Posted on Leave a comment

June 2023: Qubit efficient quantum algorithms for the vehicle routing problem on quantum computers of the NISQ era

Qubit efficient quantum algorithms for the vehicle routing problem on quantum computers of the NISQ era
Ioannis D. Leonidas, Alexander Dukakis, Benjamin Tan, Dimitris G. Angelakis
arXiv:2306.08507

The vehicle routing problem with time windows (VRPTW) is a classic optimization problem that arises in many different areas, such as logistics and transportation. The goal of the VRPTW is to find the shortest possible route for a fleet of vehicles to visit a set of destinations. In recent years, there has been growing interest in using variational quantum algorithms (VQAs), to find approximate solutions to problems that can be formulated as quadratic unconstrained binary optimization (QUBO) problems. In this work, we formulate the VRPTW as a QUBO and apply a quantum variational approach to the VRPTW using our earlier suggested encoding scheme described in [1] to reduce drastically the number of qubits required. We evaluate our approach on a set of VRPTW instances ranging from 11 to 3964 routes constructed with data provided by researchers from ExxonMobil. We compare the solutions obtained with standard full encoding approaches for which the max problems size possible in NISQ era are of the order of 20-30 routes. We run our algorithms in simulators as well as cloud quantum hardware provided by IBMQ, AWS (Rigetti) and IonQ and benchmark our results against each other as well as on the simulators. We show that our approach can find approximate solutions to the VRPTW that are comparable to the solutions found by quantum algorithms using the full encoding. Our results suggest that our unique encoding approach, provides a promising approach to drastically reducing the number of qubits required to find decent approximate solutions for industry-based optimization problems.

Posted on Leave a comment

Jan 2023: Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer

Shallow quantum circuits for efficient preparation of Slater determinants and correlated states on a quantum computer
Chong Hian Chee, Daniel Leykam, Adrian M. Mak, Dimitris G. Angelakis
C. H. Chee et al., Phys. Rev. A 108, 022416 (2023)

Preparing quantum ansatzes is a necessary prerequisite in many quantum algorithms for quantum chemistry such as the variational quantum eigensolver. Widely-used ansatzes including the Slater determinants and Unitary Coupled Cluster, employ parameterized fermionic excitation gates, with the latter resulting in deep quantum circuits that scale at least polynomially with the system size N. Here we propose an alternate paradigm for fermionic ansatz state preparation inspired by data-loading circuits methods developed for quantum machine learning. Our approach provides a shallower, yet scalable O(dlog2^N) two-qubit gate depth preparation of d-fermion Slater determinants and correlated states, a subexponential improvement in gate depth over existing approaches. This is particularly important as it can be implemented on planar architectures without qubit swapping overheads, thereby enabling the use of larger basis sets needed for high-precision quantum chemistry studies on near-term quantum devices.

Posted on Leave a comment

October 2022: Efficiently Extracting Multi-Point Correlations of a Floquet Thermalized System

Efficiently Extracting Multi-Point Correlations of a Floquet Thermalized System
Yong-Guang Zheng, Wei-Yong Zhang, Ying-Chao Shen, An Luo, Ying Liu, Ming-Gen He, Hao-Ran Zhang, Wan Lin, Han-Yi Wang, Zi-Hang Zhu, Ming-Cheng Chen, Chao-Yang Lu, Supanut Thanasilp, Dimitris G. Angelakis, Zhen-Sheng Yuan, Jian-Wei Pan
arXiv:2210.08556

Nonequilibrium dynamics of many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analogue quantum simulators. It is proposed to be classically intractable to sample driven thermalized many-body states of Bose-Hubbard systems, and further extract multi-point correlations for characterizing quantum phases. Here, leveraging dedicated precise manipulations and number-resolved detection through a quantum gas microscope, we implement and sample a 32-site driven Hubbard chain in the thermalized phase. Multi-point correlations of up to 14th-order extracted from experimental samples offer clear distinctions between the thermalized and many-body-localized phases. In terms of estimated computational powers, the quantum simulator is comparable to the fastest supercomputer with currently known best algorithms. Our work paves the way towards practical quantum advantage in simulating Floquet dynamics of many-body systems.

Posted on Leave a comment

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, Panagiotis Kl Barkoutsos, Dimitris G. Angelakis
C. H. Chee et al., Quantum Sci. Technol. 9, 025003 (2024)

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.

Posted on Leave a comment

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.

Posted on Leave a comment

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.

Posted on Leave a comment

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.

Posted on Leave a comment

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.

Posted on Leave a comment

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.

Posted on Leave a comment

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