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Encoding discrete variables into qubits is an important task for applying quantum computing to combinatorial optimisation problems, both under the context of quantum annealing and gate model algorithms such as QAOA. Traditionally discrete variables are encoded by implementing a &#39;one hot&#39; constraint on a set of qubits. I demonstrate that a superior method to encode such variables is to encode them as a domain wall on an Ising chain as discussed in [1]. I discuss how this method works and present numerical evidence for it&#39;s superior performance. As an extreme example, in some cases for quantum annealing using a domain wall encoding instead of one hot can have as much impact as completely re-engineering the hardware. I also discuss the cases in which unary encodings (one hot or domain wall) may be preferable to binary encodings or vice-versa. I further discuss how this encoding can be used in quantum simulation of field theories as discussed in [2]

[1] Chancellor N 2019 Quantum Sci. Technol. 4 045004 https://doi.org/10.1088/2058-9565/ab33c2

[2] Abel S, Chancellor N, Spannowsky M https://arxiv.org/abs/2003.07374 (see also: arXiv:2006.06003)

Quantum 2020

A domain wall encoding for quantum annealing and QAOA

variable encoding

quantum optimisation

quantum simulation

The Institute of Physics and IOP Publishing, in partnership with the Chinese Physical Society (CPS) and the University of Science and Technology of China (USTC) are proud to have brought together the international quantum science community online for this inaugural conference.


Early career and leading researchers from universities, industry and government worldwide came together to share, learn and collaborate on the latest research and emerging areas of high interest across quantum science and technology. The broad themes covered by Quantum 2020 included:

Quantum communication;
Quantum computing and quantum simulation;
Quantum sensing, metrology and imaging;
Quantum information theory, software and algorithms;
Quantum foundations;
Quantum technology in industry.
The four-day event featured talks from world-renowned scientists, interactive poster sessions and two exciting panel discussions on the themes of Quantum Technology in Industry and Quantum Technology Programmes Around the World.


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The Institute of Physics and IOP Publishing, in partnership with the Chinese Physical Society (CPS) and the University of Science and Technology of China (USTC) are proud to have brought together the international quantum science community online for this inaugural conference.

Early career and leading researchers from universities, industry and government worldwide came together to share, learn and collaborate on the latest research and emerging areas of high interest across quantum science and technology. 

Encoding discrete variables into qubits is an important task for applying quantum computing to combinatorial optimisation problems, both under the context of quantum annealing and gate model algorithms such as QAOA. Traditionally discrete variables are encoded by implementing a 'one hot' constraint on a set of qubits. I demonstrate that a superior method to encode such variables is to encode them as a domain wall on an Ising chain as discussed in [1]. I discuss how this method works and present numerical evidence for it's superior performance. As an extreme example, in some cases for quantum annealing using a domain wall encoding instead of one hot can have as much impact as completely re-engineering the hardware. I also discuss the cases in which unary encodings (one hot or domain wall) may be preferable to binary encodings or vice-versa. I further discuss how this encoding can be used in quantum simulation of field theories as discussed in [2]

[1] Chancellor N 2019 Quantum Sci. Technol. 4 045004 https://doi.org/10.1088/2058-9565/ab33c2

[2] Abel S, Chancellor N, Spannowsky M https://arxiv.org/abs/2003.07374 (see also: arXiv:2006.06003)

poster

Well-developed theoretical tools exist to analyse how quantum dynamics can solve computational problems by varying Hamiltonians slowly (adiabatically). However, relatively few tools exist for the opposite limit of rapid quenches, used in quantum annealing and quantum walks. We develop a theoretical understanding and several practical tools for this regime. By analysing various energy expectation values, we show that monotonic quenches will yield a better result on average than random guessing. By characterising local dynamics, we identify cases where rapid quenches will lead to a substantially improved numerical scaling. We then use these tools to develop heuristics for choosing control parameters.

The poster is based on the work in Callison et al, NJP 21 123022 (2019) and Callison et al, arXiv:2007.11599(2020). It offers an introduction to the framework of continuous-time quantum computing, and an explanation of where rapid quenches sit within it. Along with some useful examples, an outline of the theoretical understanding and tools we have developed are presented. Finally, some examples are shown to illustrate how to use the heuristic methods these tools provide; in particular, we show how to choose quantum walk hopping rates and rapid quench schedules.

An energetic perspective on rapid quenches in quantum annealing

The past few years have seen numerous attempts to leverage the power of deep networks to solve the quantum many-body problem, and neural representations of many body wavefunctions have proliferated. These prior applications of neural networks to quantum mechanics have sought representations of the wavefunction. However, there are several mathematically equivalent formulations of quantum mechanics, and hence alternative routes for the application of machine learning. 


We demonstrate how reinforcement learning may be used to solve problems in quantum mechanics via the path integral representation. In our work we provide a novel neural approach to many-body quantum mechanics that leverages optimal control to approximate the Feynman–Kac path measure. The drift of the quantum stochastic control process is chosen to match the distribution of paths in the Feynman–Kac (FK) representation of the solution of the imaginary time Schrodinger equation. This provides a variational principle that can be used for reinforcement learning of a neural representation and a new alternative to earlier deep learning approaches that start from the Schrodinger picture. Further, our approach learns an optimal importance sampler for the FK trajectories, providing a drop-in replacement for path integral Monte Carlo.


Reinforcement Learning for Quantum System

Atom-light interface is at the core of quantum metrology and quantum information science. Associated noises during interaction processes are always inevitable and adverse. In this paper, we perform the stimulated Raman scattering (SRS) in a hot 87Rb vapor cell and demonstrate the reduction of related noises originated from mode mismatch via optimizing the temporal waveform of input seed. By using the seed with optimized mode, the intensity fluctuation of the signal field generated in atom-light interaction is decreased by 4.3 dB. And furthermore, the fluctuation of intensity difference between signal and atomic spin wave is reduced by 3.1 dB. Such temporal mode cleaning method can be applied to improve the precision of atom interferometry using SRS and should be helpful for quantum information processing based on atom-light correlated system.


Reducing the mode mismatch noises in atom-light interactions via optimization of the temporal waveform


Quantum entanglement is an essential resource in many quantum applications including quantum networks. It serves as a foundation for quantum key distribution (QKD) protocols and provides the advantage of device-independent security without using trusted nodes. Since quantum entanglement will be fundamental to any future quantum networking scenarios, the distribution mechanism of entangled photons pairs is a critical and emerging issue in quantum networks. To address this challenge, we present a wavelengths / virtual links assignment method for quantum networks using Planning Domain Definition Language (PDDL) which is a standard encoding language for classical planning tasks. The PDDL model that describes the actions to solve the given problem is used by the Fast-Forward (FF) planner, which is a forward-chaining heuristic state-space planner that relax the main task into a simpler task to obtain a heuristic estimate of the solution. We employ the FF planner using our planning domain model for wavelength/path assignment while observing weight factors, including the link priority, the Secret Key Rate (SKR), and Quantum Bit Error Rate (QBER), as planning metrics that determine the quality of the virtual links.

Wavelengths assignment of entangled photons pairs for quantum networks

A powerful control method in experimental quantum computing is the use of spin echoes, employed to select a desired term in the system’s internal Hamiltonian, while refocusing others. Here, we address a more general problem, describing a method to not only turn on and off particular interactions but also to rescale their strengths so that we can generate any desired effective internal Hamiltonian. We propose an algorithm based on linear programming for achieving time-optimal rescaling solutions in fully coupled systems of tens of qubits, which can be modified to obtain near-time-optimal solutions for rescaling systems with hundreds of qubits. Further, we propose an analytic method based on graph colouring to address the rescaling problem in systems with any number of qubits, however, with only nearest/next-nearest neighbour couplings.



[1] Rescaling interactions for quantum control, G. Bhole, T. Tsunoda, P. J. Leek, and J. A. Jones, Phys. Rev. Appl. 13, 034002 (2020).

[2] Efficient Hamiltonian programming in qubit arrays with nearest-neighbour couplings, T. Tsunoda, G. Bhole, S. A. Jones, J. A. Jones, and P. J. Leek, Phys. Rev. A 102 032405 (2020).

Efficient Hamiltonian programming in qubit arrays with nearest-neighbour couplings

Quantum Computation and Quantum versions of classical algorithms holds a great potential to provide ultra fast and absolutely effficient solutions to various problems as compared to what classical computers could provide. Hence, myriad of Quantum based applications could be deployed to various sectors such as finance, medicine and healthcare, defence, agriculture, communications, retail, supply chain management, banking, traffic control, weather prediction, cyber security and education etc. These sectors are already facing one on other constraints regarding their optimization and efficiency. Though various classical artificial intelligence machine learning algorithms and models are providing relevant solutions, but when it comes to big and complex data often accompanied by errors and noise then these classical algorithms become slow and inefficient. This also leads to lower accuracy and precision of their models. When supplemented or used in a hybrid form with Quantum programs, it provides great pursuits to overcome all those hurdles encountered by the classical programmes and algorithms. Here, different quantum based methodologies has been browsed to provide a broad spectrum understanding of Quantum based application in various sectors

The industries would be benefited such as clustering overall aspects of Optimization which includes Supply Chain Management which classical computing is at its limit trying to solve large scale problems whereas Quantum gates are able to produce all possible solution instantly at a quick pace using entanglement and superposition. Further, Quantum Optimization models will also revolutionize the Financial modelling which on classical computers uses inefficient Monte-carlo simulations for advanced portfolio optimization.In finance it would prove its worth in detecting market instabilities, developing trading strategies, optimising portfolios and asset pricing.In healthcare Quantum Computing in likely to bring absolute enhancement from discovering new drugs to decreasing the side effects. Generating targeted cancer drug therapies, Optimizing radiotherapy treatments.Further in ML and AI Quantum Computing applications range from classifying unstructured data, finding anomalies, training neural networks etc.

Also, a Quantum Computing could be extremely be worthy in field of Astronomy. As Astronomy is truly at the data extensive stage. Petabytes of data are being accumulated each night through various observation programmes and they are highly complex. Quantum computation can tap into these issues and provide extremely useful explanation and solution.

Overall perspective of quantum computing optimization gives never before solutions and outcomes.


Quantum Computing and Applied Quantum Optimization Models to accelerate every sector of economy as compared to its classical counterpart

The Hamiltonian of a quantum system often have some symmetry in various fields of physics, e.g., high energy physics and condensed matter physics, and it is demanding to compute the spectrum of the Hamiltonian that resides in each symmetry sector. For this purpose, we can utilize the variational quantum eigensolver (VQE), which is a promising algorithm to compute eigenstates and their energies of a given quantum system that can be performed on a near-term quantum computer, to compute energy eigenstates possessing such symmetry by adding a penalty term in its cost function. 
The systematic analysis of such penalty terms, however, has been lacking and a heuristic way to set the penalty is adopted so far. In this work, we investigate two types of penalty terms for the VQE that have been previously proposed. We discover a convenient formula to set the penalty for one of the two types, which rigorously guarantees the resulting eigenstates by the VQE have desired symmetry. Meanwhile, we prove that the other type of penalty does not work well in a rigorous sense and gives completely wrong results in some cases. We also provide numerical simulations to validate our analysis.
Our results lay the theoretical foundation for the VQE with the penalty that applies to general quantum systems, and contribute to further application of a near-term quantum computer.

Penalty methods for variational quantum eigensolver

We show that for the two widely used configurations of the double-$\Lambda$ atom-light coupling scheme, one where the control fields are applied in the same $\Lambda$-subsystem and another where they applied in different $\Lambda$-subsystems, the forward propagation of the probe and signal fields is described by the same set of equations. We then use optimal control theory to find the spatially-dependent optimal control fields which maximize the conversion efficiency from the probe to the signal field, for a given optical density. The present work is expected to find application in the implementation of efficient frequency and orbital angular momentum conversion devices for quantum information processing, as well as to be useful to many other applications using the double-$\Lambda$ atom-light coupling scheme.

Optimal conversion efficiency in the forward double-Λ atom-light coupling system

We investigate whether a trade-off relation between the diagonal elements of the mean square error matrix exists for the two-parameter unitary models with mutually commuting generators. We show that the error trade-off relation which exists in our models of a finite dimension system is a generic phenomenon in the sense that it occurs with a finite volume in the spate space. We analyze a qutrit system to show that there can be an error trade-off relation given by the SLD and RLD Cramer-Rao bounds that intersect each other. First, we analyze an example of the reference state showing the non-trivial trade-off relation numerically, and find that its eigenvalues must be in a certain range to exhibit the trade-off relation. For another example, one-parameter family of reference states, we analytically show that the non-trivial relation always exists and that the range where the trade-off relation exists is up to about a half of the possible range.

Error trade-off relations for two-parameter unitary model with commuting generators

Stimulated Raman adiabatic passage (STIRAP) is one of the most successful quantum control methods for coherent population transfer between two energy levels of a quantum system. A major advantage of STIRAP is its robustness against moderate variations of experimental parameters, while a drawback is that adiabatic transfer requires long times, leading to reduced efficiency when undesirable interactions with the environment are present leading to dephasing and dissipation. The efficiency of STIRAP can be increased when it is combined with shortcuts to adiabaticity techniques. One successful protocol that can be implemented is the superadiabatic STIRAP (SA-STIRAP), where the prototype Λ-type three-level system is driven by three laser pulses, forming a closed-loop configuration [1]. In this work we assess the efficiency of STIRAP and SA-STIRAP, in the presence of noise and dissipation. For the dissipation, we use the typical decay from the excited state, while for noise we use classical Ornstein-Ulhenbeck noise processes with exponential correlation functions leading to dephasing [2]. The performance of the two control protocols are compared for different system parameters.
1. L. Giannelli and E. Arimondo, Phys. Rev. A 89, 033419 (2014).
2. K. Blekos, D. Stefanatos, and E. Paspalakis, Phys. Rev. A 102, 023715 (2020).

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A domain wall encoding for quantum annealing and QAOA

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