground-state optimization of the $H_2$ molecular dissociation, search of the transmon qubit ground-state, and biprime factorization. Since our algorithm is hybrid, quantum/classical technologies such as error mitigation and adaptive variational ansatzes can easily be incorporated into the algorithm. Due to the shallow quantum circuit requirements, we anticipate large-scale implementation and adoption of the proposed algorithm across current major quantum hardware.Comment: 17 pages, 7 figure

Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations

We present a quantum algorithm based on the Generalized Quantum Master Equation (GQME) approach to simulate open quantum system dynamics on noisy intermediate-scale quantum (NISQ) computers. This approach overcomes the limitations of the Lindblad equation, which assumes weak system-bath coupling and Markovity, by providing a rigorous derivation of the equations of motion for any subset of elements of the reduced density matrix. The memory kernel resulting from the effect of the remaining degrees of freedom is used as input to calculate the corresponding non-unitary propagator. We demonstrate how the Sz.-Nagy dilation theorem can be employed to transform the non-unitary propagator into a unitary one in a higher-dimensional Hilbert space, which can then be implemented on quantum circuits of NISQ computers. We validate our quantum algorithm as applied to the spin-boson benchmark model by analyzing the impact of the quantum circuit depth on the accuracy of the results when the subset is limited to the diagonal elements of the reduced density matrix. Our findings demonstrate that our approach yields reliable results on NISQ IBM computers.Comment: 47 pages, 10 figures, updated to the most current version of the manuscrip

Tensor-Train Split Operator KSL (TT-SOKSL) Method for Quantum Dynamics Simulations

Numerically exact simulations of quantum reaction dynamics, including non-adiabatic effects in excited electronic states, are essential to gain fundamental insights into ultrafast chemical reactivity and rigorous interpretations of molecular spectroscopy. Here, we introduce the tensor-train split-operator KSL (TT-SOKSL) method for quantum simulations in tensor-train (TT)/matrix product state (MPS) representations. TT-SOKSL propagates the quantum state as a tensor train using the Trotter expansion of the time-evolution operator, as in the tensor-train split-operator Fourier transform (TT-SOFT) method. However, the exponential operators of the Trotter expansion are applied using a rank adaptive TT-KSL scheme instead of using the scaling and squaring approach as in TT-SOFT. We demonstrate the accuracy and efficiency of TT-SOKSL as applied to simulations of the photoisomerization of the retinal chromophore in rhodopsin, including non-adiabatic dynamics at a conical intersection of potential energy surfaces. The quantum evolution is described in full dimensionality by a time-dependent wavepacket evolving according to a two-state 25-dimensional model Hamiltonian. We find that TT-SOKSL converges faster than TT-SOFT with respect to the maximally allowed memory requirement of the tensor-train representation and better preserves the norm of the time-evolving state. When compared to the corresponding simulations based on the TT-KSL method, TT-SOKSL has the advantage of avoiding the need of constructing the matrix product state Laplacian by exploiting the linear scaling of multidimensional tensor train Fourier transforms

Ultrafast Charge Migration Dynamics in Enol Keto Tautomerization Monitored with a Local Soft-X-Ray Probe

Proton-coupled electron transfer (PCET) is the underlying mechanism governing important reactions ranging from water splitting in photosynthesis to oxygen reduction in hydrogen fuel cells. The interplay of proton and electronic charge distribution motions can vary from sequential to concerted schemes, with elementary steps occurring on ultrafast time scales. We demonstrate with a simulation study that femtosecond soft-X-ray spectroscopy provides key insight into the PCET mechanism of a photoinduced intramolecular enol* $\rightarrow$ keto* tautomerization reaction. A full quantum treatment of electronic and nuclear dynamics of 2-(2-hydroxyphenyl-)benzothiazole upon electronic excitation reveals how spectral signatures of local excitations from core to frontier orbitals display the distinct stages of charge migration for the H atom, donating, and accepting sites. Our findings indicate UV/X-ray pump-probe spectroscopy provides a unique way to probe ultrafast electronic structure rearrangements in photoinduced chemical reactions essential to understanding the mechanism of PCET