arXiv subjects

Tim Byrnes

Publications and source records attributed to Tim Byrnes.

At least 55 records · Page 3Linked to original sources

arXiv2023

Imaginary time evolution with quantum nondemolition measurements: multi-qubit interactions via measurement nonlinearities

We show that quantum nondemolition (QND) measurements can be used to realize measurement-based imaginary time evolution. In our proposed scheme, repeated weak QND measurements are used to estimate the energy of a given Hamiltonian. Based on this estimated energy, adaptive unitary operations are applied such that only the targeted energy eigenstates are fixed points of the evolution. In this way, the system is deterministically driven towards the desired state. The nonlinear nature of the QND measurement, which allows for producing interactions between systems, is explicitly derived in terms of measurement operators. We show that for suitable interaction times, single qubit QND Hamiltonians can be converted to effective multi-qubit imaginary time operations. We illustrate our techniques with the example of preparing a four qubit cluster state, which is prepared using only collective single qubit QND measurements and single qubit adaptive operations.

quant-ph↗

arXiv2023

Optical and atomic decoherence in entangled atomic ensembles generated by quantum nondemolition measurements

We study the effects of decoherence in the form of optical phase diffusion, photon loss and gain, and atomic dephasing in entangled atomic ensembles produced via quantum nondemolition (QND) measurements. For the optical decoherence channels, we use the technique of integration within ordered operators (IWOP) to obtain the Kraus operators that describe the decoherence. We analyze the effect of different decoherence channels on a variety of quantities such as the variances of the spin operators, entanglement and correlation criteria, logarithmic negativity, and the Bell-CHSH inequality. We generally find a smooth decay of correlations and entanglement in the presence of decoherence. We find that various quantities retain showing non-classical properties under all three types of decoherence, in the short interaction time range. Our results show that such QND measurements are one of the most promising methods for entanglement generation between two Bose-Einstein condensates.

quant-ph↗

arXiv2023

Measurement operator for quantum nondemolition measurements

We derive a measurement operator corresponding to a quantum nondemolition (QND) measurement of an atomic ensemble. The quantum measurement operator takes the form of a positive operator valued measure (POVM) and is valid for arbitrary interaction times, initial coherent state amplitudes, and final photon measurement outcomes. We analyze the dependence on various parameters and show that the effect of the QND measurement for short interaction times is to apply a Gaussian modulation of the initial state wavefunction. We derive approximate expressions for the POVM in various limits, such as the short interaction time regime and projective measurement limit. Several examples are shown which shows how spin squeezing and Schrodinger cat states can be generated using the measurement.

quant-ph↗

arXiv2022

Simple determination of dark states in a general multi-level system

In a multi-level energy system with energy transitions, dark states are eigenstates of a Hamiltonian that consist entirely of ground states, with zero amplitude in the excited states. We present several criteria which allows one to deduce the presence of dark states in a general multi-level system based on the submatrices of the Hamiltonian. The dark states can be shown to be the right-singular vectors of the submatrix that connect the ground states to the excited states. Furthermore, we show a simple way of finding the dark state involving the determinant of a matrix constructed from the same submatrix.

quant-ph↗

arXiv2022

Decoherence effects in quantum nondemolition measurement induced entanglement between Bose-Einstein condensates

We study the robustness of quantum nondemolition (QND) measurement-induced entanglement between Bose-Einstein Condensates (BECs). We consider an experimental scheme where two BECs are placed in the paths of a Mach-Zehnder interferometer, and a QND interaction creates entanglement between coherent light and the atoms. We analyze the two dominant channels of decoherence, atomic dephasing and photon loss on the entangled states produced by this scheme. We calculate the effect of dephasing on the variance and expectation values of the spin operators, entanglement, and correlation criteria. Our analysis does not use the Holstein-Primakoff approximation and is capable of modeling long light-atom interaction times, producing non-Gaussian states beyond the two-mode squeezed states. In the presence of dephasing, the entangled states are robust in the macroscopic limit as long as the dimensionless interaction time is less than $ 1/\sqrt{N}$, where $ N $ is the number of atoms in the BEC. For photon loss, the entangled states generated by long interaction times show remarkable robustness that makes the scheme promising for various quantum information applications.

physics.atom-ph↗

arXiv2022

Quantum supremacy with spin squeezed atomic ensembles

We propose a method to achieve quantum supremacy using ensembles of qubits, using only spin squeezing, basis rotations, and Fock state measurements. Each ensemble is assumed to be controllable only with its total spin. Using a repeated sequence of random basis rotations followed by squeezing, we show that the probability distribution of the final measurements quickly approaches a Porter-Thomas distribution. We show that the sampling probability can be related to a #P-hard problem with a complexity scaling as $(N+1)^M$, where $N$ is the number of qubits in an ensemble and $ M $ is the number of ensembles. The scheme can be implemented with hot or cold atomic ensembles. Due to the large number of atoms in typical atomic ensembles, this allows access to the quantum supremacy regime with a modest number of ensembles or gate depth.

quant-ph↗

arXiv2022

Deterministic preparation of supersinglets with collective spin projections

We introduce a procedure to generate supersinglets, the multipartite generalization of angular momentum singlet states. A supersinglet is defined as a total spin zero state consisting of $ N $ spin-$ j $ particles. They are highly entangled and have zero spin variance in any direction, and as such are potentially useful for quantum metrology. Our scheme is based on projective measurements that measure the collective spin of the whole spin ensemble. A local unitary rotation is applied conditionally on the measurement outcome, such as to maximize the probability of obtaining spin zero on the subsequent measurement. The sequence is repeated in the $ z $- and $ x $-basis until convergence is obtained towards the supersinglet state. Our sequence works regardless of the initial state, and no postselection is required. Due to the use of strong projective measurements, very fast convergence towards zero spin variance is obtained. We discuss an example implementation using quantum nondemolition measurements in atomic ensembles, and perform numerical simulations to demonstrate the procedure.

quant-ph↗

arXiv2022

Ising machines as hardware solvers of combinatorial optimization problems

Ising machines are hardware solvers which aim to find the absolute or approximate ground states of the Ising model. The Ising model is of fundamental computational interest because it is possible to formulate any problem in the complexity class NP as an Ising problem with only polynomial overhead. A scalable Ising machine that outperforms existing standard digital computers could have a huge impact for practical applications for a wide variety of optimization problems. In this review, we survey the current status of various approaches to constructing Ising machines and explain their underlying operational principles. The types of Ising machines considered here include classical thermal annealers based on technologies such as spintronics, optics, memristors, and digital hardware accelerators; dynamical-systems solvers implemented with optics and electronics; and superconducting-circuit quantum annealers. We compare and contrast their performance using standard metrics such as the ground-state success probability and time-to-solution, give their scaling relations with problem size, and discuss their strengths and weaknesses.

quant-ph↗

arXiv2022

A large-scale single-mode array laser based on a topological edge mode

Topological lasers have been intensively investigated as a strong candidate for robust single-mode lasers. A typical topological laser employs a single-mode topological edge state, which appears deterministically in a designed topological bandgap and exhibits robustness to disorder. These properties seem to be highly attractive in pursuit of high power lasers capable of single mode operation. In this paper, we theoretically analyze a large-scale single-mode laser based on a topological edge state. We consider a sizable array laser consisting of a few hundreds of site resonators, which support a single topological edge mode broadly distributed among the resonators. We build a basic model describing the laser using the tight binding approximation and evaluate the stability of single mode lasing based on the threshold gain difference $Δα$ between the first-lasing edge mode and the second-lasing competing bulk mode. Our calculations demonstrate that stronger couplings between the cavities and lower losses are advantageous for achieving stable operation of the device. When assuming an average coupling of 100 cm$^{-1}$ between site resonators and other realistic parameters, the threshold gain difference $Δα$ can reach about 2 cm$^{-1}$, which would be sufficient for stable single mode lasing using a conventional semiconductor laser architecture. We also consider the effects of possible disorders and long-range interactions to assess the robustness of the laser under non-ideal situations. These results lay the groundwork for developing single-mode high-power topological lasers.

physics.optics↗

arXiv2022

Gaussian boson sampling with partial distinguishability

Gaussian boson sampling (GBS) allows for a way to demonstrate quantum supremacy with the relatively modest experimental resources of squeezed light sources, linear optics, and photon detection. In a realistic experimental setting, numerous effects can modify the complexity of the sampling, in particular loss, partial distinguishability of the photons, and the use of threshold detectors rather than photon counting detectors. In this paper, we investigate GBS with partial distinguishability using an approach based on virtual modes and indistinguishability efficiency. We develop a model using these concepts and derive the probabilities of measuring a specific output pattern from partially distinguishable and lossy GBS for both types of detectors. In the case of threshold detectors, the probability as calculated by the Torontonian is a special case under our framework. By analyzing the expressions of these probabilities we propose an efficient auxiliary classical simulation algorithm which can be used to calculate the probabilities. Our model and the auxiliary algorithm provide foundations for an approximation method for the probability calculation and simulation algorithms not only compatible with existing state-of-the-art simulation algorithms for ideal GBS but also reduce their complexities exponentially depending on the indistinguishability. Using the approximation method and the simulation algorithms we show how the boundary of quantum supremacy in GBS can be pushed further by partial distinguishability.

quant-ph↗

arXiv2022

Stroboscopic quantum nondemolition measurements for enhanced entanglement generation between atomic ensembles

We develop a measurement operator formalism to handle quantum nondemolition (QND) measurement induced entanglement generation between two atomic gases. We first derive how the QND entangling scheme reduces to a positive operator-valued measure, and consider its limiting case when it can be used to construct a projection operator that collapses the state to a total spin projection state. We then analyze how a stroboscopic sequence of such projections made in the x and z basis evolves the initial wave function. Such a sequence of QND projections can enhance the entanglement between the atomic ensembles and makes the state converge towards a highly entangled state. We show several mathematical identities which greatly simplify the state evolution in the projection sequence and allow one to derive the exact state in a highly efficient manner. Our formalism does not use the Holstein-Primakoff approximation as is conventionally done, and treats the spins of the atomic gases in an exact way.

quant-ph↗

arXiv2022

Multiparameter quantum metrology and mode entanglement with spatially split nonclassical spin states

We identify the multiparameter sensitivity of split nonclassical spin states, such as spin-squeezed and Dicke states spatially distributed into several addressable modes. Analytical expressions for the spin-squeezing matrix of a family of states that are accessible by current atomic experiments reveal the quantum gain in multiparameter metrology, as well as the optimal strategies to maximize the sensitivity. We further study the mode entanglement of these states by deriving a witness for genuine $k$-partite mode entanglement from the spin-squeezing matrix. Our results highlight the advantage of mode entanglement for distributed sensing, and outline optimal protocols for multiparameter estimation with nonclassical spatially-distributed spin ensembles.

quant-ph↗

arXiv2021

Nonlinear quantum error correction

We introduce a theory of quantum error correction (QEC) for a subclass of states within a larger Hilbert space. In the standard theory of QEC, the set of all encoded states is formed by an arbitrary linear combination of the codewords. However, this can be more general than required for a given quantum protocol which may only traverse a subclass of states within the Hilbert space. Here we propose the concept of nonlinear QEC (NLQEC), where the encoded states are not necessarily a linear combination of codewords. We introduce a sufficiency criterion for NLQEC with respect to the subclass of states. The new criterion gives a more relaxed condition for the formation of a QEC code, such that under the assumption that the states are within the subclass of states, the errors are correctable. This allows us, for instance, to effectively circumvent the no-go theorems regarding optical QEC for Gaussian states and channels, for which we present explicit examples.

quant-ph↗

arXiv2021

Bell correlations in a split two-mode-squeezed Bose-Einstein condensate

We propose and analyze a protocol for observing a violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality using two spatially separated Bose-Einstein condensates (BECs). To prepare the Bell-correlated state, spin-changing collisions are used to first prepare a two-mode squeezed BEC. This is then split into two BECs by controlling the spatial wavefunction, e.g., by modifying the trapping potential. Finally, spin-changing collisions are also exploited locally, to compensate local squeezing terms. The correlators appearing in the inequality are evaluated using three different approaches. In the first approach, correlators are estimated using normalized expectation values of number operators, in a similar way to evaluating continuous-variable Bell inequalities. An improvement to this approach is developed using the sign-binning of total spin measurements, which allows for the construction of two-outcome measurements and violations of the CHSH inequality without auxiliary assumptions. Finally, we show a third approach where maximal violations of the CH inequality can be obtained by assigning zero values to local vacua outcomes under a no-enhancement assumption. The effect of loss and imperfect detection efficiency is investigated and the observed violations are found to be robust to noise.

quant-ph↗

arXiv2021

Quadratic Quantum Speedup for Perceptron Training

Perceptrons, which perform binary classification, are the fundamental building blocks of neural networks. Given a data set of size~$N$ and margin~$γ$ (how well the given data are separated), the query complexity of the best-known quantum training algorithm scales as either $(\nicefrac{\sqrt{N}}{γ^2})\log(\nicefrac1{γ^2)}$ or $\nicefrac{N}{\sqrtγ}$, which is achieved by a hybrid of classical and quantum search. In this paper, we improve the version space quantum training method for perceptrons such that the query complexity of our algorithm scales as $\sqrt{\nicefrac{N}γ}$. This is achieved by constructing an oracle for the perceptrons using quantum counting of the number of data elements that are correctly classified. We show that query complexity to construct such an oracle has a quadratic improvement over classical methods. Once such an oracle is constructed, bounded-error quantum search can be used to search over the hyperplane instances. The optimality of our algorithm is proven by reducing the evaluation of a two-level AND-OR tree (for which the query complexity lower bound is known) to a multi-criterion search. Our quantum training algorithm can be generalized to train more complex machine learning models such as neural networks, which are built on a large number of perceptrons.

quant-ph↗

arXiv2021

Remote state preparation of two-component Bose-Einstein condensates

A protocol for remote state preparation is proposed for spin ensembles, where the aim is to prepare a state with a given set of spin expectation values on a remote spin ensemble using entanglement, local spin rotations, and measurements in the Fock basis. The spin ensembles could be realized by thermal atomic ensembles or spinor Bose-Einstein condensates. The protocol works beyond the Holstein-Primakoff approximation, such that spin expectation values for the full Bloch sphere can be prepared. The main practical obstacle is the preparation of the maximally entangled state between the spin ensembles. To overcome this, we examine using states based on the two-axis two-spin (2A2S) Hamiltonian in place of the maximally entangled state and examine its performance. We find that the version of the protocol with 2A2S squeezing well-approximates the maximally entangled state, such that spin averages can be remotely prepared. We evaluate the errors of using 2A2S squeezed states, and find that it decreases with the ensemble size. With post-selection, errors can be systematically decreased further.

quant-ph↗

arXiv2021

A Two-Kind-Boson Mixture Honeycomb Hamiltonian of Bloch Exciton-Polaritons

The electronic bandstructure of a solid is a collection of allowed bands separated by forbidden bands, revealing the geometric symmetry of the crystal structures. Comprehensive knowledge of the bandstructure with band parameters explains intrinsic physical, chemical and mechanical properties of the solid. Here we report the artificial polaritonic bandstructures of two-dimensional honeycomb lattices for microcavity exciton-polaritons using GaAs semiconductors in the wide-range detuning values, from cavity-photon-like (red-detuned) to exciton-like (blue-detuned) regimes. In order to understand the experimental bandstructures and their band parameters, such as gap energies, bandwidths, hopping integrals and density of states, we originally establish a polariton band theory within an augmented plane wave method with two-kind-bosons, cavity photons trapped at the lattice sites and freely moving excitons. In particular, this two-kind-band theory is absolutely essential to elucidate the exciton effect in the bandstructures of blue-detuned exciton-polaritons, where the flattened exciton-like dispersion appears at larger in-plane momentum values captured in our experimental access window. We reach an excellent agreement between theory and experiments in all detuning values.

cond-mat.mes-hall↗

arXiv2021

Faraday imaging induced squeezing of a double-well Bose-Einstein condensate

We examine how non-destructive measurements generate spin squeezing in an atomic Bose-Einstein condensate confined in a double-well trap. The condensate in each well is monitored using coherent light beams in a Mach-Zehnder configuration that interacts with the atoms through a quantum nondemolition Hamiltonian. We solve the dynamics of the light-atom system using an exact wavefunction approach, in the presence of dephasing noise, which allows us to examine arbitrary interaction times and a general initial state. We find that monitoring the condensate at zero detection current and with identical coherent light beams minimizes the backaction of the measurement on the atoms. In the weak atom-light interaction regime, we find the mean spin direction is relatively unaffected, while the variance of the spins is squeezed along the axis coupled to the light. Additionally, squeezing persists in the presence of tunneling and dephasing noise.

quant-ph↗