Practical verification protocols for analog quantum simulators

AbstractAnalog quantum simulation is expected to be a significant application of near-term quantum devices. Verification of these devices without comparison to known simulation results will be an important task as the system size grows beyond the regime that can be simulated classically. We introduce a set of experimentally-motivated verification protocols for analog quantum simulators, discussing their sensitivity to a variety of error sources and their scalability to larger system sizes. We demonstrate these protocols experimentally using a two-qubit trapped-ion analog quantum simulator and numerically using models of up to five qubits.

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Initialization of quantum simulators by sympathetic cooling

Science Advances ◽

10.1126/sciadv.aaw9268 ◽

2020 ◽

Vol 6 (10) ◽

pp. eaaw9268 ◽

Cited By ~ 1

Author(s):

Meghana Raghunandan ◽

Fabian Wolf ◽

Christian Ospelkaus ◽

Piet O. Schmidt ◽

Hendrik Weimer

Keyword(s):

Energy State ◽

Hamiltonian Dynamics ◽

Many Body ◽

Sympathetic Cooling ◽

Trapped Ion ◽

Physical Chemical ◽

Quantum Simulators ◽

Auxiliary Particle ◽

Quantum Simulator ◽

Chemical And Biological Systems

Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum simulator has already been demonstrated in many experiments, the problem of initialization of quantum simulators to a suitable quantum state has hitherto remained mostly unsolved. Here, we show that already a single dissipatively driven auxiliary particle can efficiently prepare the quantum simulator in a low-energy state of largely arbitrary Hamiltonians. We demonstrate the scalability of our approach and show that it is robust against unwanted sources of decoherence. While our initialization protocol is largely independent of the physical realization of the simulation device, we provide an implementation example for a trapped ion quantum simulator.

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Digital quantum simulation, Trotter errors, and quantum chaos of the kicked top

npj Quantum Information ◽

10.1038/s41534-019-0192-5 ◽

2019 ◽

Vol 5 (1) ◽

Cited By ~ 12

Author(s):

Lukas M. Sieberer ◽

Tobias Olsacher ◽

Andreas Elben ◽

Markus Heyl ◽

Philipp Hauke ◽

...

Keyword(s):

Time Evolution ◽

Quantum Chaos ◽

Threshold Value ◽

Quantum Simulation ◽

Spin Systems ◽

Step Size ◽

Sharp Threshold ◽

Trapped Ion ◽

Quantum Simulators ◽

Atomic Spins

Abstract This work aims at giving Trotter errors in digital quantum simulation (DQS) of collective spin systems an interpretation in terms of quantum chaos of the kicked top. In particular, for DQS of such systems, regular dynamics of the kicked top ensures convergence of the Trotterized time evolution, while chaos in the top, which sets in above a sharp threshold value of the Trotter step size, corresponds to the proliferation of Trotter errors. We show the possibility to analyze this phenomenology in a wide variety of experimental realizations of the kicked top, ranging from single atomic spins to trapped-ion quantum simulators which implement DQS of all-to-all interacting spin-1/2 systems. These platforms thus enable in-depth studies of Trotter errors and their relation to signatures of quantum chaos, including the growth of out-of-time-ordered correlators.

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Efficient variational simulation of non-trivial quantum states

SciPost Physics ◽

10.21468/scipostphys.6.3.029 ◽

2019 ◽

Vol 6 (3) ◽

Cited By ~ 17

Author(s):

Wen Wei Ho ◽

Timothy H. Hsieh

Keyword(s):

Transverse Field ◽

System Size ◽

Quantum States ◽

Quantum Simulator ◽

Near Term ◽

The One ◽

Transverse Field Ising Model ◽

Classical Computer ◽

Model Phase ◽

Ordered State

We provide an efficient and general route for preparing non-trivial quantum states that are not adiabatically connected to unentangled product states. Our approach is a hybrid quantum-classical variational protocol that incorporates a feedback loop between a quantum simulator and a classical computer, and is experimentally realizable on near-term quantum devices of synthetic quantum systems. We find explicit protocols which prepare with perfect fidelities (i) the Greenberger-Horne-Zeilinger (GHZ) state, (ii) a quantum critical state, and (iii) a topologically ordered state, with \bm{L}𝐋 variational parameters and physical runtimes \bm{T}𝐓 that scale linearly with the system size \bm{L}𝐋. We furthermore conjecture and support numerically that our protocol can prepare, with perfect fidelity and similar operational costs, the ground state of every point in the one dimensional transverse field Ising model phase diagram. Besides being practically useful, our results also illustrate the utility of such variational Ansätze as good descriptions of non-trivial states of matter.

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Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

Proceedings of the National Academy of Sciences ◽

10.1073/pnas.2006373117 ◽

2020 ◽

Vol 117 (41) ◽

pp. 25396-25401 ◽

Cited By ~ 3

Author(s):

Guido Pagano ◽

Aniruddha Bapat ◽

Patrick Becker ◽

Katherine S. Collins ◽

Arinjoy De ◽

...

Keyword(s):

Ising Model ◽

Long Range ◽

Ground State Energy ◽

Ground State ◽

State Energy ◽

System Size ◽

Single Shot ◽

Trapped Ion ◽

Approximate Optimization ◽

Quantum Simulator

Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.

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Circuit Design for K-coloring Problem and its Implementation on Near-term Quantum Devices

2020 IEEE International Symposium on Smart Electronic Systems (iSES) (Formerly iNiS) ◽

10.1109/ises50453.2020.00015 ◽

2020 ◽

Author(s):

Amit Saha ◽

Debasri Saha ◽

Amlan Chakrabarti

Keyword(s):

Circuit Design ◽

Quantum Devices ◽

Coloring Problem ◽

Near Term

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Classifying data using near-term quantum devices

International Journal of Quantum Information ◽

10.1142/s0219749918400014 ◽

2018 ◽

Vol 16 (08) ◽

pp. 1840001

Author(s):

Johannes Bausch

Keyword(s):

Neural Network ◽

Classification Task ◽

Training Procedure ◽

Quantum Annealing ◽

Quantum Neural Network ◽

Training Scheme ◽

Trained Classifier ◽

Coupling Strengths ◽

Quantum Simulator ◽

Near Term

The goal of this work is to define a notion of a “quantum neural network” to classify data, which exploits the low-energy spectrum of a local Hamiltonian. As a concrete application, we build a binary classifier, train it on some actual data and then test its performance on a simple classification task. More specifically, we use Microsoft’s quantum simulator, LIQ[Formula: see text][Formula: see text], to construct local Hamiltonians that can encode trained classifier functions in their ground space, and which can be probed by measuring the overlap with test states corresponding to the data to be classified. To obtain such a classifier Hamiltonian, we further propose a training scheme based on quantum annealing which is completely closed-off to the environment and which does not depend on external measurements until the very end, avoiding unnecessary decoherence during the annealing procedure. For a network of size [Formula: see text], the trained network can be stored as a list of [Formula: see text] coupling strengths. We address the question of which interactions are most suitable for a given classification task, and develop a qubit-saving optimization for the training procedure on a simulated annealing device. Furthermore, a small neural network to classify colors into red versus blue is trained and tested, and benchmarked against the annealing parameters.

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A quantum convolutional neural network on NISQ devices

AAPPS Bulletin ◽

10.1007/s43673-021-00030-3 ◽

2022 ◽

Vol 32 (1) ◽

Author(s):

ShiJie Wei ◽

YanHu Chen ◽

ZengRong Zhou ◽

GuiLu Long

Keyword(s):

Neural Network ◽

Machine Learning ◽

Convolutional Neural Network ◽

Quantum Circuits ◽

Image Smoothing ◽

Quantum Devices ◽

Computing Complexity ◽

Machine Learning Model ◽

Mask Size ◽

Near Term

AbstractQuantum machine learning is one of the most promising applications of quantum computing in the noisy intermediate-scale quantum (NISQ) era. We propose a quantum convolutional neural network(QCNN) inspired by convolutional neural networks (CNN), which greatly reduces the computing complexity compared with its classical counterparts, with O((log2M)6) basic gates and O(m2+e) variational parameters, where M is the input data size, m is the filter mask size, and e is the number of parameters in a Hamiltonian. Our model is robust to certain noise for image recognition tasks and the parameters are independent on the input sizes, making it friendly to near-term quantum devices. We demonstrate QCNN with two explicit examples. First, QCNN is applied to image processing, and numerical simulation of three types of spatial filtering, image smoothing, sharpening, and edge detection is performed. Secondly, we demonstrate QCNN in recognizing image, namely, the recognition of handwritten numbers. Compared with previous work, this machine learning model can provide implementable quantum circuits that accurately corresponds to a specific classical convolutional kernel. It provides an efficient avenue to transform CNN to QCNN directly and opens up the prospect of exploiting quantum power to process information in the era of big data.

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Quantum Chemistry Calculations on a Trapped-Ion Quantum Simulator

Physical Review X ◽

10.1103/physrevx.8.031022 ◽

2018 ◽

Vol 8 (3) ◽

Cited By ~ 102

Author(s):

Cornelius Hempel ◽

Christine Maier ◽

Jonathan Romero ◽

Jarrod McClean ◽

Thomas Monz ◽

...

Keyword(s):

Quantum Chemistry ◽

Trapped Ion ◽

Quantum Chemistry Calculations ◽

Quantum Simulator

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Molecular docking with Gaussian Boson Sampling

Science Advances ◽

10.1126/sciadv.aax1950 ◽

2020 ◽

Vol 6 (23) ◽

pp. eaax1950 ◽

Cited By ~ 4

Author(s):

Leonardo Banchi ◽

Mark Fingerhuth ◽

Tomas Babej ◽

Christopher Ing ◽

Juan Miguel Arrazola

Keyword(s):

Molecular Docking ◽

Tumor Necrosis ◽

Practical Interest ◽

Binding Mode ◽

Quantum Devices ◽

Immune System Diseases ◽

Classical Systems ◽

Near Term ◽

Factor Α ◽

Necrosis Factor

Gaussian Boson Samplers are photonic quantum devices with the potential to perform intractable tasks for classical systems. As with other near-term quantum technologies, an outstanding challenge is to identify specific problems of practical interest where these devices can prove useful. Here, we show that Gaussian Boson Samplers can be used to predict molecular docking configurations, a central problem for pharmaceutical drug design. We develop an approach where the problem is reduced to finding the maximum weighted clique in a graph, and show that Gaussian Boson Samplers can be programmed to sample large-weight cliques, i.e., stable docking configurations, with high probability, even with photon losses. We also describe how outputs from the device can be used to enhance the performance of classical algorithms. To benchmark our approach, we predict the binding mode of a ligand to the tumor necrosis factor-α converting enzyme, a target linked to immune system diseases and cancer.

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