Search

We use the mapping between two computation frameworks , Adiabatic Grover Search (AGS) and Adiabatic Quantum Computing (AQC), to translate the Grover search algorithm into the AQC regime. We then apply Trotterization on the schedule-dependent Hamiltonian of AGS to obtain the values of variational parameters in the Quantum Approximate Optimization Algorithm (QAOA) framework. The goal is to carry the optimal behavior of Grover search algorithm into the QAOA framework without the iterative machine learning processes., Comment: 5 pages, 2 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:2204.09830

We describe the quantum mechanical rotation of a photon state, the Wigner rotation—a quantum effect that couples a transformation of a reference frame to a particle’s spin, to investigate geometric phases induced by Earth’s gravitational field for observers in various orbits. We find a potentially measurable quantum phase of the Wigner rotation angle in addition to the rotation of standard fame, the latter of which is computed and agrees well with the geodetic rotation. When an observer is in either a circular or a spiraling orbit containing non-zero angular momentum, the additional quantum phase contributes 10−6 degree to 10−4 degree respectively, depending on the altitude of the Earth orbit. In the former case, the additional quantum phase is dominant over the near-zero classical geodetic rotation. Our results show that the Wigner rotation represents a non-trivial semi-classical effect of quantum field theory on a background classical gravitational field.

In the geometry of quantum evolutions, a geodesic path is viewed as a path of minimal statistical length connecting two pure quantum states along which the maximal number of statistically distinguishable states is minimum. In this paper, we present an explicit geodesic analysis of the dynamical trajectories that emerge from the quantum evolution of a single-qubit quantum state. The evolution is governed by an Hermitian Hamiltonian operator that achieves the fastest possible unitary evolution between given initial and final pure states. Furthermore, in addition to viewing geodesics in ray space as paths of minimal length, we also verify the geodesicity of paths in terms of unit geometric efficiency and vanishing geometric phase. Finally, based on our analysis, we briefly address the main hurdles in moving to the geometry of quantum evolutions for open quantum systems in mixed quantum states., 19 pages, 1 figure, 2 tables

We revisit a method for mapping arbitrary single-mode pure states into superpositions of N00N states using an asymmetric non-linear Mach–Zehnder interferometer (ANLMZI). This method would allow one to tailor-make superpositions of N00N states where each axis of the two-mode joint-photon number distribution is weighted by the statistics of any single-mode pure state. The non-linearity of the ANLMZI comes in the form of a [Formula: see text] self-Kerr interaction occurring on one of the intermediary modes of the interferometer. Motivated by the non-classical interference effects that occur at a beam splitter, we introduce inverse-engineering techniques aimed toward extrapolating optimal transformations for generating N00N state superpositions. These techniques are general enough so as to be employed to probe the means of generating states of any desired quantum properties.

Macroscopic quantum phenomena, such as observed in superfluids and superconductors, have led to promising technological advancements and some of the most important tests of fundamental physics. At present, quantum detection of light is mostly relegated to the microscale, where avalanche photodiodes are very sensitive to distinguishing single-photon events from vacuum but cannot differentiate between larger photon-number events. Beyond this, the ability to perform measurements to resolve photon numbers is highly desirable for a variety of quantum information applications including computation, sensing, and cryptography. True photon-number resolving detectors do exist, but they are currently limited to the ability to resolve on the order of 10 photons, which is too small for several quantum state generation methods based on heralded detection. In this work, we extend photon measurement into the mesoscopic regime by implementing a detection scheme based on multiplexing highly quantum-efficient transition-edge sensors to accurately resolve photon numbers between zero and 100. We then demonstrate the use of our system by implementing a quantum random number generator with no inherent bias. This method is based on sampling a coherent state in the photon-number basis and is robust against environmental noise, phase and amplitude fluctuations in the laser, loss and detector inefficiency as well as eavesdropping. Beyond true random number generation, our detection scheme serves as a means to implement quantum measurement and engineering techniques valuable for photonic quantum information processing., 16 pages, 9 figures

Every quantum algorithm is represented by set of quantum circuits. Any optimization scheme for a quantum algorithm and quantum computation is very important especially in the arena of quantum computation with limited number of qubit resources. Major obstacle to this goal is the large number of elemental quantum gates to build even small quantum circuits. Here, we propose and demonstrate a general technique that significantly reduces the number of elemental gates to build quantum circuits. This is impactful for the design of quantum circuits, and we show below this could reduce the number of gates by 60% and 46% for the four- and five-qubit Toffoli gates, two key quantum circuits, respectively, as compared with simplest known decomposition. Reduced circuit complexity often goes hand-in-hand with higher efficiency and bandwidth. The quantum circuit optimization technique proposed in this work would provide a significant step forward in the optimization of quantum circuits and quantum algorithms, and has the potential for wider application in quantum computation.

Quantum random walks, which drew much attention over the past few decades for their distinctly nonclassical behavior, are a promising subfield within quantum computing. Theoretical framework and applications for these walks have seen many great mathematical advances, with experimental demonstrations now catching up. In this study, we examine the viability of implementing coin quantum random walks using a Quantum Adder-based Shift Operator, with quantum circuit designs specifically for superconducting qubits. We focus on the strengths and weaknesses of these walks, particularly circuit depth, gate count, connectivity requirements and scalability. We propose and analyze a novel approach to implementing boundary conditions for these walks, demonstrating the technique explicitly in one and two dimensions. Finally, we present several fidelity results from running our circuits on IBM’s quantum volume 32 ‘Toronto’ chip, showcasing the extent to which these noisy intermediate-scale quantum devices can currently handle quantum walks.

In this paper, we construct the metric tensor and volume for the manifold of purifications associated with an arbitrary reduced density operator $\rho_S$. We also define a quantum coarse-graining (CG) to study the volume where macrostates are the manifolds of purifications, which we call surfaces of ignorance (SOI), and microstates are the purifications of $\rho_S$. In this context, the volume functions as a multiplicity of the macrostates that quantifies the amount of information missing from $\rho_S$. Using examples where the SOI are generated using representations of $SU(2)$, $SO(3)$, and $SO(N)$, we show two features of the CG. (1) A system beginning in an atypical macrostate of smaller volume evolves to macrostates of greater volume until it reaches the equilibrium macrostate in a process in which the system and environment become strictly more entangled, and (2) the equilibrium macrostate takes up the vast majority of the coarse-grainied space especially as the dimension of the total system becomes large. Here, the equilibrium macrostate corresponds to maximum entanglement between system and environment. To demonstrate feature (1) for the examples considered, we show that the volume behaves like the von Neumann entropy in that it is zero for pure states, maximal for maximally mixed states, and is a concave function w.r.t the purity of $\rho_S$. These two features are essential to typicality arguments regarding thermalization and Boltzmann's original CG., Comment: 12 pages, 10 figures. arXiv admin note: text overlap with arXiv:2111.07836

We show that any odd parity state entering one input port of a 50:50 beam splitter, with an arbitrary state entering the other input port, produces zero coincidence counts. This result extends the HOM effect.

We propose a photonics-based, continuous-variable (CV) form of remote entanglement utilizing strictly second-order nonlinear optical interactions that does not require the implementation of a state-projective measurement (i.e. remote entanglement without conditioning). This scheme makes use of two separate down-converters, wherein the corresponding nonlinear crystals are driven by strong classical fields as prescribed by the parametric approximation, as well as a fully quantum mechanical model of nondegenerate second harmonic generation (SHG) whose evolution is described by the trilinear Hamiltonian of the form $\hat{H}_{\text{shg}} = i\hbar\kappa\big(\hat{a}\hat{b}\hat{c}^{\dagger} - \hat{a}^{\dagger}\hat{b}^{\dagger}\hat{c}\big)$. By driving the SHG process with the signal modes of the two down-converters, we show entanglement formation between the generated second-harmonic mode (SH-mode) and the non-interacting joint-idler subsystem without the need for any state-reductive measurements on the interacting modes.

We show that the parity (evenness or oddness) of a nonclassical state of light has a dominant influence on the interference effects at a balanced beam splitter, irrespective of the state initially occupying the other input mode. Specifically, the parity of the nonclassical state gives rise to destructive interference effects that result in deep valleys in the output joint number distribution of which the Hong-Ou-Mandel (HOM) effect is a limiting case. The counter-intuitive influence of even a single photon to control the output of a beam splitter illuminated by any field, be it a coherent or even a noisy thermal field, demonstrates the extraordinary power of non-classicality. The canonical example of total destructive interference of quantum amplitudes leading to the absence of coincidence counts from a 50/50 beam splitter is the celebrated HOM effect, characterized by the vanishing of the joint probability of detecting singe photons in each of the output beams. We show that this is a limiting case of more general input states upon which a 50/50 BS can create total, or near total, destructive interference of quantum amplitudes. For odd photon number input Fock states of arbitrary value n>0 we show that the joint photon number probabilities vanish when detecting identical photon numbers in each output beams. We examine the mixing of photon number states of n = 1, 2, and 3 with a CV state, such as a coherent state of arbitrary amplitude, and a thermal state. These vanishing joint probabilities form what we call a central nodal line -- a contiguous set of zeros representing complete destructive interference of quantum amplitudes. For odd or even photon number Fock states with n>1 there will be additional off-diagonal pseudo-nodal curves along which the joint photon number probabilities are either zero, or near zero, which constitute a near, but not complete, destructive interference., 27 pages, 13 figures; v2: minor editorial fixes (minor notational corrections in Appendix D), additional clarification comments at end of Appendix A

It is recognized that Grover arrived at his original quantum search algorithm inspired by his comprehension of the interference of classical waves originating from an array of antennas. It is also known that quantum-mechanical characterization of electromagnetic radiation is isomorphic to the treatment of the orientation of a spin-1/2 particle. In this paper, motivated by Grover's original intuition and starting from this mathematical equivalence, we present a quantitative link between the geometry of time-independent optimal-speed Hamiltonian evolutions on the Bloch sphere and the geometry of intensity-preserving propagation of light with maximal degree of coherence on the Poincar\'e sphere. Finally, identifying interference as the fundamental physical ingredient underlying both physical phenomena, we propose that our work can provide in retrospect a quantitative geometric background underlying Grover's powerful intuition., Comment: 22 pages, 1 figure, 3 tables

The prototype quantum random number (random bit) generator (QRNG) consists of one photon at a time falling on a 50:50 beam splitter followed by random detection in one or the other output beams due to the irreducible probabilistic nature of quantum mechanics. Due to the difficulties in producing single photons on demand, in practice, pulses of weak coherent (laser) light are used. In this paper, we take a different approach, one that uses moderate coherent light. It is shown that a QRNG can be implemented by performing photon-number parity measurements. For moderate coherent light, the probabilities of obtaining even or odd parity in photon counts are 0.5 each. Photon counting with single-photon resolution can be performed through use of a cascade of beam splitters and single-photon detectors, as was done recently in a photon-number parity-based interferometry experiment involving coherent light. We highlight the point that unlike most quantum-based random number generators, our proposal does not require the use of classical de-biasing algorithms or post-processing of the generated bit sequence.

We investigate the presence of spin- and planar-squeezing in generalized superpositions of atomic (or spin) coherent states. Spin-squeezing has been shown to be a useful tool in determining the presence of entanglement in multipartite systems, such as collections of two-level atoms, as well as being an indication of reduced projection noise and sub-shot-noise-limited phase uncertainty in Ramsey spectroscopy, suitable for measuring phases ϕ ∼ 0 . On the other hand, planar-squeezed states display reduced projection noise in two directions simultaneously and have been shown to lead to enhanced metrological precision in measuring phases without the need for explicit prior knowledge of the phase value. In this paper, we show that the generalized superposition state can be parametrized to display both spin-squeezing along all orthogonal axes and planar-squeezing along all orthogonal planes for all values of J > 1 / 2 . We close with an application of the maximally spin- and planar-squeezed states to quantum metrology.

Quantum mechanics can produce correlations that are stronger than classically allowed. This stronger-than-classical correlation is the "fuel" for quantum computing. In 1991 Schumacher forwarded a beautiful geometric approach, analogous to the well-known result of Bell, to capture non-classicality of this correlation for a singlet state. He used well-established information distance defined on an ensemble of identically-prepared states. He calculated that for certain detector settings used to measure the entangled state, the resulting geometry violated a triangle inequality -- a violation that is not possible classically. This provided a novel information-based geometric Bell inequality in terms of a "covariance distance." Here we experimentally-reproduce his construction and demonstrate a definitive violation for a Bell state of two photons based on the usual spontaneous parametric down-conversion in a paired BBO crystal. The state we produced had a visibility of $V_{ad}=0.970$. We discuss generalizations to higher dimensional multipartite quantum states., Comment: 10 pages, 4 figures

We present a unifying variational calculus derivation of Groverian geodesics for both quantum state vectors and quantum probability amplitudes. In the first case, we show that horizontal affinely parametrized geodesic paths on the Hilbert space of normalized vectors emerge from the minimization of the length specified by the Fubini-Study metric on the manifold of Hilbert space rays. In the second case, we demonstrate that geodesic paths for probability amplitudes arise by minimizing the length expressed in terms of the Fisher information. In both derivations, we find that geodesic equations are described by simple harmonic oscillators (SHOs). However, while in the first derivation the frequency of oscillations is proportional to the (constant) energy dispersion of the Hamiltonian system, in the second derivation the frequency of oscillations is proportional to the square-root of the (constant) Fisher information. Interestingly, by setting these two frequencies equal to each other, we recover the well-known Anandan-Aharonov relation linking the squared speed of evolution of an Hamiltonian system with its energy dispersion. Finally, upon transitioning away from the quantum setting, we discuss the universality of the emergence of geodesic motion of SHO type in the presence of conserved quantities by analyzing two specific phenomena of gravitational and thermodynamical origin, respectively., Comment: 30 pages, 1 table

In the paper by Weedbrook et. al,1 a post-selected model of Lloyd's original formulation of quantum illumination (QI)2 was used to show that quantum discord explains the underlying advantage of QI over conventional illumination. The same model was used by Ray et. al3 to show that the normalized Hilbert-Schmidt inner product (HSIP) is a valid distinguishability measure when analyzing quantum illumination. This post-selected model assumes that the detector always detects a photon whether it be from the signal or noise from the environment; thus, the vacuum is excluded from this model. In this paper, we include the vacuum back into these analyses. In the case of,1 we show that the conclusion is unaffected by the inclusion of the vacuum. We then analyze the effects of including the vacuum when distinguishing between a noisy signal and noise. In this analysis, we found that the normalized HSIP is not monotonic with respect to the parameter that controls the brightness of the noise. Because of this, the normalized Hilbert-Schmidt inner product cannot be used as a distinguishability as was seen in the post-selected model. To reconcile this problem, we used the proposed alternative fidelity measure defined in,4 and found that it is monotonic in the vacuum added model for all the examples considered.

We use geometric concepts originally proposed by Anandan and Aharonov to show that the Farhi-Gutmann time optimal analog quantum search evolution between two orthogonal quantum states is characterized by unit efficiency dynamical trajectories traced on a projective Hilbert space. In particular, we prove that these optimal dynamical trajectories are the shortest geodesic paths joining the initial and the final states of the quantum evolution. In addition, we verify they describe minimum uncertainty evolutions specified by an uncertainty inequality that is tighter than the ordinary time-energy uncertainty relation. We also study the effects of deviations from the time optimality condition from our proposed Riemannian geometric perspective. Furthermore, after pointing out some physically intuitive aspects offered by our geometric approach to quantum searching, we mention some practically relevant physical insights that could emerge from the application of our geometric analysis to more realistic time-dependent quantum search evolutions. Finally, we briefly discuss possible extensions of our work to the geometric analysis of the efficiency of thermal trajectories of relevance in quantum computing tasks., 14 pages, 1 figure, 1 table

We present an information geometric analysis of both entropic speeds and entropy production rates arising from geodesic evolution on manifolds parametrized by pure quantum states. In particular, we employ pure states that emerge as outputs of suitably chosen su(2; C) time-dependent Hamiltonian operators that characterize analog quantum search algorithms of specific types. The su(2; C) Hamiltonian models under consideration are specified by external time-dependent magnetic fields within which spin-1/2 test particles are immersed. The positive definite Riemannian metrization of the parameter manifold is furnished by the Fisher information function. The Fisher information function is evaluated along parametrized squared probability amplitudes obtained from the temporal evolution of these spin-1/2 test particles. A minimum action approach is then utilized to induce the transfer of the quantum system from its initial state to its final state on the parameter manifold over a finite temporal interval. We demonstrate in an explicit manner that the minimal (that is, optimum) path corresponds to the shortest (that is, geodesic) path between the initial and final states. Furthermore, we show that the minimal path serves also to minimize the total entropy production occurring during the transfer of states. Finally, upon evaluating the entropic speed as well as the total entropy production along optimal transfer paths within several scenarios of physical interest in analog quantum searching algorithms, we demonstrate in a transparent quantitative manner a correspondence between a faster transfer and a higher rate of entropy production. We therefore conclude that higher entropic speed is associated with lower entropic efficiency within the context of quantum state transfer., 25 pages, 4 figures, 3 tables

Secure quantum key distribution (QKD) is limited by the Earth’s horizon, weather, and turbulence in the atmosphere. We will outline the analysis, design, and early stages of our mobile small unmanned aircraft system (sUAS) free-space optical quantum communication system. This reconfigurable, quantum-secure communication platform can potentially open up a novel communication layer that can avoid local weather interruptions as well as provide a substantial reduction in turbulence-related loss by transmitting above ground level. We review the design and testing of a custom cage-system mode analyzer to be implemented as the receiving optics module on a sUAS. The tests of our design, within predicted operational parameters, suggests that this is a feasible option for a mode analyzer on a light-weight mobile platform.

We show how to quantify tri-partite entanglement using entropies derived from experimental correlations. We use a multi-partite generalization of the entanglement of formation that is greater than zero if and only if the state is genuinely multi-partite entangled. We develop an entropic witness for tripartite entanglement, and show that the degree of violation of this witness places a lower limit on the tripartite entanglement of formation. We test our results in the three-qubit regime using the GHZ-Werner state and the W-Werner state, and in the high-dimensional pure-state regime using the triple-Gaussian wavefunction describing the spatial and energy-time entanglement in photon triplets generated in third-order spontaneous parametric down-conversion. In addition, we discuss the challenges in quantifying the entanglement for progressively larger numbers of parties, and give both entropic and target-state-based witnesses of multi-partite entanglement that circumvent this issue., 14 pages, 6 figures (removed inequality (formerly appendix B4) due to typo)

We present an information geometric analysis of entropic speeds and entropy production rates in geodesic evolution on manifolds of parametrized quantum states. These pure states emerge as outputs of suitable su(2; C) time-dependent Hamiltonian operators used to describe distinct types of analog quantum search schemes. The Riemannian metrization on the manifold is specified by the Fisher information evaluated along the parametrized squared probability amplitudes obtained from analysis of the temporal quantum mechanical evolution of a spin-1/2 particle in an external time-dependent magnetic field that specifies the su(2; C) Hamiltonian model. We employ a minimum action method to transfer a quantum system from an initial state to a final state on the manifold in a finite temporal interval. Furthermore, we demonstrate that the minimizing (optimum) path is the shortest (geodesic) path between the two states, and, in particular, minimizes also the total entropy production that occurs during the transfer. Finally, by evaluating the entropic speed and the total entropy production along the optimum transfer paths in a number of physical scenarios of interest in analog quantum search problems, we show in a clear quantitative manner that to a faster transfer there corresponds necessarily a higher entropy production rate. Thus, we conclude that lower entropic efficiency values appear to accompany higher entropic speed values in quantum transfer processes., 12 pages, 3 figures, 3 tables. Accepted for publication in Physical Review E (2020)

We investigate the effect of the cumulative phase on the photon statistics of the three-mode state whose evolution is described by the trilinear Hamiltonian $\hat{H}_{I}=i\hbar\kappa\big(\hat{a}\hat{b}\hat{c}^{\dagger}-\hat{a}^{\dagger}\hat{b}^{\dagger}c\big)$, wherein the pump is taken to be quantized (and prepared in a coherent state) and the signal and idler modes are initially seeded with coherent states. We provide a brief review of the two-mode squeezed coherent states generated by non-degenerate coherently-stimulated parametric down-conversion, whereby the nonlinear crystal is driven by a strong classical field. The statistics of the resulting two mode state have been shown to depend greatly on the cumulative phase $\Phi=\theta_{s}+\theta_{i}-2\phi$ where $\theta_{s\left(i\right)}$ are the signal(idler) coherent state phases and $2\phi$ is the classical pump phase. Using perturbation theory, we analytically show for short times how the photon statistics and entanglement properties of the resultant state depends strictly on this phase combination. We also present numerical results of the relevant quantities to show the evolution of the three modes and provide a qualitative analysis of the steady state valid for long times., Comment: 16 pages, 9 figures

We present an information geometric analysis of off-resonance effects on classes of exactly solvable generalized semi-classical Rabi systems. Specifically, we consider population transfer performed by four distinct off-resonant driving schemes specified by su(2; C) time-dependent Hamiltonian models. For each scheme, we study the consequences of a departure from the on-resonance condition in terms of both geodesic paths and geodesic speeds on the corresponding manifold of transition probability vectors. In particular, we analyze the robustness of each driving scheme against off-resonance effects. Moreover, we report on a possible tradeoff between speed and robustness in the driving schemes being investigated. Finally, we discuss the emergence of a different relative ranking in terms of performance among the various driving schemes when transitioning from on-resonant to off-resonant scenarios., Comment: 20 pages, 5 figures, feature paper

In this paper, we review the use of parity as a detection observable in quantum metrology as well as introduce some original findings with regards to measurement resolution in Ramsey spectroscopy and quantum non-demolition (QND) measures of atomic parity. Parity was first introduced in the context of Ramsey spectroscopy as an alternative to atomic state detection. It was latter adapted for use in quantum optical interferometry where it has been shown to be the optimal detection observable saturating the quantum Cram\'{e}r-Rao bound for path symmetric states. We include a brief review of the basics of phase estimation and the connection between parity-based detection and the quantum Fisher information as it applies to quantum optical interferometry. We also discuss the efforts made in experimental methods of measuring photon-number parity and close the paper with a discussion on the use of parity leading to enhanced measurement resolution in multi-atom spectroscopy. We show how this may be of use in the construction of high-precision multi-atom atomic clocks., Comment: 35 pages, 19 figures; We dedicate this paper to the memory of Jonathan P. Dowling, whose body of work had a tremendous impact on the fields of quantum optical interferometry and quantum metrology

We suggest a dynamical vector model of entanglement in a three qubit system based on isomorphism between $su(4)$ and $so(6)$ Lie algebras. Generalizing Pl\"ucker-type description of three-qubit local invariants we introduce three pairs of real-valued $3D$ vector (denoted here as $A_{R,I}$ , $B_{R,I}$ and $C_{R,I}$). Magnitudes of these vectors determine two- and three-qubit entanglement parameters of the system. We show that evolution of vectors $A$, $B$ , $C$ under local $SU(2)$ operations is identical to $SO(3)$ evolution of single-qubit Bloch vectors of qubits $a$, $b$ and $c$ correspondingly. At the same time, general two-qubit $su(4)$ Hamiltonians incorporating $a-b$, $a-c$ and $b-c$ two-qubit coupling terms generate $SO(6)$ coupling between vectors $A$ and $B$, $A$ and $C$, and $B$ and $C$, correspondingly. It turns out that dynamics of entanglement induced by different two-qubit coupling terms is entirely determined by mutual orientation of vectors $A$, $B$, $C$ which can be controlled by single-qubit transformations. We illustrate the power of this vector description of entanglement by solving quantum control problems involving transformations between $W$, Greenberg-Horne-Zeilinger ($GHZ$ ) and biseparable states., Comment: 26 pages, no figures; Accepted Phys. Rev. A 29Jul2020

Geometry is often a valuable guide to complex problems in physics. In this paper, we introduce a novel geometric quantity called quantum reactivity (QR) to probe quantum correlations in higher-dimensional quantum systems. Much like quantum discord, QR is not a measure of quantum entanglement but can be useful in quantum information processes where a notion of quantum correlation in higher dimensions is needed. Both quantum discord and QR are extendable to an arbitrarily large number of qubits, however, unlike discord, QR satisfies the invariance under unitary operations. Our approach parallels Schumacher&rsquo, s singlet state triangle inequality, which used an information geometry-based entropic distance. We use a generalization of information distance to area, volume, and higher-dimensional volumes and then use these to define a quantity that we call QR, which is the familiar ratio of surface area to volume. We examine a spectrum of multipartite states (Werner, W, GHZ, randomly generated density matrices, etc.) and demonstrate that QR can provide an ordering of these quantum states as to their degree of quantum correlation.

Hamilton's Ricci flow (RF) equations were recently expressed in terms of a sparsely-coupled system of autonomous first-order nonlinear differential equations for the edge lengths of a d-dimensional piecewise linear (PL) simplicial geometry. More recently, this system of discrete Ricci flow (DRF) equations was further simplified by explicitly constructing the Forman-Ricci tensor associated to each edge, thereby diagonalizing the first-order differential operator and avoiding the need to invert large sparse matrices at each time step. We recently showed analytically and numerically that these equations converge for axisymmetric 3-geometries to the corresponding continuum RF equations. We demonstrate here that these DRF equations yield an explicit numerical realization of Thurston's geometrization procedure for a discrete 3D axially-symmetric neckpinch geometry by using surgery to explicitly integrate through its Type-1 neck pinch singularity. A cubic-spline-based adaptive mesh was required to complete the evolution. Our numerically efficient simulations yield the expected Thurston decomposition of the sufficiently pinched axially symmetric geometry into its unique geometric structure -- a direct product of two lobes, each collapsing toward a 3-sphere geometry. The structure of our curvature may be used to better inform one of the vertex and edge weighting factors that appear in the Forman's expression of Ricci curvature on graphs., 8 pages, 6 figures. arXiv admin note: text overlap with arXiv:1308.4148