scholarly journals Noise-robust exploration of many-body quantum states on near-term quantum devices

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Johannes Borregaard ◽  
Matthias Christandl ◽  
Daniel Stilck França
Keyword(s):  
Broad Class ◽  
Quantum Algorithms ◽  
Quantum States ◽  
Generation Model ◽  
Many Body ◽  
Quantum Devices ◽  
Near Term ◽  
Network States ◽  
Noise Robust ◽  
Sequential Generation

AbstractWe describe a resource-efficient approach to studying many-body quantum states on noisy, intermediate-scale quantum devices. We employ a sequential generation model that allows us to bound the range of correlations in the resulting many-body quantum states. From this, we characterize situations where the estimation of local observables does not require the preparation of the entire state. Instead smaller patches of the state can be generated from which the observables can be estimated. This can potentially reduce circuit size and number of qubits for the computation of physical properties of the states. Moreover, we show that the effect of noise decreases along the computation. Our results apply to a broad class of widely studied tensor network states and can be directly applied to near-term implementations of variational quantum algorithms.

scholarly journals Neural network operations and Susuki–Trotter evolution of neural network states

2018 ◽  
Vol 16 (08) ◽  
pp. 1840008 ◽  
Author(s):  
Nahuel Freitas ◽  
Giovanna Morigi ◽  
Vedran Dunjko
Keyword(s):  
Neural Network ◽  
Optimization Techniques ◽  
Quantum States ◽  
Stochastic Methods ◽  
Many Body ◽  
Boltzmann Machines ◽  
Quantum Operations ◽  
Model Complex ◽  
Network States ◽  
Hidden Nodes

It was recently proposed to leverage the representational power of artificial neural networks, in particular Restricted Boltzmann Machines, in order to model complex quantum states of many-body systems [G. Carleo and M. Troyer, Science 355(6325) (2017) 602.]. States represented in this way, called Neural Network States (NNSs), were shown to display interesting properties like the ability to efficiently capture long-range quantum correlations. However, identifying an optimal neural network representation of a given state might be challenging, and so far this problem has been addressed with stöchastic optimization techniques. In this work, we explore a different direction. We study how the action of elementary quantum operations modifies NNSs. We parametrize a family of many body quantum operations that can be directly applied to states represented by Unrestricted Boltzmann Machines, by just adding hidden nodes and updating the network parameters. We show that this parametrization contains a set of universal quantum gates, from which it follows that the state prepared by any quantum circuit can be expressed as a Neural Network State with a number of hidden nodes that grows linearly with the number of elementary operations in the circuit. This is a powerful representation theorem (which was recently obtained with different methods) but that is not directly useful, since there is no general and efficient way to extract information from this unrestricted description of quantum states. To circumvent this problem, we propose a step-wise procedure based on the projection of Unrestricted quantum states to Restricted quantum states. In turn, two approximate methods to perform this projection are discussed. In this way, we show that it is in principle possible to approximately optimize or evolve Neural Network States without relying on stochastic methods such as Variational Monte Carlo, which are computationally expensive.

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 Variational Quantum Singular Value Decomposition

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 483
Author(s):  
Xin Wang ◽  
Zhixin Song ◽  
Youle Wang
Keyword(s):  
Singular Value Decomposition ◽  
Variational Principles ◽  
Quantum Algorithms ◽  
Singular Values ◽  
Singular Value ◽  
Quantum Devices ◽  
Singular Vectors ◽  
Fan Theorem ◽  
Near Term ◽  
Value Decomposition

Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although these algorithms are promising, the required quantum subroutines and resources are too costly on near-term quantum devices. In this work, we propose a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantum neural networks (or parameterized quantum circuits) could be trained to learn the singular vectors and output the corresponding singular values. Furthermore, we conduct numerical simulations of VQSVD for random matrices as well as its applications in image compression of handwritten digits. Finally, we discuss the applications of our algorithm in recommendation systems and polar decomposition. Our work explores new avenues for quantum information processing beyond the conventional protocols that only works for Hermitian data, and reveals the capability of matrix decomposition on near-term quantum devices.

scholarly journals Hardware efficient quantum algorithms for vibrational structure calculations

2020 ◽  
Vol 11 (26) ◽  
pp. 6842-6855
Author(s):  
Pauline J. Ollitrault ◽  
Alberto Baiardi ◽  
Markus Reiher ◽  
Ivano Tavernelli
Keyword(s):  
Excited State ◽  
Quantum Algorithms ◽  
Vibrational Structure ◽  
Quantum Devices ◽  
Near Term ◽  
Structure Calculations ◽  
Vibrational Structure Calculations

We introduce a framework for the calculation of ground and excited state energies of bosonic systems suitable for near-term quantum devices and apply it to molecular vibrational anharmonic Hamiltonians.

scholarly journals Near-term quantum algorithms for linear systems of equations with regression loss functions

2021 ◽  
Vol 23 (11) ◽  
pp. 113021
Author(s):  
Hsin-Yuan Huang ◽  
Kishor Bharti ◽  
Patrick Rebentrost
Keyword(s):  
Linear Systems ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Systems Of Equations ◽  
Quantum Devices ◽  
Near Term ◽  
Variational Algorithms ◽  
Core Idea ◽  
Classical Combination ◽  
Linear Systems Of Equations

Abstract Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum resources are not immediately available on near-term quantum devices. In this work, we study near-term quantum algorithms for linear systems of equations, with a focus on the two-norm and Tikhonov regression settings. We investigate the use of variational algorithms and analyze their optimization landscapes. There exist types of linear systems for which variational algorithms designed to avoid barren plateaus, such as properly-initialized imaginary time evolution and adiabatic-inspired optimization, suffer from a different plateau problem. To circumvent this issue, we design near-term algorithms based on a core idea: the classical combination of variational quantum states (CQS). We exhibit several provable guarantees for these algorithms, supported by the representation of the linear system on a so-called ansatz tree. The CQS approach and the ansatz tree also admit the systematic application of heuristic approaches, including a gradient-based search. We have conducted numerical experiments solving linear systems as large as 2300 × 2300 by considering cases where we can simulate the quantum algorithm efficiently on a classical computer. Our methods may provide benefits for solving linear systems within the reach of near-term quantum devices.

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 Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information

Science ◽  
2013 ◽  
Vol 340 (6137) ◽  
pp. 1205-1208 ◽  
Author(s):  
Michael Walter ◽  
Brent Doran ◽  
David Gross ◽  
Matthias Christandl
Keyword(s):  
Quantum Computing ◽  
Single Particle ◽  
Local Information ◽  
Geometric Object ◽  
Quantum States ◽  
Many Body ◽  
Arbitrary Size ◽  
Global Entanglement ◽  
Low Levels ◽  
Essential Resource

Entangled many-body states are an essential resource for quantum computing and interferometry. Determining the type of entanglement present in a system usually requires access to an exponential number of parameters. We show that in the case of pure, multiparticle quantum states, features of the global entanglement can already be extracted from local information alone. This is achieved by associating any given class of entanglement with an entanglement polytope—a geometric object that characterizes the single-particle states compatible with that class. Our results, applicable to systems of arbitrary size and statistics, give rise to local witnesses for global pure-state entanglement and can be generalized to states affected by low levels of noise.

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