Parallel Quantum Chemistry on Noisy Intermediate-Scale Quantum Computers
Paderborn University（帕德博恩大学）；Paderborn Center for Parallel Computing, Paderborn University（帕德博恩大学并行计算中心）；Dynamics of Condensed Matter and Institute for Sustainable Systems Design, Chair of Theoretical Chemistry, Paderborn University（帕德博恩大学凝聚态动力学与可持续系统设计研究所理论化学教席）；Department for Computer Science, Paderborn University（帕德博恩大学计算机科学系）
Robert Schade, Carsten Bauer, Konstantin Tamoev, Lukas Mazur, Christian Plessl, Thomas D. Kühne
A novel parallel hybrid quantum-classical algorithm for the solution of the quantum-chemical ground-state energy problem on gate-based quantum computers is presented. This approach is based on the reduced density-matrix functional theory (RDMFT) formulation of the electronic structure problem. For that purpose, the density-matrix functional of the full system is decomposed into an indirectly coupled sum of density-matrix functionals for all its subsystems using the adaptive cluster approximation to RDMFT. The approximations involved in the decomposition and the adaptive cluster approximation itself can be systematically converged to the exact result. The solutions for the density-matrix functionals of the effective subsystems involves a constrained minimization over many-particle states that are approximated by parametrized trial states on the quantum computer similarly to the variational quantum eigensolver. The independence of the density-matrix functionals of the effective subsystems introduces a new level of parallelization and allows for the computational treatment of much larger molecules on a quantum computer with a given qubit count. In addition, for the proposed algorithm techniques are presented to reduce the qubit count, the number of quantum programs, as well as its depth. The new approach is demonstrated for Hubbard-like systems on IBM quantum computers based on superconducting transmon qubits.
We propose a modification of the Variational Quantum Eigensolver algorithm for electronic structure optimization using quantum computers, named non-unitary Variational Quantum Eigensolver (nu-VQE), in which a non-unitary operator is combined with the original system Hamiltonian leading to a new variational problem with a simplified wavefunction Ansatz. In the present work, we use, as non-unitary operator, the Jastrow factor, inspired from classical Quantum Monte Carlo techniques for simulation of strongly correlated electrons. The method is applied to prototypical molecular Hamiltonians for wh…
The opportunities afforded by near-term quantum computers to calculate the ground-state properties of small molecules depend on the structure of the computational ansatz as well as the errors induced by device noise. Here we investigate the behavior of these noisy quantum circuits using numerical simulations to estimate the accuracy and fidelity of the prepared quantum states relative to the ground truth obtained by conventional means. We implement several different types of ansatz circuits derived from unitary coupled cluster theory for the purposes of estimating the ground-state energy of So…
Quantum computing brings a promise of new approaches into computational quantum chemistry. While universal, fault-tolerant quantum computers are still not available, we want to utilize today's noisy quantum processors. One of their flagship applications is the variational quantum eigensolver (VQE) -- an algorithm to calculate the minimum energy of a physical Hamiltonian. In this study, we investigate how various types of errors affect the VQE, and how to efficiently use the available resources to produce precise computational results. We utilize a simulator of a noisy quantum device, an exact …
We present a quantum chemistry benchmark for noisy intermediate-scale quantum computers that leverages the variational quantum eigensolver, active space reduction, a reduced unitary coupled cluster ansatz, and reduced density purification as error mitigation. We demonstrate this benchmark on the 20 qubit IBM Tokyo and 16 qubit Rigetti Aspen processors via the simulation of alkali metal hydrides (NaH, KH, RbH),with accuracy of the computed ground state energy serving as the primary benchmark metric. We further parameterize this benchmark suite on the trial circuit type, the level of symmetry re…
A central problem in biophysics and computational drug design is accurate modeling of biomolecules. The current molecular dynamics simulation methods can answer how a molecule inhibits a cancerous cell signaling pathway, or the role of protein misfolding in neurodegenerative diseases. However, the accuracy of current force fields (interaction potential) limits the reliability of computer simulations. Fundamentally a quantum chemistry problem, here we discuss optimizing force fields using scalable ab initio quantum chemistry calculations on quantum computers and estimate the quantum resources r…
We review two algorithmic advances that bring us closer to reliable quantum simulations of model systems in high energy physics and beyond on noisy intermediate-scale quantum (NISQ) devices. The first method is the dimensional expressivity analysis of quantum circuits, which allows for constructing minimal but maximally expressive quantum circuits. The second method is an efficient mitigation of readout errors on quantum devices. Both methods can lead to significant improvements in quantum simulations, e.g., when variational quantum eigensolvers are used.
Real-time clustering of big performance data generated by the telecommunication networks requires domain-specific high performance compute infrastructure to detect anomalies. In this paper, we evaluate noisy intermediate-scale quantum (NISQ) computers characterized by low decoherence times, for K-means clustering and propose three strategies to generate shorter-depth quantum circuits needed to overcome the limitation of NISQ computers. The strategies are based on exploiting; i) quantum interference, ii) negative rotations and iii) destructive interference. By comparing our implementations on I…
The development of Noisy Intermediate Scale Quantum Computers (NISQC) provides for the Quantum Information community new tools to perform quantum experiences from an individual laptop. It facilitates interdisciplinary research in the sense that theoretical descriptions of properties of quantum physics can be translated to experiments easily implementable on a NISCQ. In this note I test large state-independent inequalities for quantum contextuality on finite geometric structures encoding the commutation relations of the generalized N-qubit Pauli group. The bounds predicted by Non-Contextual Hid…
We present an accreditation protocol for the outputs of noisy intermediate-scale quantum devices. By testing entire circuits rather than individual gates, our accreditation protocol can provide an upper-bound on the variation distance between noisy and noiseless probability distribution of the outputs of the target circuit of interest. Our accreditation protocol requires implementation of quantum circuits no larger than the target circuit, therefore it is practical in the near term and scalable in the long term. Inspired by trap-based protocols for the verification of quantum computations, our…
In the era of noisy-intermediate-scale quantum computers, we expect to see quantum devices with increasing numbers of qubits emerge in the foreseeable future. To practically run quantum programs, logical qubits have to be mapped to the physical qubits by a qubit allocation algorithm. However, on present day devices, qubits differ by their error rate and connectivity. Here, we establish and demonstrate on current experimental devices a new allocation algorithm that combines the simulated annealing method with local search of the solution space using Dijkstra's algorithm. Our algorithm takes int…
Several noisy intermediate-scale quantum computations can be regarded as logarithmic-depth quantum circuits on a sparse quantum computing chip, where two-qubit gates can be directly applied on only some pairs of qubits. In this paper, we propose a method to efficiently verify such noisy intermediate-scale quantum computation. To this end, we first characterize small-scale quantum operations with respect to the diamond norm. Then by using these characterized quantum operations, we estimate the fidelity $\langleψ_t|\hatρ_{\rm out}|ψ_t\rangle$ between an actual $n$-qubit output state $\hatρ_{\rm …
We study the performance and resource usage of the variational quantum factoring (VQF) algorithm for different instance sizes and optimization algorithms. Our simulations show better chance of finding the ground state when using VQE rather than QAOA for optimization. In gradient-based optimization we find that the time required for quantum circuit gradient estimation is a significant problem if VQF is to become competitive with classical factoring algorithms. Further, we compare entangled and non-entangled circuits in VQE optimization and fail to see significant evidence in favour of including…
Quantum search algorithm (also known as Grover's algorithm) lays the foundation for many other quantum algorithms. Although it is very simple, its implementation is limited on noisy intermediate-scale quantum (NISQ) processors. Grover's algorithm was designed without considering the physical resources, such as depth, in the real implementations. Therefore, Grover's algorithm can be improved for NISQ devices. In this paper, we demonstrate how to implement quantum search algorithms better on NISQ devices. We present detailed benchmarks of the five-qubit quantum search algorithm on different quan…
The recent advent of noisy intermediate-scale quantum devices, especially near-term quantum computers, has sparked extensive research efforts concerned with their possible applications. At the forefront of the considered approaches are variational methods that use parametrized quantum circuits. The classical and quantum Fisher information are firmly rooted in the field of quantum sensing and have proven to be versatile tools to study such parametrized quantum systems. Their utility in the study of other applications of noisy intermediate-scale quantum devices, however, has only been discovered…
We propose a realistic hybrid classical-quantum linear solver to solve systems of linear equations of a specific type, and demonstrate its feasibility using Qiskit on IBM Q systems. This algorithm makes use of quantum random walk that runs in $\mathcal{O}(N\log(N))$ time on a quantum circuit made of $\mathcal{O}(\log(N))$ qubits. The input and output are classical data, and so can be easily accessed. It is robust against noise, and ready for implementation in applications such as machine learning.
We present a collection of optimizers tuned for usage on Noisy Intermediate-Scale Quantum (NISQ) devices. Optimizers have a range of applications in quantum computing, including the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization (QAOA) algorithms. They are also used for calibration tasks, hyperparameter tuning, in machine learning, etc. We analyze the efficiency and effectiveness of different optimizers in a VQE case study. VQE is a hybrid algorithm, with a classical minimizer step driving the next evaluation on the quantum processor. While most results to date conc…
To bridge the gap between limited hardware access and the huge demand for experiments for Noisy Intermediate-Scale Quantum (NISQ) computing system study, a simulator which can capture the modeling of both the quantum processor and its classical control system to realize early-stage evaluation and design space exploration, is naturally invoked but still missing. This paper presents SANQ, a Simulation framework for Architecting NISQ computing system. SANQ consists of two components, 1) an optimized noisy quantum computing (QC) simulator with flexible error modeling accelerated by eliminating red…
Quantum phase estimation is a paradigmatic problem in quantum sensing andmetrology. Here we show that adaptive methods based on classical machinelearning algorithms can be used to enhance the precision of quantum phase estimation when noisy non-entangled qubits are used as sensors. We employ the Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms to this task and we identify the optimal feedback policies which minimize the Holevo variance. We benchmark these schemes with respect to scenarios that include Gaussian and Random Telegraph fluctuations as well as reduced Ram…
We present a continuous monitoring system for intermediate-scale quantum processors that allows extracting estimates of noisy native gate and read-out measurements based on the set of executed quantum circuits and resulting measurement outcomes. In contrast to standard approaches for calibration and benchmarking quantum processors, the executed circuits, which are input to the monitoring system, are assumed to be out of any control. We provide the results of applying our system to the synthetically generated data obtained from a quantum emulator, as well as to the experimental data collected f…
Rapid advancement in the domain of quantum technologies has opened up researchers to the real possibility of experimenting with quantum circuits and simulating small-scale quantum programs. Nevertheless, the quality of currently available qubits and environmental noise poses a challenge in the smooth execution of the quantum circuits. Therefore, efficient design automation flows for mapping a given algorithm to the Noisy Intermediate Scale Quantum (NISQ) computer becomes of utmost importance. State-of-the-art quantum design automation tools are primarily focused on reducing logical depth, gate…
In a recent milestone experiment, Google's processor Sycamore heralded the era of "quantum supremacy" by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the build…
Quantum error mitigation (QEM) is vital for noisy intermediate-scale quantum (NISQ) devices. While most conventional QEM schemes assume discrete gate-based circuits with noise appearing either before or after each gate, the assumptions are inappropriate for describing realistic noise that may have strong gate-dependence and complicated nonlocal effects, and general computing models such as analog quantum simulators. To address these challenges, we first extend the scenario, where each computation process, being either digital or analog, is described by a continuous time evolution. For noise fr…
Quantum computing is moving beyond its early stage and seeking for commercial applications in chemical and biomedical sciences. In the current noisy intermediate-scale quantum computing era, quantum resource is too scarce to support these explorations. Therefore, it is valuable to emulate quantum computing on classical computers for developing quantum algorithms and validating quantum hardware. However, existing simulators mostly suffer from the memory bottleneck so developing the approaches for large-scale quantum chemistry calculations remains challenging. Here we demonstrate a high-performa…
First quantum computers very recently have demonstrated "quantum supremacy" or "quantum advantage": Executing a computation that would have been impossible on a classical machine. Today's quantum computers follow the NISQ paradigm: They exhibit error rates that are much higher than in conventional electronics and have insufficient quantum resources to support powerful error correction protocols. This raises questions which relevant computations are within the reach of NISQ architectures. Several "NISQ-era algorithms" are assumed to match the specifics of such computers; for instance, variation…
Support vector machine algorithms are considered essential for the implementation of automation in a radio access network. Specifically, they are critical in the prediction of the quality of user experience for video streaming based on device and network-level metrics. Quantum SVM is the quantum analogue of the classical SVM algorithm, which utilizes the properties of quantum computers to speed up the algorithm exponentially. In this work, we derive an optimized preprocessing unit for a quantum SVM that allows classifying any two-dimensional datasets that are linearly separable. We further pro…
Quantum computing is on the cusp of reality with Noisy Intermediate-Scale Quantum (NISQ) machines currently under development and testing. Some of the most promising algorithms for these machines are variational algorithms that employ classical optimization coupled with quantum hardware to evaluate the quality of each candidate solution. Recent work used GRadient Descent Pulse Engineering (GRAPE) to translate quantum programs into highly optimized machine control pulses, resulting in a significant reduction in the execution time of programs. This is critical, as quantum machines can barely sup…
The computation of interaction energies on noisy intermediate-scale quantum (NISQ) computers appears to be challenging with straightforward application of existing quantum algorithms. For example, use of the standard supermolecular method with the variational quantum eigensolver (VQE) would require extremely precise resolution of the total energies of the fragments to provide for accurate subtraction to the interaction energy. Here we present a symmetry-adapted perturbation theory (SAPT) method that may provide interaction energies with high quantum resource efficiency. Of particular note, we …
Variational algorithms are a promising paradigm for utilizing near-term quantum devices for modeling electronic states of molecular systems. However, previous bounds on the measurement time required have suggested that the application of these techniques to larger molecules might be infeasible. We present a measurement strategy based on a low rank factorization of the two-electron integral tensor. Our approach provides a cubic reduction in term groupings over prior state-of-the-art and enables measurement times three orders of magnitude smaller than those suggested by commonly referenced bound…
In order to understand the bounds of utilization of the Grover's search algorithm for the large unstructured data in presence of the quantum computer noise, we undertake a series of simulations by inflicting various types of noise, modelled by the IBM QISKit. We apply three forms of Grover's algorithms: (1) the standard one, with 4-10 qubits, (2) recently published modified Grover's algorithm, set to reduce the circuit depth, and (3) the algorithms in (1) and (2) with multi-control Toffoli's modified by addition of an ancilla qubit. Based on these simulations, we find the upper bound of noise …
In this work, we present an efficient rank-compression approach for the classical simulation of Kraus decoherence channels in noisy quantum circuits. The approximation is achieved through iterative compression of the density matrix based on its leading eigenbasis during each simulation step without the need to store, manipulate, or diagonalize the full matrix. We implement this algorithm in an in-house simulator, and show that the low rank algorithm speeds up simulations by more than two orders of magnitude over an existing implementation of full rank simulator, and with negligible error in th…
The reconstruction of trajectories of charged particles is a key computational challenge for current and future collider experiments. Considering the rapid progress in quantum computing, it is crucial to explore its potential for this and other problems in high-energy physics. The problem can be formulated as a quadratic unconstrained binary optimization (QUBO) and solved using the variational quantum eigensolver (VQE) algorithm. In this work the effects of dividing the QUBO into smaller sub-QUBOs that fit on the hardware available currently or in the near term are assessed. Then, the performa…
Quantum computers are expected to help us to achieve accurate simulation of the dynamics of many-body quantum systems. However, the limitations of current NISQ devices prevents us from realising this goal today. Recently an algorithm for performing quantum simulations called quantum assisted simulator has been proposed that promises realization on current experimental devices. In this work, we extend the quantum assisted simulator to simulate the dynamics of a class of time-dependent Hamiltonians. We show that the quantum assisted simulator is easier to implement as well as can realize multi-q…
Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；University of Toronto（多伦多大学）；Imperial College London（伦敦帝国理工学院）；Boehringer（勃林格）
A universal fault-tolerant quantum computer that can solve efficiently problems such as integer factorization and unstructured database search requires millions of qubits with low error rates and long coherence times. While the experimental advancement towards realizing such devices will potentially take decades of research, noisy intermediate-scale quantum (NISQ) computers already exist. These computers are composed of hundreds of noisy qubits, i.e. qubits that are not error-corrected, and therefore perform imperfect operations in a limited coherence time. In the search for quantum advantage …
The study and prediction of chemical reactivity is one of the most important application areas of molecular quantum chemistry. Large-scale, fully error-tolerant quantum computers could provide exact or near-exact solutions to the underlying electronic structure problem with exponentially less effort than a classical computer thus enabling highly accurate predictions for comparably large molecular systems. In the nearer future, however, only "noisy" devices with a limited number of qubits that are subject to decoherence will be available. For such near-term quantum computers the hybrid quantum-…
Hybrid quantum-classical algorithms are central to much of the current research in quantum computing, particularly when considering the noisy intermediate-scale quantum (NISQ) era, with a number of experimental demonstrations having already been performed. In this perspective, we discuss in a very broad sense what it means for an algorithm to be hybrid quantum-classical. We first explore this concept very directly, by building a definition based on previous work in abstraction/representation theory, arguing that what makes an algorithm hybrid is not directly how it is run (or how many classica…
Decoherence and gate errors severely limit the capabilities of state-of-the-art quantum computers. This work introduces a strategy for reference-state error mitigation (REM) of quantum chemistry that can be straightforwardly implemented on current and near-term devices. REM can be applied alongside existing mitigation procedures, while requiring minimal post-processing and only one or no additional measurements. The approach is agnostic to the underlying quantum mechanical ansatz and is designed for the variational quantum eigensolver (VQE). Two orders-of-magnitude improvement in the computati…
Accurate quantum chemistry simulations remain challenging on classical computers for problems of industrially relevant sizes and there is reason for hope that quantum computing may help push the boundaries of what is technically feasible. While variational quantum eigensolver (VQE) algorithms may already turn noisy intermediate scale quantum (NISQ) devices into useful machines, one has to make all efforts to use the scarce quantum resources as efficiently as possible. We combine the so-called seniority-zero, or paired-electron, approximation of computational quantum chemistry with techniques f…
Determining Hamiltonian ground states and energies is a challenging task with many possible approaches on quantum computers. While variational quantum eigensolvers are popular approaches for near term hardware, adiabatic state preparation is an alternative that does not require noisy optimization of parameters. Beyond adiabatic schedules, QAOA is an important method for optimization problems. In this work we modify QAOA to apply to finding ground states of molecules and empirically evaluate the modified algorithm on several molecules. This modification applies physical insights used in classic…
Crosstalk is a major source of noise in Noisy Intermediate-Scale Quantum (NISQ) systems and is a fundamental challenge for hardware design. When multiple instructions are executed in parallel, crosstalk between the instructions can corrupt the quantum state and lead to incorrect program execution. Our goal is to mitigate the application impact of crosstalk noise through software techniques. This requires (i) accurate characterization of hardware crosstalk, and (ii) intelligent instruction scheduling to serialize the affected operations. Since crosstalk characterization is computationally expen…
