arXiv subjects

Yudong Cao

Publications and source records attributed to Yudong Cao.

36 records · Page 2Linked to original sources

arXiv2018

Quantum Chemistry in the Age of Quantum Computing

Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced, the complexity of quantum mechanics remains hard to appease. The advent of quantum computation brings new pathways to navigate this challenging complexity landscape. By manipulating quantum states of matter and taking advantage of their unique features such as superposition and entanglement, quantum computers promise to efficiently deliver accurate results for many important problems in quantum chemistry such as the electronic structure of molecules. In the past two decades significant advances have been made in developing algorithms and physical hardware for quantum computing, heralding a revolution in simulation of quantum systems. This article is an overview of the algorithms and results that are relevant for quantum chemistry. The intended audience is both quantum chemists who seek to learn more about quantum computing, and quantum computing researchers who would like to explore applications in quantum chemistry.

quant-ph↗

arXiv2018

qTorch: The Quantum Tensor Contraction Handler

Classical simulation of quantum computation is necessary for studying the numerical behavior of quantum algorithms, as there does not yet exist a large viable quantum computer on which to perform numerical tests. Tensor network (TN) contraction is an algorithmic method that can efficiently simulate some quantum circuits, often greatly reducing the computational cost over methods that simulate the full Hilbert space. In this study we implement a tensor network contraction program for simulating quantum circuits using multi-core compute nodes. We show simulation results for the Max-Cut problem on 3- through 7-regular graphs using the quantum approximate optimization algorithm (QAOA), successfully simulating up to 100 qubits. We test two different methods for generating the ordering of tensor index contractions: one is based on the tree decomposition of the line graph, while the other generates ordering using a straight-forward stochastic scheme. Through studying instances of QAOA circuits, we show the expected result that as the treewidth of the quantum circuit's line graph decreases, TN contraction becomes significantly more efficient than simulating the whole Hilbert space. The results in this work suggest that tensor contraction methods are superior only when simulating Max-Cut/QAOA with graphs of regularities approximately five and below. Insight into this point of equal computational cost helps one determine which simulation method will be more efficient for a given quantum circuit. The stochastic contraction method outperforms the line graph based method only when the time to calculate a reasonable tree decomposition is prohibitively expensive. Finally, we release our software package, qTorch (Quantum TensOR Contraction Handler), intended for general quantum circuit simulation.

quant-ph↗

arXiv2018

A framework for algorithm deployment on cloud-based quantum computers

In recent years, the field of quantum computing has significantly developed in both the improvement of hardware as well as the assembly of various software tools and platforms, including cloud access to quantum devices. Unfortunately, many of these resources are rapidly changing and thus lack accessibility and stability for robust algorithm prototyping and deployment. Effectively leveraging the array of hardware and software resources at a higher level, that can adapt to the rapid development of software and hardware, will allow for further advancement and democratization of quantum technologies to achieve useful computational tasks. As a way to approach this challenge, we present a flexible, high-level framework called algo2qpu that is well-suited for designing and testing instances of algorithms for near-term quantum computers on the cloud. Algorithms that employ adaptive protocols for optimizations of algorithm parameters can be grouped under the umbrella of "adaptive hybrid quantum-classical" (AHQC) algorithms. We demonstrate the utility of algo2qpu for near-term algorithm development by applying the framework to implement proof-of-principle instances of two AHQC algorithms that have applications in quantum chemistry and/or quantum machine learning, namely the quantum autoencoder and the variational quantum classifier, using Rigetti Computing's Forest platform.

quant-ph↗

arXiv2018

Variational Quantum Factoring

Integer factorization has been one of the cornerstone applications of the field of quantum computing since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor's algorithm is well beyond the capabilities of today's noisy intermediate-scale quantum (NISQ) devices. In this work, we revisit the problem of factoring, developing an alternative to Shor's algorithm, which employs established techniques to map the factoring problem to the ground state of an Ising Hamiltonian. The proposed variational quantum factoring (VQF) algorithm starts by simplifying equations over Boolean variables in a preprocessing step to reduce the number of qubits needed for the Hamiltonian. Then, it seeks an approximate ground state of the resulting Ising Hamiltonian by training variational circuits using the quantum approximate optimization algorithm (QAOA). We benchmark the VQF algorithm on various instances of factoring and present numerical results on its performance.

quant-ph↗

arXiv2017

Quantum Neuron: an elementary building block for machine learning on quantum computers

Even the most sophisticated artificial neural networks are built by aggregating substantially identical units called neurons. A neuron receives multiple signals, internally combines them, and applies a non-linear function to the resulting weighted sum. Several attempts to generalize neurons to the quantum regime have been proposed, but all proposals collided with the difficulty of implementing non-linear activation functions, which is essential for classical neurons, due to the linear nature of quantum mechanics. Here we propose a solution to this roadblock in the form of a small quantum circuit that naturally simulates neurons with threshold activation. Our quantum circuit defines a building block, the "quantum neuron", that can reproduce a variety of classical neural network constructions while maintaining the ability to process superpositions of inputs and preserve quantum coherence and entanglement. In the construction of feedforward networks of quantum neurons, we provide numerical evidence that the network not only can learn a function when trained with superposition of inputs and the corresponding output, but that this training suffices to learn the function on all individual inputs separately. When arranged to mimic Hopfield networks, quantum neural networks exhibit properties of associative memory. Patterns are encoded using the simple Hebbian rule for the weights and we demonstrate attractor dynamics from corrupted inputs. Finally, the fact that our quantum model closely captures (traditional) neural network dynamics implies that the vast body of literature and results on neural networks becomes directly relevant in the context of quantum machine learning.

quant-ph↗

arXiv2017

QVECTOR: an algorithm for device-tailored quantum error correction

Current approaches to fault-tolerant quantum computation will not enable useful quantum computation on near-term devices of 50 to 100 qubits. Leading proposals, such as the color code and surface code schemes, must devote a large fraction of their physical quantum bits to quantum error correction. Building from recent quantum machine learning techniques, we propose an alternative approach to quantum error correction aimed at reducing this overhead, which can be implemented in existing quantum hardware and on a myriad of quantum computing architectures. This method aims to optimize the average fidelity of encoding and recovery circuits with respect to the actual noise in the device, as opposed to that of an artificial or approximate noise model. The quantum variational error corrector (QVECTOR) algorithm employs a quantum circuit with parameters that are variationally-optimized according to processed data originating from quantum sampling of the device, so as to learn encoding and error-recovery gate sequences. We develop this approach for the task of preserving quantum memory and analyze its performance with simulations. We find that, subject to phase damping noise, the simulated QVECTOR algorithm learns a three-qubit encoding and recovery which extend the effective T2 of a quantum memory six-fold. Subject to a continuous-time amplitude- plus phase-damping noise model on five qubits, the simulated QVECTOR algorithm learns encoding and decoding circuits which exploit the coherence among Pauli errors in the noise model to outperform the five-qubit stabilizer code and any other scheme that does not leverage such coherence. Both of these schemes can be implemented with existing hardware.

quant-ph↗

arXiv2017

Efficient optimization of perturbative gadgets

Perturbative gadgets are general techniques for reducing many-body spin interactions to two-body ones using perturbation theory. This allows for potential realization of effective many-body interactions using more physically viable two-body ones. In parallel with prior work (arXiv:1311.2555 [quant-ph]), here we consider minimizing the physical resource required for implementing the gadgets initially proposed by Kempe, Kitaev and Regev (arXiv:quant-ph/0406180) and later generalized by Jordan and Farhi (arXiv:0802.1874v4). The main innovation of our result is a set of methods that efficiently compute tight upper bounds to errors in the perturbation theory. We show that in cases where the terms in the target Hamiltonian commute, the bounds produced by our algorithm are sharp for arbitrary order perturbation theory. We provide numerics which show orders of magnitudes improvement over gadget constructions based on trivial upper bounds for the error term in the perturbation series. We also discuss further improvement of our result by adopting the Schrieffer-Wolff formalism of perturbation theory and supplement our observation with numerical results.

quant-ph↗

arXiv2017

Quantum Information and Computation for Chemistry

The NSF Workshop in Quantum Information and Computation for Chemistry assembled experts from directly quantum-oriented fields such as algorithms, chemistry, machine learning, optics, simulation, and metrology, as well as experts in related fields such as condensed matter physics, biochemistry, physical chemistry, inorganic and organic chemistry, and spectroscopy. The goal of the workshop was to summarize recent progress in research at the interface of quantum information science and chemistry as well as to discuss the promising research challenges and opportunities in the field. Furthermore, the workshop hoped to identify target areas where cross fertilization among these fields would result in the largest payoff for developments in theory, algorithms, and experimental techniques. The ideas can be broadly categorized in two distinct areas of research that obviously have interactions and are not separated cleanly. The first area is quantum information for chemistry, or how quantum information tools, both experimental and theoretical can aid in our understanding of a wide range of problems pertaining to chemistry. The second area is chemistry for quantum information, which aims to discuss the several aspects where research in the chemical sciences can aid progress in quantum information science and technology. The results of the workshop are summarized in this report.

quant-ph↗

arXiv2017

Quasi-Reliable Estimates of Effective Sample Size

The efficiency of a Markov chain Monte Carlo algorithm might be measured by the cost of generating one independent sample, or equivalently, the total cost divided by the effective sample size, defined in terms of the integrated autocorrelation time. To ensure the reliability of such an estimate, it is suggested that there be an adequate sampling of state space--- to the extent that this can be determined from the available samples. A possible method for doing this is derived and evaluated.

stat.CO↗

arXiv2016

Solving Set Cover with Pairs Problem Using Quantum Annealing

Here we consider using quantum annealing to solve Set Cover with Pairs (SCP), an NP-hard combinatorial optimization problem that play an important role in networking, computational biology, and biochemistry. We show an explicit construction of Ising Hamiltonians whose ground states encode the solution of SCP instances. We numerically simulate the time-dependent Schrödinger equation in order to test the performance of quantum annealing for random instances and compare with that of simulated annealing. We also discuss explicit embedding strategies for realizing our Hamiltonian construction on the D-wave type restricted Ising Hamiltonian based on Chimera graphs. Our embedding on the Chimera graph preserves the structure of the original SCP instance and in particular, the embedding for general complete bipartite graphs and logical disjunctions may be of broader use than that the specific problem we deal with.

quant-ph↗

arXiv2016

Quantum computation using arrays of N polar molecules in pendular states

We investigate several aspects of realizing quantum computation using entangled polar molecules in pendular states. Quantum algorithms typically start from a product state |00...0> and we show that up to a negligible error, the ground states of polar molecule arrays can be considered as the unentangled qubit basis state |00...0>. This state can be prepared by simply allowing the system to reach thermal equilibrium at low temperature (<1 mK). We also evaluate entanglement, characterized by the concurrence of pendular state qubits in dipole arrays as governed by the external electric field, dipole-dipole coupling and number N of molecules in the array. In the parameter regime that we consider for quantum computing, we find that qubit entanglement is modest, typically no greater than 0.0001, confirming the negligible entanglement in the ground state. We discuss methods for realizing quantum computation in the gate model, measurement based model, instantaneous quantum polynomial time circuits and the adiabatic model using polar molecules in pendular states.

quant-ph↗

arXiv2016

Efficient estimation of perturbative error with cellular automata

From celestial mechanics to quantum theory of atoms and molecules, perturbation theory has played a central role in natural sciences. Particularly in quantum mechanics, the amount of information needed for specifying the state of a many-body system commonly scales exponentially as the system size. This poses a fundamental difficulty in using perturbation theory at arbitrary order. As one computes the terms in the perturbation series at increasingly higher orders, it is often important to determine whether the series converges and if so, what is an accurate estimation of the total error that comes from the next order of perturbation up to infinity. Here we present a set of efficient algorithms that compute tight upper bounds to perturbation terms at arbitrary order. We argue that these tight bounds often take the form of symmetric polynomials on the parameter of the quantum system. We then use cellular automata as our basic model of computation to compute the symmetric polynomials that account for all of the virtual transitions at any given order. At any fixed order, the computational cost of our algorithm scales polynomially as a function of the system size. We present a non-trivial example which shows that our error estimation is nearly tight with respect to exact calculation.

quant-ph↗

arXiv2015

Hamiltonian gadgets with reduced resource requirements

Application of the adiabatic model of quantum computation requires efficient encoding of the solution to computational problems into the lowest eigenstate of a Hamiltonian that supports universal adiabatic quantum computation. Experimental systems are typically limited to restricted forms of 2-body interactions. Therefore, universal adiabatic quantum computation requires a method for approximating quantum many-body Hamiltonians up to arbitrary spectral error using at most 2-body interactions. Hamiltonian gadgets, introduced around a decade ago, offer the only current means to address this requirement. Although the applications of Hamiltonian gadgets have steadily grown since their introduction, little progress has been made in overcoming the limitations of the gadgets themselves. In this experimentally motivated theoretical study, we introduce several gadgets which require significantly more realistic control parameters than similar gadgets in the literature. We employ analytical techniques which result in a reduction of the resource scaling as a function of spectral error for the commonly used subdivision, 3- to 2-body and $k$-body gadgets. Accordingly, our improvements reduce the resource requirements of all proofs and experimental proposals making use of these common gadgets. Next, we numerically optimize these new gadgets to illustrate the tightness of our analytical bounds. Finally, we introduce a new gadget that simulates a $YY$ interaction term using Hamiltonians containing only $\{X,Z,XX,ZZ\}$ terms. Apart from possible implications in a theoretical context, this work could also be useful for a first experimental implementation of these key building blocks by requiring less control precision without introducing extra ancillary qubits.

quant-ph↗

arXiv2014

Perturbative gadgets without strong interactions

Perturbative gadgets are used to construct a quantum Hamiltonian whose low-energy subspace approximates a given quantum $k$-body Hamiltonian up to an absolute error $ε$. Typically, gadget constructions involve terms with large interaction strengths of order $\text{poly}(ε^{-1})$. Here we present a 2-body gadget construction and prove that it approximates a target many-body Hamiltonian of interaction strength $γ= O(1)$ up to absolute error $ε\llγ$ using interactions of strength $O(ε)$ instead of the usual inverse polynomial in $ε$. A key component in our proof is a new condition for the convergence of the perturbation series, allowing our gadget construction to be applied in parallel on multiple many-body terms. We also show how to apply this gadget construction for approximating 3- and $k$-body Hamiltonians. The price we pay for using much weaker interactions is a large overhead in the number of ancillary qubits, and the number of interaction terms per particle, both of which scale as $O(\text{poly}(ε^{-1}))$. Our strong-from-weak gadgets have their primary application in complexity theory (QMA hardness of restricted Hamiltonians, a generalized area law counterexample, gap amplification), but could also motivate practical implementations with many weak interactions simulating a much stronger quantum many-body interaction.

quant-ph↗

arXiv2014

Infrared-dressed entanglement of cold open-shell polar molecules for universal matchgate quantum computing

Implementing a scalable quantum information processor using polar molecules in optical lattices requires precise control over the long-range dipole-dipole interaction between molecules in selected lattice sites. We present here a scheme using trapped open-shell $^2Σ$ polar molecules that allows dipolar exchange processes between nearest and next-nearest neighbors to be controlled to construct a generalized transverse Ising spin Hamiltonian with tunable $XX$, $YY$ and $XY$ couplings in the rotating frame of the driving lasers. The scheme requires a moderately strong bias magnetic field with near-infrared light to provide local tuning of the qubit energy gap, and mid-infrared pulses to perform rotational state transfer via stimulated Raman adiabatic passage. No interaction between qubits is present in the absence of the infrared driving. We analyze the fidelity of the resulting two-qubit matchgate, and demonstrate its robustness as a function of the driving parameters. We discuss a realistic application of the system for universal matchgate quantum computing in optical lattices.

quant-ph↗

arXiv2013

Quantum Circuit Design for Solving Linear Systems of Equations

Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key aspects of the algorithm from the standpoint of finding its efficient quantum circuit implementation using only elementary quantum operations, which is important for determining the potential usefulness of the algorithm in practical settings. Then we present a small-scale quantum circuit that solves a 2x2 linear system. The quantum circuit uses only 4 qubits, implying a tempting possibility for experimental realization. Furthermore, the circuit is numerically simulated and its performance under different circuit parameter settings is demonstrated.

quant-ph↗

arXiv2013

Experimental realization of quantum algorithm for solving linear systems of equations

Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$ matrix $A$ and a vector $\vec b$, find the vector $\vec x$ that satisfies $A\vec x = \vec b$. It has been shown that using the algorithm one could obtain the solution encoded in a quantum state $|x$ using $O(\log{N})$ quantum operations, while classical algorithms require at least O(N) steps. If one is not interested in the solution $\vec{x}$ itself but certain statistical feature of the solution ${x}|M|x$ ($M$ is some quantum mechanical operator), the quantum algorithm will be able to achieve exponential speedup over the best classical algorithm as $N$ grows. Here we report a proof-of-concept experimental demonstration of the quantum algorithm using a 4-qubit nuclear magnetic resonance (NMR) quantum information processor. For all the three sets of experiments with different choices of $\vec b$, we obtain the solutions with over 96% fidelity. This experiment is a first implementation of the algorithm. Because solving linear systems is a common problem in nearly all fields of science and engineering, we will also discuss the implication of our results on the potential of using quantum computers for solving practical linear systems.

quant-ph↗

arXiv2012

Quantum algorithm and circuit design solving the Poisson equation

The Poisson equation occurs in many areas of science and engineering. Here we focus on its numerical solution for an equation in d dimensions. In particular we present a quantum algorithm and a scalable quantum circuit design which approximates the solution of the Poisson equation on a grid with error \varepsilon. We assume we are given a supersposition of function evaluations of the right hand side of the Poisson equation. The algorithm produces a quantum state encoding the solution. The number of quantum operations and the number of qubits used by the circuit is almost linear in d and polylog in \varepsilon^{-1}. We present quantum circuit modules together with performance guarantees which can be also used for other problems.

quant-ph↗