scholarly journals Variational Quantum Computation of Excited States

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 156 ◽  
Author(s):  
Oscar Higgott ◽  
Daochen Wang ◽  
Stephen Brierley
Keyword(s):  
Excited State ◽  
Excited States ◽  
Quantum Algorithms ◽  
Reaction Rates ◽  
Mitigation Strategies ◽  
Quantum Computers ◽  
Error Mitigation ◽  
Near Term ◽  
Ground State Energies ◽  
High Depth

The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap estimation can be used to deflate eigenstates once they are found, enabling the calculation of excited state energies and their degeneracies. We propose an implementation that requires the same number of qubits as VQE and at most twice the circuit depth. Our method is robust to control errors, is compatible with error-mitigation strategies and can be implemented on near-term quantum computers.

scholarly journals Quantum chemistry as a benchmark for near-term quantum computers

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Alexander J. McCaskey ◽  
Zachary P. Parks ◽  
Jacek Jakowski ◽  
Shirley V. Moore ◽  
Titus D. Morris ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Mitigation Strategies ◽  
Quantum Computers ◽  
Molecular Systems ◽  
Active Space ◽  
Space Reduction ◽  
Error Mitigation ◽  
Near Term ◽  
Reduced Density ◽  
Specific Error

AbstractWe 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 using 4 of the available qubits 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 reduction, and error mitigation strategies. Our results demonstrate the characteristically high noise level present in near-term superconducting hardware, but provide a relevant baseline for future improvement of the underlying hardware, and a means for comparison across near-term hardware types. We also demonstrate how to reduce the noise in post processing with specific error mitigation techniques. Particularly, the adaptation of McWeeny purification of noisy density matrices dramatically improves accuracy of quantum computations, which, along with adjustable active space, significantly extends the range of accessible molecular systems. We demonstrate that for specific benchmark settings and a selected range of problems, the accuracy metric can reach chemical accuracy when computing over the cloud on certain quantum computers.

scholarly journals Coreset Clustering on Small Quantum Computers

Electronics ◽  
2021 ◽  
Vol 10 (14) ◽  
pp. 1690
Author(s):  
Teague Tomesh ◽  
Pranav Gokhale ◽  
Eric R. Anschuetz ◽  
Frederic T. Chong
Keyword(s):  
Quantum Algorithms ◽  
Quantum Computers ◽  
Data Sets ◽  
New Paradigm ◽  
Data Set ◽  
Small Quantum ◽  
Natural Data ◽  
Near Term ◽  
Classical Computing ◽  
Quantum Speedup

Many quantum algorithms for machine learning require access to classical data in superposition. However, for many natural data sets and algorithms, the overhead required to load the data set in superposition can erase any potential quantum speedup over classical algorithms. Recent work by Harrow introduces a new paradigm in hybrid quantum-classical computing to address this issue, relying on coresets to minimize the data loading overhead of quantum algorithms. We investigated using this paradigm to perform k-means clustering on near-term quantum computers, by casting it as a QAOA optimization instance over a small coreset. We used numerical simulations to compare the performance of this approach to classical k-means clustering. We were able to find data sets with which coresets work well relative to random sampling and where QAOA could potentially outperform standard k-means on a coreset. However, finding data sets where both coresets and QAOA work well—which is necessary for a quantum advantage over k-means on the entire data set—appears to be challenging.

scholarly journals Application of Quantum Computing to Biochemical Systems: A Look to the Future

2020 ◽  
Vol 8 ◽  
Author(s):  
Hai-Ping Cheng ◽  
Erik Deumens ◽  
James K. Freericks ◽  
Chenglong Li ◽  
Beverly A. Sanders
Keyword(s):  
Quantum Computing ◽  
Physical System ◽  
Quantum Computer ◽  
Quantum Algorithms ◽  
Active Regions ◽  
Quantum Computers ◽  
The Future ◽  
Biochemical Systems ◽  
Near Term ◽  
Different Levels

Chemistry is considered as one of the more promising applications to science of near-term quantum computing. Recent work in transitioning classical algorithms to a quantum computer has led to great strides in improving quantum algorithms and illustrating their quantum advantage. Because of the limitations of near-term quantum computers, the most effective strategies split the work over classical and quantum computers. There is a proven set of methods in computational chemistry and materials physics that has used this same idea of splitting a complex physical system into parts that are treated at different levels of theory to obtain solutions for the complete physical system for which a brute force solution with a single method is not feasible. These methods are variously known as embedding, multi-scale, and fragment techniques and methods. We review these methods and then propose the embedding approach as a method for describing complex biochemical systems, with the parts not only treated with different levels of theory, but computed with hybrid classical and quantum algorithms. Such strategies are critical if one wants to expand the focus to biochemical molecules that contain active regions that cannot be properly explained with traditional algorithms on classical computers. While we do not solve this problem here, we provide an overview of where the field is going to enable such problems to be tackled in the future.

scholarly journals Algorithmic Error Mitigation Scheme for Current Quantum Processors

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 492
Author(s):  
Philippe Suchsland ◽  
Francesco Tacchino ◽  
Mark H. Fischer ◽  
Titus Neupert ◽  
Panagiotis Kl. Barkoutsos ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Ground State ◽  
State Of The Art ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Lanczos Method ◽  
Error Mitigation ◽  
Near Term ◽  
The Impact ◽  
Different Sources

We present a hardware agnostic error mitigation algorithm for near term quantum processors inspired by the classical Lanczos method. This technique can reduce the impact of different sources of noise at the sole cost of an increase in the number of measurements to be performed on the target quantum circuit, without additional experimental overhead. We demonstrate through numerical simulations and experiments on IBM Quantum hardware that the proposed scheme significantly increases the accuracy of cost functions evaluations within the framework of variational quantum algorithms, thus leading to improved ground-state calculations for quantum chemistry and physics problems beyond state-of-the-art results.

scholarly journals Multi-exponential error extrapolation and combining error mitigation techniques for NISQ applications

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Zhenyu Cai
Keyword(s):  
Estimation Accuracy ◽  
Quantum Computers ◽  
Practical Application ◽  
Combined Method ◽  
Error Mitigation ◽  
Sampling Cost ◽  
Mitigation Techniques ◽  
Near Term ◽  
Quantum Error ◽  
Error Count

AbstractNoise in quantum hardware remains the biggest roadblock for the implementation of quantum computers. To fight the noise in the practical application of near-term quantum computers, instead of relying on quantum error correction which requires large qubit overhead, we turn to quantum error mitigation, in which we make use of extra measurements. Error extrapolation is an error mitigation technique that has been successfully implemented experimentally. Numerical simulation and heuristic arguments have indicated that exponential curves are effective for extrapolation in the large circuit limit with an expected circuit error count around unity. In this Article, we extend this to multi-exponential error extrapolation and provide more rigorous proof for its effectiveness under Pauli noise. This is further validated via our numerical simulations, showing orders of magnitude improvements in the estimation accuracy over single-exponential extrapolation. Moreover, we develop methods to combine error extrapolation with two other error mitigation techniques: quasi-probability and symmetry verification, through exploiting features of these individual techniques. As shown in our simulation, our combined method can achieve low estimation bias with a sampling cost multiple times smaller than quasi-probability while without needing to be able to adjust the hardware error rate as required in canonical error extrapolation.

scholarly journals Optimizing quantum heuristics with meta-learning

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Max Wilson ◽  
Rachel Stromswold ◽  
Filip Wudarski ◽  
Stuart Hadfield ◽  
Norm M. Tubman ◽  
...  
Keyword(s):  
Quantum Algorithms ◽  
Evolutionary Strategies ◽  
Quantum Computers ◽  
Parameter Setting ◽  
Present Evidence ◽  
Machine Learning Methods ◽  
Meta Learning ◽  
Global Optima ◽  
Near Term ◽  
Important Indication

AbstractVariational quantum algorithms, a class of quantum heuristics, are promising candidates for the demonstration of useful quantum computation. Finding the best way to amplify the performance of these methods on hardware is an important task. Here, we evaluate the optimization of quantum heuristics with an existing class of techniques called “meta-learners.” We compare the performance of a meta-learner to evolutionary strategies, L-BFGS-B and Nelder-Mead approaches, for two quantum heuristics (quantum alternating operator ansatz and variational quantum eigensolver), on three problems, in three simulation environments. We show that the meta-learner comes near to the global optima more frequently than all other optimizers we tested in a noisy parameter setting environment. We also find that the meta-learner is generally more resistant to noise, for example, seeing a smaller reduction in performance in Noisy and Sampling environments, and performs better on average by a “gain” metric than its closest comparable competitor L-BFGS-B. Finally, we present evidence that indicates the meta-learner trained on small problems will generalize to larger problems. These results are an important indication that meta-learning and associated machine learning methods will be integral to the useful application of noisy near-term quantum computers.

scholarly journals Fisher Information in Noisy Intermediate-Scale Quantum Applications

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 539
Author(s):  
Johannes Jakob Meyer
Keyword(s):  
Fisher Information ◽  
Quantum Algorithms ◽  
Quantum Fisher Information ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Quantum Devices ◽  
Intermediate Scale ◽  
Quantum Sensing ◽  
Near Term

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 recently. Hoping to stimulate more such applications, this article aims to further popularize classical and quantum Fisher information as useful tools for near-term applications beyond quantum sensing. We start with a tutorial that builds an intuitive understanding of classical and quantum Fisher information and outlines how both quantities can be calculated on near-term devices. We also elucidate their relationship and how they are influenced by noise processes. Next, we give an overview of the core results of the quantum sensing literature and proceed to a comprehensive review of recent applications in variational quantum algorithms and quantum machine learning.

scholarly journals Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 257 ◽  
Author(s):  
Filip B. Maciejewski ◽  
Zoltán Zimborás ◽  
Michał Oszmaniec
Keyword(s):  
Quantum Algorithms ◽  
Probability Distributions ◽  
Post Processing ◽  
Measurement Device ◽  
Quantum Devices ◽  
Quantum Process ◽  
Error Mitigation ◽  
Process Tomography ◽  
State Tomography ◽  
Near Term

We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-term quantum devices, we characterize measurements implemented in IBM's and Rigetti's quantum processors. We find that for these devices, based on superconducting transmon qubits, classical noise is indeed the dominant source of readout errors. Moreover, we analyze the influence of the presence of coherent errors and finite statistics on the performance of our error-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we observe a significant improvement of the results of a number of single- and two-qubit tasks including Quantum State Tomography (QST), Quantum Process Tomography (QPT), the implementation of non-projective measurements, and certain quantum algorithms (Grover's search and the Bernstein-Vazirani algorithm). Finally, we present results showing improvement for the implementation of certain probability distributions in the case of five qubits.

scholarly journals On the depth overhead incurred when running quantum algorithms on near-term quantum computers with limited qubit connectivity

2020 ◽  
Vol 20 (9&10) ◽  
pp. 787-806 ◽  
Author(s):  
Steven Herbert
Keyword(s):  
Quantum Algorithms ◽  
Quantum Circuit ◽  
The Other ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Interaction Graph ◽  
Finite Degree ◽  
Near Term

This paper addresses the problem of finding the depth overhead that will be incurred when running quantum circuits on near-term quantum computers. Specifically, it is envisaged that near-term quantum computers will have low qubit connectivity: each qubit will only be able to interact with a subset of the other qubits, a reality typically represented by a qubit interaction graph in which a vertex represents a qubit and an edge represents a possible direct 2-qubit interaction (gate). Thus the depth overhead is unavoidably incurred by introducing swap gates into the quantum circuit to enable general qubit interactions. This paper proves that there exist quantum circuits where a depth overhead in Omega(\log n) must necessarily be incurred when running quantum circuits with n qubits on quantum computers whose qubit interaction graph has finite degree, but that such a logarithmic depth overhead is achievable. The latter is shown by the construction of a 4-regular qubit interaction graph and associated compilation algorithm that can execute any quantum circuit with only a logarithmic depth overhead.

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