Quantum-classical Algorithm Research Articles

ADAPT-QSCI: Adaptive Construction of an Input State for Quantum-Selected Configuration Interaction.

We present a quantum-classical hybrid algorithm for calculating the ground state and its energy of the quantum many-body Hamiltonian by proposing an adaptive construction of a quantum state for the quantum-selected configuration interaction (QSCI) method. QSCI allows us to select important electronic configurations in the system to perform configuration interaction (CI) calculation (subspace diagonalization of the Hamiltonian) by sampling measurement for a proper input quantum state on a quantum computer, but how we prepare a desirable input state remains a challenge. We propose an adaptive construction of the input state for QSCI in which we run QSCI repeatedly to grow the input state iteratively. We numerically illustrate that our method, dubbed ADAPT-QSCI, can yield accurate ground-state energies for small molecules, including a noisy situation for eight qubits where error rates of two-qubit gates and the measurement are both as large as 1%. ADAPT-QSCI serves as a promising method to take advantage of current noisy quantum devices and pushes forward its application to quantum chemistry.

Leveraging Variational Quantum-Classical Algorithms for Enhanced Lung Cancer Prediction

Leveraging Variational Quantum-Classical Algorithms for Enhanced Lung Cancer Prediction

Two-Stage Estimation and Variance Modeling for Latency-Constrained Variational Quantum Algorithms

The quantum approximate optimization algorithm (QAOA) has enjoyed increasing attention in noisy, intermediate-scale quantum computing with its application to combinatorial optimization problems. QAOA has the potential to demonstrate a quantum advantage for NP-hard combinatorial optimization problems. As a hybrid quantum-classical algorithm, the classical component of QAOA resembles a simulation optimization problem in which the simulation outcomes are attainable only through a quantum computer. The simulation that derives from QAOA exhibits two unique features that can have a substantial impact on the optimization process: (i) the variance of the stochastic objective values typically decreases in proportion to the optimality gap, and (ii) querying samples from a quantum computer introduces an additional latency overhead. In this paper, we introduce a novel stochastic trust-region method derived from a derivative-free, adaptive sampling trust-region optimization method intended to efficiently solve the classical optimization problem in QAOA by explicitly taking into account the two mentioned characteristics. The key idea behind the proposed algorithm involves constructing two separate local models in each iteration: a model of the objective function and a model of the variance of the objective function. Exploiting the variance model allows us to restrict the number of communications with the quantum computer and also helps navigate the nonconvex objective landscapes typical in QAOA optimization problems. We numerically demonstrate the superiority of our proposed algorithm using the SimOpt library and Qiskit when we consider a metric of computational burden that explicitly accounts for communication costs. History: Accepted by Giacomo Nannicini, Area Editor for Quantum Computing and Operations Research. Accepted for Special Issue. Funding: This material is based upon work supported by the U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers and the Office of Advanced Scientific Computing Research, Accelerated Research for Quantum Computing program under contract number DE-AC02-06CH11357. Y. Ha and S. Shashaani also gratefully acknowledge the U.S. National Science Foundation Division of Civil, Mechanical and Manufacturing Innovation Grant CMMI-2226347 and the U.S. Office of Naval Research [Grant N000142412398]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0575 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0575 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Simulation of a Rohksar–Kivelson ladder on a NISQ device

We present a quantum-classical algorithm to study the dynamics of the Rohksar–Kivelson plaquette ladder on NISQ devices. We show that complexity is largely reduced using gauge invariance, additional symmetries, and a crucial property associated to how plaquettes are blocked against ring-exchange in the ladder geometry. This allows for an efficient simulation of sizable plaquette ladders with a small number of qubits, well suited for the capabilities of present NISQ devices. We illustrate the procedure for ladders with simulation of up to 8 plaquettes in an IBM-Q machine, employing scaled quantum gates.

Efficient quantum circuits based on the quantum natural gradient

Efficient preparation of arbitrary entangled quantum states is crucial for quantum computation. This is particularly important for noisy intermediate-scale quantum simulators relying on variational hybrid quantum-classical algorithms. To that end, we propose symmetry-conserving modified quantum approximate optimization algorithm (SCom-QAOA) circuits. The depths of these circuits depend not only on the desired fidelity to the target state but also on the amount of entanglement the state contains. The parameters of the SCom-QAOA circuits are optimized using the quantum natural gradient method based on the Fubini-Study metric. The SCom-QAOA circuit transforms an unentangled state into a ground state of a gapped one-dimensional Hamiltonian with a circuit depth that depends not on the system size but rather on the finite correlation length. In contrast, the circuit depth grows proportionally to the system size for preparing low-lying states of critical one-dimensional systems. Even in the latter case, SCom-QAOA circuits with depth less than the system size were sufficient to generate states with fidelity in excess of 99%, which is relevant for near-term applications. The proposed scheme enlarges the set of the initial states accessible for variational quantum algorithms and widens the scope of investigation of nonequilibrium phenomena in quantum simulators. Published by the American Physical Society 2024

Evaluating a quantum-classical quantum Monte Carlo algorithm with Matchgate shadows

Solving the electronic structure problem of molecules and solids to high accuracy is a major challenge in quantum chemistry and condensed matter physics. The rapid emergence and development of quantum computers offer a promising route to systematically tackle this problem. Recent work by [Huggins , ] proposed a hybrid quantum-classical quantum Monte Carlo (QC-QMC) algorithm using Clifford shadows to determine the ground state of a Fermionic Hamiltonian. This approach displayed inherent noise resilience and the potential for improved accuracy compared to its purely classical counterpart. Nevertheless, the use of Clifford shadows introduces an exponentially scaling postprocessing cost. In this work, we investigate an improved QC-QMC scheme utilizing the recently developed Matchgate shadows technique [], which removes the aforementioned exponential bottleneck. We observe from experiments on quantum hardware that the use of Matchgate shadows in QC-QMC is inherently noise robust. We show that this noise resilience has a more subtle origin than in the case of Clifford shadows. Nevertheless, we find that classical postprocessing, while asymptotically efficient, requires hours of runtime on thousands of classical CPUs for even the smallest chemical systems, presenting a major challenge to the scalability of the algorithm. Published by the American Physical Society 2024

Random Natural Gradient

Hybrid quantum-classical algorithms appear to be the most promising approach for near-term quantum applications. An important bottleneck is the classical optimization loop, where the multiple local minima and the emergence of barren plateaux make these approaches less appealing. To improve the optimization the Quantum Natural Gradient (QNG) method \cite{stokes2020quantum} was introduced – a method that uses information about the local geometry of the quantum state-space. While the QNG-based optimization is promising, in each step it requires more quantum resources, since to compute the QNG one requires O(m2) quantum state preparations, where m is the number of parameters in the parameterized circuit. In this work we propose two methods that reduce the resources/state preparations required for QNG, while keeping the advantages and performance of the QNG-based optimization. Specifically, we first introduce the Random Natural Gradient (RNG) that uses random measurements and the classical Fisher information matrix (as opposed to the quantum Fisher information used in QNG). The essential quantum resources reduce to linear O(m) and thus offer a quadratic "speed-up", while in our numerical simulations it matches QNG in terms of accuracy. We give some theoretical arguments for RNG and then benchmark the method with the QNG on both classical and quantum problems. Secondly, inspired by stochastic-coordinate methods, we propose a novel approximation to the QNG which we call Stochastic-Coordinate Quantum Natural Gradient that optimizes only a small (randomly sampled) fraction of the total parameters at each iteration. This method also performs equally well in our benchmarks, while it uses fewer resources than the QNG.

Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit

Hybrid quantum-classical algorithm for the transverse-field Ising model in the thermodynamic limit

Photonic counterdiabatic quantum optimization algorithm

One of the key applications of near-term quantum computers has been the development of quantum optimization algorithms. However, these algorithms have largely been focused on qubit-based technologies. Here, we propose a hybrid quantum-classical approximate optimization algorithm for photonic quantum computing, specifically tailored for addressing continuous-variable optimization problems. Inspired by counterdiabatic protocols, our algorithm reduces the required quantum operations for optimization compared to adiabatic protocols. This reduction enables us to tackle non-convex continuous optimization within the near-term era of quantum computing. Through illustrative benchmarking, we show that our approach can outperform existing state-of-the-art hybrid adiabatic quantum algorithms in terms of convergence and implementability. Our algorithm offers a practical and accessible experimental realization, bypassing the need for high-order operations and overcoming experimental constraints. We conduct a proof-of-principle demonstration on Xanadu’s eight-mode nanophotonic quantum chip, successfully showcasing the feasibility and potential impact of the algorithm.

Distributed hybrid quantum-classical performance prediction for hyperparameter optimization

Hyperparameter optimization (HPO) of neural networks is a computationally expensive procedure, which requires a large number of different model configurations to be trained. To reduce such costs, this work presents a distributed, hybrid workflow, that runs the training of the neural networks on multiple graphics processing units (GPUs) on a classical supercomputer, while predicting the configurations’ performance with quantum-trained support vector regression (QT-SVR) on a quantum annealer (QA). The workflow is shown to run on up to 50 GPUs and a QA at the same time, completely automating the communication between the classical and the quantum systems. The approach is evaluated extensively on several benchmarking datasets from the computer vision (CV), high-energy physics (HEP), and natural language processing (NLP) domains. Empirical results show that resource costs for performing HPO can be reduced by up to 9% when using the hybrid workflow with performance prediction, compared to using a plain HPO algorithm without performance prediction. Additionally, the workflow obtains similar and in some cases even better accuracy of the final hyperparameter configuration, when combining multiple heuristically obtained predictions from the QA, compared to using just a single classically obtained prediction. The results highlight the potential of hybrid quantum-classical machine learning algorithms. The workflow code is made available open-source to foster adoption in the community.

The Localized Active Space Method with Unitary Selective Coupled Cluster.

We introduce a hybrid quantum-classical algorithm, the localized active space unitary selective coupled cluster singles and doubles (LAS-USCCSD) method. Derived from the localized active space unitary coupled cluster (LAS-UCCSD) method, LAS-USCCSD first performs a classical LASSCF calculation, then selectively identifies the most important parameters (cluster amplitudes used to build the multireference UCC ansatz) for restoring interfragment interaction energy using this reduced set of parameters with the variational quantum eigensolver method. We benchmark LAS-USCCSD against LAS-UCCSD by calculating the total energies of (H2)2, (H2)4, and trans-butadiene, and the magnetic coupling constant for a bimetallic compound [Cr2(OH)3(NH3)6]3+. For these systems, we find that LAS-USCCSD reduces the number of required parameters and thus the circuit depth by at least 1 order of magnitude, an aspect which is important for the practical implementation of multireference hybrid quantum-classical algorithms like LAS-UCCSD on near-term quantum computers.

Exact factorization of the photon-electron-nuclear wavefunction: Formulation and coupled-trajectory dynamics.

We employ the exact-factorization formalism to study the coupled dynamics of photons, electrons, and nuclei at the quantum mechanical level, proposing illustrative examples of model situations of nonadiabatic dynamics and spontaneous emission of electron-nuclear systems in the regime of strong light-matter coupling. We make a particular choice of factorization for such a multi-component system, where the full wavefunction is factored as a conditional electronic amplitude and a marginal photon-nuclear amplitude. Then, we apply the coupled-trajectory mixed quantum-classical (CTMQC) algorithm to perform trajectory-based simulations, by treating photonic and nuclear degrees of freedom on equal footing in terms of classical-like trajectories. The analysis of the time-dependent potentials of the theory along with the assessment of the performance of CTMQC allows us to point out some limitations of the current approximations used in CTMQC. Meanwhile, comparing CTMQC with other trajectory-based algorithms, namely multi-trajectory Ehrenfest and Tully surface hopping, demonstrates the better quality of CTMQC predictions.

Implementation and analysis of quantum-classical hybrid interactive image segmentation algorithm based on quantum annealer

Implementation and analysis of quantum-classical hybrid interactive image segmentation algorithm based on quantum annealer

Detecting Measurement-Induced Entanglement Transitions with Unitary Mirror Circuits.

Monitored random circuits, consisting of alternating layers of entangling two-qubit gates and projective single-qubit measurements applied to some fraction p of the qubits, have been a topic of recent interest. In particular, the resulting steady state exhibits a phase transition from highly correlated states with "volume-law" entanglement at p<p_{c} to localized states with "area-law" entanglement at p>p_{c}. It is hard to access this transition experimentally, as it cannot be seen at the ensemble level. Naively, to observe it one must repeat the experiment until the set of measurement results repeats itself, with likelihood that is exponentially small in the number of measurements. To overcome this issue, we present a hybrid quantum-classical algorithm which creates a matrix product state (MPS) based "unitary mirror" of the projected circuit. Polynomial-sized tensor networks can represent quantum states with area-law entanglement, and so the unitary mirror can well approximate the experimental state above p_{c} but fails exponentially below it. The breaking of this mirror can thus pinpoint the critical point. We outline the algorithm and how such results would be obtained. We present a bound on the maximum entanglement entropy of any given state that is well represented by an MPS, and from the bound suggest how the volume-law phase can be bounded. We consider whether the entanglement could similarly be bounded from below where the MPS fails. Finally, we present numerical results for small qubit numbers and for monitored circuits with random Clifford gates.

Quantum deep generative prior with programmable quantum circuits

Exploiting the utility of near-term quantum devices is a long-standing challenge whereas hybrid quantum machine learning emerges as a promising candidate. Here we propose a quantum-enhanced deep generative algorithm based on programmable quantum circuit-induced quantum latent codes. To validate the effectiveness of the algorithm, we conduct optical ghost imaging experiments, collecting dataset under varying physical sampling rates. Leveraging a physically enhanced loss function and a pretrained neural network, the quantum algorithm exhibits superior reconstruction performance compared to conventional algorithms. We observe the learnable quantum latent space enhances the out-of-distribution generalization capability of the pretrained model. In the context of computer vision problems, numerical results indicate that quantum latent space can increase the generation diversity of the pretrained model. Furthermore, the algorithm outperforms classical counterparts, particularly in image inpainting and colorization, by a significant margin. Our study demonstrates the utility of hybrid quantum-classical algorithms in enhancing generalization capability, highlighting the potential of near-term quantum devices in large-scale generative artificial intelligence.

Measuring the Loschmidt Amplitude for Finite-Energy Properties of the Fermi-Hubbard Model on an Ion-Trap Quantum Computer

Calculating the equilibrium properties of condensed-matter systems is one of the promising applications of near-term quantum computing. Recently, hybrid quantum-classical time-series algorithms have been proposed to efficiently extract these properties from a measurement of the Loschmidt amplitude ⟨ψ|e−iH^t|ψ⟩ from initial states |ψ⟩ and a time evolution under the Hamiltonian H^ up to short times t. In this work, we study the operation of this algorithm on a present-day quantum computer. Specifically, we measure the Loschmidt amplitude for the Fermi-Hubbard model on a 16-site ladder geometry (32 orbitals) on the Quantinuum H2-1 trapped-ion device. We assess the effect of noise on the Loschmidt amplitude and implement algorithm-specific error-mitigation techniques. By using a thus-motivated error model, we numerically analyze the influence of noise on the full operation of the quantum-classical algorithm by measuring expectation values of local observables at finite energies. Finally, we estimate the resources needed for scaling up the algorithm. Published by the American Physical Society 2024

Learning quantum symmetries with interactive quantum-classical variational algorithms

A symmetry of a state |ψ⟩ is a unitary operator of which |ψ⟩ is an eigenvector. When |ψ⟩ is an unknown state supplied by a black-box oracle, the state’s symmetries provide key physical insight into the quantum system; symmetries also boost many crucial quantum learning techniques. In this paper, we develop a variational hybrid quantum–classical learning scheme to systematically probe for symmetries of |ψ⟩ with no a priori assumptions about the state. This procedure can be used to learn various symmetries at the same time. In order to avoid re-learning already known symmetries, we introduce an interactive protocol with a classical deep neural net. The classical net thereby regularizes against repetitive findings and allows our algorithm to terminate empirically with all possible symmetries found. An iteration of the learning algorithm can be implemented efficiently with non-local SWAP gates; we also give a less efficient algorithm with only local operations, which may be more appropriate for current noisy quantum devices. We simulate our algorithm on representative families of states, including cluster states and ground states of Rydberg and Ising Hamiltonians. We also find that the numerical query complexity scales well for up to moderate system sizes.

Fighting Noise with Noise: A Stochastic Projective Quantum Eigensolver.

In the current noisy intermediate scale quantum era of quantum computation, available hardware is severely limited by both qubit count and noise levels, precluding the application of many current hybrid quantum-classical algorithms to nontrivial quantum chemistry problems. In this paper we propose applying some of the fundamental ideas of conventional Quantum Monte Carlo algorithms─stochastic sampling of both the wave function and the Hamiltonian─to quantum algorithms in order to significantly decrease quantum resource costs. In the context of an imaginary-time propagation based projective quantum eigensolver, we present a novel approach to estimating physical observables which can lead to an order of magnitude reduction in the required sampling of the quantum state to converge the ground state energy of a system relative to current state-of-the-art eigensolvers. The method can be equally applied to excited-state calculations and, combined with stochastic approximations of the system Hamiltonian, provides a promising near-term approach to Hamiltonian simulation for general chemistry on quantum devices.

Solving fractional differential equations on a quantum computer: A variational approach

We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap history states. The proposed algorithm is not only efficient in terms of time complexity but also has lower memory costs compared to classical methods. Our results indicate that solution fidelity is insensitive to the fractional index and that gradient evaluation costs scale economically with the number of time steps. As a proof of concept, we apply our algorithm to solve a range of fractional partial differential equations commonly encountered in engineering applications, such as the subdiffusion equation, the nonlinear Burgers' equation, and a coupled diffusive epidemic model. We assess quantum hardware performance under realistic noise conditions, further validating the practical utility of our algorithm.

Quantum Algorithm for Imaginary-Time Green's Functions.

Green's function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function. The calculation of the exact one-particle Green's function remains a significant challenge for classical computers and was attempted only on very small systems. Here, we present a hybrid quantum-classical algorithm to calculate the imaginary-time one-particle Green's function. The proposed algorithm combines the variational quantum eigensolver and the quantum subspace expansion methods to calculate Green's function in Lehmann's representation. We demonstrate the validity of this algorithm by simulating H2 and H4 on quantum simulators and on IBM's quantum devices.