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July 2022: Computing Electronic Correlation Energies using Linear Depth Quantum Circuits

Computing Electronic Correlation Energies using Linear Depth Quantum Circuits
Chong Hian Chee, Adrian M. Mak, Daniel Leykam, Dimitris G. Angelakis
arXiv:2207.03949

Efficient computation of molecular energies is an exciting application of quantum computers, but current noisy intermediate-scale quantum (NISQ) devices can only execute shallow circuits, limiting existing quantum algorithms to small molecules. Here we demonstrate a variational NISQ-friendly algorithm for computing electronic correlation energies perturbatively, trading deep circuits in exchange for more shallow circuits with depth linear in the number of qubits. We tested the algorithm on several small molecules, both with classical simulations including noise models and on cloud quantum processors, showing that it not only reproduces the equilibrium molecular energies but it also captures the perturbative electronic correlation effects at longer bond distances. As fidelities of quantum processors continue to improve our algorithm will enable the study of larger molecules compared to existing approaches with higher-order polynomial circuit depth.

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June 2022: Topological data analysis and machine learning

Topological data analysis and machine learning
Daniel Leykam, Dimitris G. Angelakis
arXiv:2206.15075

Topological data analysis refers to approaches for systematically and reliably computing abstract “shapes” of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest among physicists. We present a concise yet (we hope) comprehensive review of applications of topological data analysis to physics and machine learning problems in physics including the detection of phase transitions. We finish with a preview of anticipated directions for future research.

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July 2021: Fock State-enhanced Expressivity of Quantum Machine Learning Models

Fock State-enhanced Expressivity of Quantum Machine Learning Models
Beng Yee Gan, Daniel Leykam, Dimitris G. Angelakis
EPJ Quantum Technology 9 (1), 16

The data-embedding process is one of the bottlenecks of quantum machine learning, potentially negating any quantum speedups. In light of this, more effective data-encoding strategies are necessary. We propose a photonic-based bosonic data-encoding scheme that embeds classical data points using fewer encoding layers and circumventing the need for nonlinear optical components by mapping the data points into the high-dimensional Fock space. The expressive power of the circuit can be controlled via the number of input photons. Our work shed some light on the unique advantages offers by quantum photonics on the expressive power of quantum machine learning models. By leveraging the photon-number dependent expressive power, we propose three different noisy intermediate-scale quantum-compatible binary classification methods with different scaling of required resources suitable for different supervised classification tasks.

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Jan 2021: Photonic band structure design using persistent homology

Photonic band structure design using persistent homology
D. Leykam, D. G. Angelakis
APL Photonics 6, 030802 (2021) 

The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to characterize physical systems such as spin models and multiqubit entangled states. Here we propose persistent homology as a tool for characterizing and optimizing band structures of periodic photonic media. Using the honeycomb photonic lattice Haldane model as an example, we show how persistent homology is able to reliably classify a variety of band structures falling outside the usual paradigms of topological band theory, including “moat band” and multi-valley dispersion relations, and thereby control the properties of quantum emitters embedded in the lattice. Our method is promising for the automated design of more complex systems such as photonic crystals and Moire superlattices.

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December 2020: Quantum supremacy and quantum phase transitions

Quantum supremacy and quantum phase transitions
S. Thanasilp, J. Tangpanitanon, M. A. Lemonde, N. Dangniam, D. G. Angelakis
Phys. Rev. B 103, 165132

Demonstrating the ability of existing quantum platforms to perform certain computational tasks intractable to classical computers represents a cornerstone in quantum computing. Despite the growing number of such proposed “quantum supreme” tasks, it remains an important challenge to identify their direct applications. In this work, we describe how the approach proposed in Ref. [arXiv:2002.11946] for demonstrating quantum supremacy in generic driven analog many-body systems, such as those found in cold atom and ion setups, can be extended to explore dynamical quantum phase transitions.

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July 2020: Qubit efficient algorithms for binary optimization problems

Qubit efficient algorithms for binary optimization problems
B. Tan, M. A. Lemonde, S. Thanasilp, J. Tangpanitanon, D. G. Angelakis
Quantum 5, 454

Doing binary optimization problems either via quantum annealing or QAOA require as many qubits as in the classical variables. Realistic quadratic optimization problems (QUBO) usually entail 10.000 classical variables which means current approaches using NISQ devices are very far from achieving anything of real applications. In this work, we proposed and analyzed a set of novel variational quantum algorithms for QUBO where n classical variables can be implemented on O(log n) number of qubits. Our encoding scheme allows for a systematic increase in correlations among the classical variables captured by a given quantum state by progressively increasing the number of qubits. We apply this minimal encoding to find approximate solutions of a general problem instances comprised of 64 classical variables using 7 qubits. Next, we show how two-body correlations can be incorporated in the variational quantum state and how it can improve the quality of the approximate solutions. We give examples by solving a 42-variable Max-Cut problem using only 8 qubits where we exploit the specific topology of the problem. We analyze whether these cases can be optimized efficiently given the limited resources available in state-of-the-art quantum platforms. Lastly, we present the general framework for extending the expressibility of the probability distribution to any multi-body correlations.

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May 2020: Expressibility and trainability of parameterized analog quantum systems for machine learning applications

Expressibility and trainability of parameterized analog quantum systems for machine learning applications
J. Tangpanitanon, S. Thanasilp, M. A. Lemonde, N. Dangniam, D. G. Angelakis
published in Physical Review Research 

In this work we analyze the trainability of analog quantum processors and applications in machine learning. We investigate how the interplay between external driving and disorder can dictate the trainability and expressibility of quantum many body systems and apply it to solve a generative modelling problem. We show that if the system thermalizes, the training fails at the expense of the a large expressibility, while the opposite happens when the system enters the many-body localized (MBL) phase.Our approach can be implemented with a variety of available quantum platforms including cold ions, atoms and superconducting circuits

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March 2020: Quantum supremacy in driven quantum many-body systems

Quantum supremacy in driven quantum many-body systems
J. Tangpanitanon, S. Thanasilp, M. A. Lemonde, N. Dangniam, D. G. Angelakis
arxiv.org/2002.11946 

A crucial milestone in the field of quantum simulation and computation is to demonstrate that a quantum device can compute certain tasks that are impossible to reproduce by a classical computer with any reasonable resources. Such a demonstration is referred to as quantum supremacy. One of the most important questions is to identify setups that exhibit quantum supremacy and can be implemented with current quantum technology. The two standard candidates are boson sampling and random quantum circuits. Here, we show that quantum supremacy can be obtained in generic periodically-driven quantum many-body systems. Our analysis is based on the eigenstate thermalization hypothesis and strongly-held conjectures in complexity theory. To illustrate our work, We give examples of simple disordered Ising chains driven by global magnetic fields and Bose-Hubbard chains with modulated hoppings. Our proposal opens the way for a large class of quantum platforms to demonstrate and benchmark quantum supremacy.

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July 2019: Quantum state transfer via acoustic edge states in a 2D optomechanical array

Marc-Antoine Lemonde, Vittorio Peano, Peter Rabl, Dimitris G. Angelakis
New J. Phys. 21 (11), 113030 (2020) [PDF]

We propose a novel hybrid platform where solid-state spin qubits are coupled to the acoustic modes of a two-dimensional array of optomechanical nano cavities. Previous studies of coupled optomechanical cavities have shown that in the presence of strong optical driving fields, the interplay between the photon-phonon interaction and their respective inter-cavity hopping allows the generation of topological phases of sound and light. In particular, the mechanical modes can enter a Chern insulator phase where the time-reversal symmetry is broken. In this context, we exploit the robust acoustic edge states as a chiral phononic waveguide and describe a state transfer protocol between spin qubits located in distant cavities. We analyze the performance of this protocol as a function of the relevant system parameters and show that a high-fidelity and purely unidirectional quantum state transfer can be implemented under experimentally realistic conditions. As a specific example, we discuss the implementation of such topological quantum networks in diamond based optomechanical crystals where point defects such as silicon-vacancy centers couple to the chiral acoustic channel via strain.

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June 2019: Quantum supremacy with analog quantum processors for material science and machine learning

Quantum supremacy with analog quantum processors for material science and machine learning
J. Tangpanitanon, S. Thanasilp, M. A. Lemonde, D. G. Angelakis
arxiv.org/1906.03860 

Quantum supremacy is the ability of quantum processors to outperform classical computers at certain tasks. In digital random quantum circuit approaches for supremacy, the output distribution produced is described by the Porter-Thomas (PT) distribution. In this regime, the system uniformly explores its entire Hilbert space, which makes simulating such quantum dynamics with classical computational resources impossible for large systems. However, the latter has no direct application so far in solving a specific problem. In this work, we show that the same sampling complexity can be achieved from driven analog quantum processors, with less stringent requirements for coherence and control. More importantly, we discuss how to apply this approach to solve problems in quantum simulations of phases of matter and machine learning. Specifically, we consider a simple quantum spin chain with nearest-neighbor interactions driven by a global magnetic field. We show how quantum supremacy is achieved as a consequence of the thermalization due to the interplay between the disorder and the driven many-body dynamics. We analyze how the achieved PT distribution can be used as an accessible reference distribution to probe the many-body localization (MBL) phase transition. In the second part of our work, we show how our setup can be used for generative modeling machine learning tasks. We propose a novel variational hybrid quantum-classical approach, exploiting the system’s inherent tunable MBL dynamics, to train the device to learn distributions of complex classical data. The performance of our training protocol depends solely on the phase that the quantum system is in, which makes fine-tuning of local parameters not necessary. The protocol is implementable in a range of driven quantum many-body systems, compatible with noisy intermediate-scale quantum devices.