We propose an alternative formulation of the sensor method presented in [Phys. Rev. Lett 109, 183601 (2012)] for the calculation of frequency-filtered and time-resolved photon correlations. Our approach is based on an algebraic expansion of the joint steady state of quantum emitter and sensors with respect to the emitter-sensor coupling parameter ε. This allows us to express photon correlations in terms of the open quantum dynamics of the emitting system only and ensures that computation of correlations are independent on the choice of a small value of ε. Moreover, using time-dependent perturbation theory, we are able to express the frequency- and time- resolved second-order photon correlation as the addition of three components, each of which gives insight into the physical processes dominating the correlation at different time scales. We consider a bio-inspired vibronic dimer model to illustrate the agreement between the original formulation and our approach.
Molecular ro-vibronic coherences, joint energy-time distributions of quantum amplitudes, are selectively prepared, manipulated, and imaged in Time-Frequency-Resolved Coherent Anti-Stokes Raman Scattering (TFRCARS) measurements using femtosecond laser pulses. The studies are implemented in iodine vapor, with its thermally occupied statistical ro-vibrational density serving as initial state. The evolution of the massive ro-vibronic superpositions, consisting of 1000 eigenstates, is followed through two-dimensional images. The first- and second-order coherences are captured using time-integrated …
Many properties of current \emph{ab initio} approaches to the quantum many-body problem, both perturbational or otherwise, are related to the singularity structure of Rayleigh--Schrödinger perturbation theory. A numerical procedure is presented that in principle computes the complete set of singularities, including the dominant singularity which limits the radius of convergence. The method approximates the singularities as eigenvalues of a certain generalized eigenvalue equation which is solved using iterative techniques. It relies on computation of the action of the perturbed Hamiltonian on a…
We point out that in the first order time-dependent perturbation theory, the transition probability may behave nonsmoothly in time and have kinks periodically. Moreover, the detailed temporal evolution can be sensitive to the exact locations of the eigenvalues in the continuum spectrum, in contrast to coarse-graining ideas. Underlying this nonsmooth and level-resolved dynamics is a simple equality about the sinc function $\sinc x \equiv \sin x / x$. These physical effects appear in many systems with approximately equally spaced spectra, and is also robust for larger-amplitude coupling beyond t…
The difficulty that the probabilities infinitely increase with time as time is long enough in time-dependent perturbation theory for some quantum systems is resolved by means of simply transforming the perturbative series into natural exponential functions of the re-summed perturbative series. Three exactly solvable models are taken to check our new formulation, and excellent agreements with the exact solution are achieved.
We analyze a system of fermionic $^{6}$Li atoms in an optical trap, and show that an atom "on demand" can be prepared with ultra-high fidelity, exceeding 0.99998. This process can be scaled to many sites in parallel, providing a realistic method to initialize N qubits at ultra-high fidelity for quantum computing. We also show how efficient quantum gate operation can be implemented in this system, and how spatially resolved single-atom detection can be performed.
Quantum simulations of the hydroxide anion and hydroxyl radical are reported, employing variational quantum algorithms for near-term quantum devices. The energy of each species is calculated along the dissociation curve, to obtain information about the stability of the molecular species being investigated. It is shown that simulations restricted to valence spaces incorrectly predict the hydroxyl radical to be more stable than the hydroxide anion. Inclusion of dynamical electron correlation from non-valence orbitals is demonstrated, through the integration of the variational quantum eigensolver…
We recently showed that the Dephasing Representation (DR) provides an efficient tool for computing ultrafast electronic spectra and that further acceleration is possible with cellularization [M. Šulc and J. Vaníček, Mol. Phys. 110, 945 (2012)]. Here we focus on increasing the accuracy of this approximation by first implementing an exact Gaussian basis method, which benefits from the accuracy of quantum dynamics and efficiency of classical dynamics. Starting from this exact method, the DR is derived together with ten other methods for computing time-resolved spectra with intermediate accuracy a…
We show how to perform universal Hamiltonian and adiabatic computing using a time-independent Hamiltonian on a 2D grid describing a system of hopping particles which string together and interact to perform the computation. In this construction, the movement of one particle is controlled by the presence or absence of other particles, an effective quantum field effect transistor that allows the construction of controlled-NOT and controlled-rotation gates. The construction translates into a model for universal quantum computation with time-independent 2-qubit ZZ and XX+YY interactions on an (almo…
Time-resolved electronic spectra can be obtained as the Fourier transform of a special type of time correlation function known as fidelity amplitude, which, in turn, can be evaluated approximately and efficiently with the dephasing representation. Here we improve both the accuracy of this approximation---with an amplitude correction derived from the phase-space propagator---and its efficiency---with an improved cellular scheme employing inverse Weierstrass transform and optimal scaling of the cell size. We demonstrate the advantages of the new methodology by computing dispersed time-resolved s…
Recently, Motes, Gilchrist, Dowling & Rohde [Phys. Rev. Lett. 113, 120501 (2014)] presented a scheme for photonic boson-sampling using a fiber-loop architecture. Here we show that the same architecture can be modified to implement full, universal linear optics quantum computing, in various incarnations. The scheme employs two embedded fiber-loops, a single push-button photon source, three dynamically controlled beamsplitters, and a single time-resolved photo-detector. The architecture has only a single point of interference, and thus may be significantly easier to align than other schemes. The…
We introduce a method based on matrix product states (MPS) for computing spectral functions of (quasi) one-dimensional spin chains, working directly in momentum space in the thermodynamic limit. We simulate the time evolution after applying a momentum operator to an MPS ground state by working with the momentum superposition of a window MPS. We show explicitly for the spin-1 Heisenberg chain that the growth of entanglement is smaller in momentum space, even inside a two-particle continuum, such that we can attain very accurate spectral functions with relatively small bond dimension. We apply o…
Variational Quantum Algorithms are among the most promising systems to implement quantum computing under the Noisy-Intermediate Scale Quantum (NISQ) technology. In variational quantum algorithm, wavefunction represented by a parametrized ansatz and variational parameters are updated iteratively with a classical computer based on the measurement outputs from the quantum computer. In this paper, we investigate perturbation theory with these algorithms and prospect the possibility of using the variational quantum algorithm to simulate quantum dynamics in perturbation theory. We illustrate the use…
We develop a quantum computing scheme utilizing McLachlan variational principle in a hybrid quantum-classical algorithm to accurately calculate the transition dynamics of a closed quantum system with many excited states subject to a strong time-dependent perturbation. A systematic approach for optimal construction of a general N-state ansatz with unary N-qubit encoding is refined. We also utilize qubit efficient encoding in McLachlan variational quantum algorithm to reduce the number of qubits to log2 N, simultaneously diminishing depths of the quantum circuits. The significant reduction of th…
The interplay between advances in stochastic and deterministic algorithms has recently led to development of interesting new selected configuration interaction (SCI) methods for solving the many body Schrödinger equation. The performance of these SCI methods can be greatly improved with a second order perturbation theory (PT2) correction, which is often evaluated in a stochastic or hybrid-stochastic manner. In this work, we present a highly efficient, fully deterministic PT2 algorithm for SCI methods and demonstrate that our approach is orders of magnitude faster than recent proposals for stoc…
Quantum computing is a unique computational approach that promises tremendous performance that cannot be achieved by classical computers, although several problems must be resolved to realize a practical quantum computing system for easy use. Here, we propose a new system and theory for quantum computing that employs single molecule confinement between electrodes. The striking features of this system are (i) an individual molecule that exhibits quantum tunneling can be regarded as a sequence of quantum gates, (ii) the quantum tunneling can be encoded onto an array of quantum bits and observed …
The Quantum Fisher Information matrix (QFIM) is a central metric in promising algorithms, such as Quantum Natural Gradient Descent and Variational Quantum Imaginary Time Evolution. Computing the full QFIM for a model with $d$ parameters, however, is computationally expensive and generally requires $\mathcal{O}(d^2)$ function evaluations. To remedy these increasing costs in high-dimensional parameter spaces, we propose using simultaneous perturbation stochastic approximation techniques to approximate the QFIM at a constant cost. We present the resulting algorithm and successfully apply it to pr…
We achieve fast, nondestructive quantum-state readout via fluorescence detection of a single $^{87}$Rb atom in the 5$S_{1/2}$ ($F=2$) ground state held in an optical dipole trap. The atom is driven by linearly-polarized readout laser beams, making the scheme insensitive to the distribution of atomic population in the magnetic sub-levels. We demonstrate a readout fidelity of $97.6\pm0.2\%$ in a readout time of $160\pm20$ $μ$s with the atom retained in $>97\%$ of the trials, representing an advancement over other magnetic-state-insensitive techniques. We demonstrate that the $F=2$ state is parti…
We propose to utilize NISQ-era quantum devices to compute short distance quantities in $(2+1)$-dimensional QED and to combine them with large volume Monte Carlo simulations and perturbation theory. On the quantum computing side, we perform a calculation of the mass gap in the small and intermediate regime, demonstrating, in the latter case, that it can be resolved reliably. The so obtained mass gap can be used to match corresponding results from Monte Carlo simulations, which can be used eventually to set the physical scale. In this paper we provide the setup for the quantum computation and sh…
