Optimal Conversion from Classical to Quantum Randomness via Quantum Chaos
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Mok, Wai-Keong (ORCID:0000000219205407)↗
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Low-depth Clifford circuits approximately solve MaxCut
We introduce a quantum-inspired approximation algorithm for MaxCut based on low-depth Clifford circuits. We start by showing that the solution unitaries found by the adaptive quantum approximation optimization algorithm (ADAPT-QAOA) for the MaxCut problem on weighted fully connected graphs are (almost) Clifford circuits. Motivated by this observation, we devise an approximation algorithm for MaxCut, ADAPT-Clifford, that searches through the Clifford manifold by combining a minimal set of generating elements of the Clifford group. Our algorithm finds an approximate solution of MaxCut on an N -vertex graph by building a depth O ( N ) Clifford circuit. The algorithm has runtime complexity O ( N 2 ) and O ( N 3 ) for sparse and dense graphs, respectively, and space complexity O ( N 2 ) , with improved solution quality achieved at the expense of more demanding runtimes. We implement ADAPT-Clifford and characterize its performance on graphs with positive and signed weights. The case of signed weights is illustrated with the paradigmatic Sherrington-Kirkpatrick model, for which our algorithm finds solutions with ground-state mean energy density corresponding to ∼ 94 % of the Parisi value in the thermodynamic limit. The case of positive weights is investigated by comparing the cut found by ADAPT-Clifford with the cut found with the Goemans-Williamson (GW) algorithm. For both sparse and dense instances we provide copious evidence that, up to hundreds of nodes, ADAPT-Clifford finds cuts of lower energy than GW. Published by the American Physical Society 2024
Muñoz-Arias, Manuel H. (ORCID:000000025711029X)↗
Dynamical Decoupling of Crosstalk on Superconducting Qubit Devices
Current NISQ devices are prone to errors. In order to be used for practical applications or achieve fault-tolerant thresholds, strategies to suppress error rates will be needed to maximize the potential of noisy devices. Dynamical decoupling (DD) is one such strategy for suppressing — or at least alleviating — the effects of decoherence, in which sequences of pulses are applied to qubits to decouple their interaction with the environment. Through experimental runs performed on several Rigetti quantum computing units (QPUs), we first demonstrate that DD is capable of improving coherence times for isolated qubits, as well as suppressing errors caused by the ZZ coupling between pairs of qubits. Extending this framework to cycles containing2-qubit gates, we show that DD can be inserted to decouple qubits from crosstalk occurring during neighboring 2-qubit gates, and demonstrate the efficacy of this procedure on quantum approximate optimization algorithm (QAOA) circuits. We also explore the usage of tailored DD sequences for the suppression of characterized error channels. We are grateful for support from the NASA Ames Research Center and from the DARPA ONISQ program under interagency agreement IAA 8839,Annex 114. HYH is supported by the USRA Feynman QuantumAcademy funded by the NAMS R&D Student Program and a UCHellman Fellowship. JS, ZGI and ZW are supported by USRA NASAAcademic Mission Service (NNA16BD14C).
Dynamical decoupling↗
Open-loop robust quantum control via sequential convex optimization.
Abstract Not Provided
Grace, Matthew↗
Almost optimal classical algorithms for a quantum generalization of Max Cut.
Abstract not provided.
Parekh, Ojas D.↗
Optimization of Realistic Silicon Double Quantum Dots through Simulation.
Abstract not provided.
Nielsen, Erik↗
Optimal control equations for the one dimensional quantum harmonic oscillator under the influence of external dipole effects
This study focuses on the construction of the optimal control equations for one dimensional quantum harmonic oscillator under the influence of external dipol effects and the solution of these equations by using Fluctuationlessness Theorem and a recently developed scheme called Characteristic Evolutions Method. The dipole function of the system has been taken as odd cubic spatial polynomial. Optimal control equations of the system under consideration are constructed by using expectation values of the position and the momentum operators instead of the wave and costate evolutions. It is shown that, the resulting equations are systems of ordinary differential equations and there are infinitely many ODEs. The solution strategy is based on the approximation of the expectation values for the operator products in the sense of Fluctuationlessness Theorem.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Accelerating the convergence of auxiliary-field quantum Monte Carlo in solids with optimized Gaussian basis sets
We investigate the use of optimized correlation-consistent Gaussian basis sets for the study of insulating solids with auxiliary-field quantum Monte Carlo (AFQMC). The exponents of the basis set are optimized through the minimization of the second-order Møller–Plesset perturbation theory (MP2) energy in a small unit cell of the solid. We compare against other alternative basis sets proposed in the literature, namely, calculations in the Kohn–Sham basis and in the natural orbitals of an MP2 calculation. We find that our optimized basis sets accelerate the convergence of the AFQMC correlation energy compared to a Kohn–Sham basis and offer similar convergence to MP2 natural orbitals at a fraction of the cost needed to generate them. We also suggest the use of an improved, method independent, MP2-based basis set correction that significantly reduces the required basis set sizes needed to converge the correlation energy. With these developments, we study the relative performance of these basis sets in LiH, Si, and MgO and determine that our optimized basis sets yield the most consistent results as a function of volume. Using these optimized basis sets, we systematically converge the AFQMC calculations to the complete basis set and thermodynamic limit and find excellent agreement with experiment for the systems studied. Although we focus on AFQMC, our basis set generation procedure is independent of the subsequent correlated wavefunction method used.
Morales, Miguel A. (ORCID:0000000263893067)↗
Compressed Optimization of Device Architectures for Semiconductor Quantum Devices
Recent advances in nanotechnology have enabled researchers to manipulate small collections of quantum-mechanical objects with unprecedented accuracy. In semiconductor quantum-dot qubits, this manipulation requires controlling the dot orbital energies, the tunnel couplings, and the electron occupations. These properties all depend on the voltages placed on the metallic electrodes that define the device, the positions of which are fixed once the device is fabricated. While there has been much success with small numbers of dots, as the number of dots grows, it will be increasingly useful to control these systems with as few electrode voltage changes as possible. Here, we introduce a protocol, which we call the "compressed optimization of device architectures" (CODA), in order both to efficiently identify sparse sets of voltage changes that control quantum systems and to introduce a metric that can be used to compare device designs. As an example of the former, we apply this method to simulated devices with up to 100 quantum dots and show that CODA automatically tunes devices more efficiently than other common nonlinear optimizers. To demonstrate the latter, we determine the optimal lateral scale for a triple quantum dot, yielding a simulated device that can be tuned with small voltage changes on a limited number of electrodes.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Generalization in quantum machine learning from few training data
Modern quantum machine learning (QML) methods involve variationally optimizing a parameterized quantum circuit on a training data set, and subsequently making predictions on a testing data set (i.e., generalizing). In this work, we provide a comprehensive study of generalization performance in QML after training on a limited number N of training data points. We show that the generalization error of a quantum machine learning model with T trainable gates scales at worst as $\sqrt{T/N}$. When only K$\ll$T gates have undergone substantial change in the optimization process, we prove that the generalization error improves to $\sqrt{K/N}$. Our results imply that the compiling of unitaries into a polynomial number of native gates, a crucial application for the quantum computing industry that typically uses exponential-size training data, can be sped up significantly. We also show that classification of quantum states across a phase transition with a quantum convolutional neural network requires only a very small training data set. Other potential applications include learning quantum error correcting codes or quantum dynamical simulation. Our work injects new hope into the field of QML, as good generalization is guaranteed from few training data.
97 MATHEMATICS AND COMPUTING↗
Feedback-based quantum algorithms for ground state preparation
The ground state properties of quantum many-body systems are a subject of interest across chemistry, materials science, and physics. Thus, algorithms for finding ground states can have broad impacts. Variational quantum algorithms are one class of ground state algorithms that has received significant attention in recent years. These algorithms utilize a hybrid quantum-classical computing framework to prepare ground states on quantum computers. However, this requires solving a classical optimization problem that can become prohibitively expensive in high dimensions. Here, we develop formulations of feedback-based quantum algorithms for ground state preparation that can be used to address this challenge for two broad classes of Hamiltonians: Fermi-Hubbard Hamiltonians, and molecular Hamiltonians represented in second quantization. Feedback-based quantum algorithms are optimization-free; in place of classical optimization, quantum circuit parameters are set according to a deterministic feedback law derived from quantum Lyapunov control principles. This feedback law guarantees a monotonic improvement in solution quality with respect to the depth of the quantum circuit. A variety of numerical illustrations are provided that analyze the convergence and robustness of feedback-based quantum algorithms for these problem classes. Published by the American Physical Society 2024
Larsen, James B. (ORCID:000000020777440X)↗
Classical combinatorial optimization scaling for random Ising models on 2D heavy-hex graphs
Motivated by near term quantum computing hardware limitations, combinatorial optimization problems that can be addressed by current quantum algorithms and noisy hardware with little or no overhead are used to probe capabilities of quantum algorithms such as the quantum approximate optimization algorithm. In this study, a specific class of near term quantum computing hardware defined combinatorial optimization problems, Ising models on heavy-hex graphs both with and without geometrically local cubic terms, are examined for their classical computational hardness via empirical computation time scaling quantification. Specifically the time-to-solution (TTS) metric using the classical heuristic simulated annealing is measured for finding optimal variable assignments (ground states), as well as the time required for the optimization software Gurobi to find an optimal variable assignment. Because of the sparsity of these Ising models, the classical algorithms are able to find optimal solutions efficiently even for large instances (i.e. 100 000 spin variables). The Ising models both with and without geometrically local cubic terms exhibit average-case linear-time or weakly quadratic scaling when solved exactly using Gurobi, and the Ising models with no cubic terms show evidence of exponential-time TTS scaling when sampled using simulated annealing. These findings point to the necessity of developing and testing more complex, namely more densely connected, optimization problems in order for quantum computing to ever have a practical advantage over classical computing. Our results are another illustration that different classical algorithms can indeed have exponentially different running times, thus making the identification of the best practical classical technique important in any quantum computing vs. classical computing comparison.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Optimizing temperature distributions for training neural quantum states using parallel tempering
Parametrized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the ANN can be slow and stymied by the presence of local minima in the parameter landscape. One approach to mitigate this issue is to use parallel tempering methods, and in this work, we focus on the role played by the temperature distribution of the parallel tempering replicas. Using an adaptive method that adjusts the temperatures in order to equate the exchange probability between neighboring replicas, we show that this temperature optimization can significantly increase the success rate of the variational algorithm with negligible computational cost by eliminating bottlenecks in the replicas' random walk. Furthermore, we demonstrate this using two different neural networks, a restricted Boltzmann machine and a feedforward network, which we use to study a toy problem based on a permutation invariant Hamiltonian with a pernicious local minimum and the 𝐽 1 −𝐽 2 model on a rectangular lattice.
Neural network simulations↗
Formation mechanism and optimization of highly luminescent N-doped graphene quantum dots
Photoluminescent graphene quantum dots (GQDs) have received enormous attention because of their unique chemical, electronic and optical properties. Here a series of GQDs were synthesized under hydrothermal processes in order to investigate the formation process and optical properties of N-doped GQDs. Citric acid (CA) was used as a carbon precursor and self-assembled into sheet structure in a basic condition and formed N-free GQD graphite framework through intermolecular dehydrolysis reaction. N-doped GQDs were prepared using a series of N-containing bases such as urea. Detailed structural and property studies demonstrated the formation mechanism of N-doped GQDs for tunable optical emissions. Hydrothermal conditions promote formation of amide between –NH2 and –COOH with the presence of amine in the reaction. The intramoleculur dehydrolysis between neighbour amide and COOH groups led to formation of pyrrolic N in the graphene framework. Further, the pyrrolic N transformed to graphite N under hydrothermal conditions. N-doping results in a great improvement of PL quantum yield (QY) of GQDs. By optimized reaction conditions, the highest PL QY (94%) of N-doped GQDs was obtained using CA as a carbon source and ethylene diamine as a N source. The obtained N-doped GQDs exhibit an excitation-independent blue emission with single exponential lifetime decay.
NANOPARTICLES↗
Cost function dependent barren plateaus in shallow parametrized quantum circuits
Variational quantum algorithms (VQAs) optimize the parameters θ of a parametrized quantum circuit V(θ) to minimize a cost function C. While VQAs may enable practical applications of noisy quantum computers, they are nevertheless heuristic methods with unproven scaling. Here, we rigorously prove two results, assuming V(θ) is an alternating layered ansatz composed of blocks forming local 2-designs. Our first result states that defining C in terms of global observables leads to exponentially vanishing gradients (i.e., barren plateaus) even when V(θ) is shallow. Hence, several VQAs in the literature must revise their proposed costs. On the other hand, our second result states that defining C with local observables leads to at worst a polynomially vanishing gradient, so long as the depth of V(θ) is Ο(logn). Our results establish a connection between locality and trainability. We illustrate these ideas with large-scale simulations, up to 100 qubits, of a quantum autoencoder implementation.
97 MATHEMATICS AND COMPUTING↗
Architecture for Quantum Time-dependent Circuits (ArQTIC) v1.0
ArQTiC is a domain-specific full-stack software package built for the dynamic simulations of materials on quantum computers. Its main contributions include providing a software library for high-level programming of such simulations on quantum computers, and providing post-processing capabilities that allow users to more efficiently analyze results from the quantum computer. Paired with the power to optimize and execute quantum circuits, ArQTiC opens the field of dynamic materials simulations on quantum computers to a broader community of scientists from a wider range of domain sciences, paving the way for accelerated progress towards physical quantum supremacy.
Bassman, Lindsay↗
Hybrid quantum-classical hierarchy for mitigation of decoherence and determination of excited states
Using quantum devices supported by classical computational resources is a promising approach to quantum-enabled computation. One powerful example of such a hybrid quantum-classical approach optimized for classically intractable eigenvalue problems is the variational quantum eigensolver, built to utilize quantum resources for the solution of eigenvalue problems and optimizations with minimal coherence time requirements by leveraging classical computational resources. These algorithms have been placed as leaders among the candidates for the first to achieve supremacy over classical computation. Here, we provide evidence for the conjecture that variational approaches can automatically suppress even nonsystematic decoherence errors by introducing an exactly solvable channel model of variational state preparation. Moreover, we develop a more general hierarchy of measurement and classical computation that allows one to obtain increasingly accurate solutions by leveraging additional measurements and classical resources. In conclusion, we demonstrate numerically on a sample electronic system that this method both allows for the accurate determination of excited electronic states as well as reduces the impact of decoherence, without using any additional quantum coherence time or formal error-correction codes.
McClean, Jarrod R.↗
Benchmarking embedded chain breaking in quantum annealing*
Quantum annealing solves combinatorial optimization problems by finding the energetic ground states of an embedded Hamiltonian. However, quantum annealing dynamics under the embedded Hamiltonian may violate the principles of adiabatic evolution and generate excitations that correspond to errors in the computed solution. Here we empirically benchmark the probability of chain breaks and identify sweet spots for solving a suite of embedded Hamiltonians. We further correlate the physical location of chain breaks in the quantum annealing hardware with the underlying embedding technique and use these localized rates in a tailored post-processing strategies. Our results demonstrate how to use characterization of the quantum annealing hardware to tune the embedded Hamiltonian and remove computational errors.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗