#qaoa

[mysteriousquantumphysics]

Cutting Quantum Circuits into Pieces - why and how?

Even though quantum computing is a promising and huge field, it is still at an early development stage. We know algorithms with clear advantage towards classical algorithms such as Grover's or Shor's - however, we are far away from implementing those algorithms on real devices for e.g. breaking state of the art RSA encriptions.

Today's Possibilities of Quantum Computing

Thus, part of current research is to make use of the kind of quantum computers which are available today: Noisy Intermediate-Scale Quantum (NISQ) devices. They are far away from ideal quantum computers since they provide only a limited number of qubits, have faulty gate implementations and measurements and the quantum states decohere rather fast [1]. As a result, algorithms which require large depth circuits cannot be realistically implemented nowadays. Instead, it is advisable to find out what can be done with the currently available NISQ devices. Good candidates are variational quantum algorithms (VQA) in which one uses both quantum and classical methods: One constructs a parametrized quantum circuit whose parameters are optimized by a classical optimizer (e.g. COBYLA). To those methods belong for instance the variational quantum eigensolver (VQE) which can be used to find the ground state energy of a Hamiltonian (a problem which is in general often tackled without quantum computing, i.e. classical computing with tensor network approaches). Another method is solving QUBO problems with the quantum approximate optimization algorithm (QAOA). These are promising ideas, but one should note that it is not sure yet whether we can obtain quantum advantage with them or not [2].

Cutting Quantum Circuits

So far, we have learned that current quantum devices are faulty, hence still far away from fault-tolerant quantum computers. Thus, it is preferable to make quantum circuits of the above mentioned VQAs smaller somehow. Imagine the case in which you want to use the ibm_cairo system with 27 quibts, but the problem you want to solve requires 50 qubits - what can you do? One prominent idea is to cut the circuit of your algorithm into pieces (in this case, bipartitioning it). How can this be done? As you can imagine, such a task requires sophisticated methods to simulate the quantum behaviour of the large circuit even though one has fewer qubits available. Let's briefly look on how this can be done.

Wire Cutting v.s. Gate Cutting

There are different ideas about where to place the cut. In some situations it might be advisable to cut a complicated gate [3, 4]. The more illustrative way is to cut one or more wires of a circuit by implementing a certain decomposition of an identity onto the wire(s) to be cut [5, 6]. In general, such a decomposition looks like

L is the space of linear operators on the d-dimensional complex vector space. How should this be understood? For example in [6] they apply a special case of this identity equation; in a run of the circuit only one of these terms (one channel) is applied at a time. This already indicates that cutting requires running the circuit multiple times in order to simulate the identity. This makes sense intuitively, since making a cut somewhere in a circuit makes it necessary to perform a measurement. As a result, some of the entanglement / quantum properties of the circuit are lost. To compensate this, one has to artifically simulate this quantum behaviour by sampling (running the circuit more often). This so-called sampling overhead can be proven to be

This can be derived with the help of defining an unbiased estimator and applying Hoeffding's inequality. A detailed derivation (which holds for general operators, not only for the identity) can be found in appendix E of [3]. The exact sampling cost depends on the explicit decomposition one wants to apply.

Closing remarks

Up to my knowledge, those circuit cutting schemes only work efficiently for special cases. Often, the cost depends on the size of the cut, i.e. how many wires are cut. Additionally, the original circuit should be able to be partitioned reasonably. In the title picture you can see a mock circuit with five qubits. You can see that on the left side of the cut, there are gates which act on the first three (1,2,3) qubits only, while on the right side they only act on qubits 3,4 and 5. Hence, the cut should be placed on the overlap on both parts, i.e. on the middle qubit (3). The cut size is only one in this case, but in useful applications the cut size might be much larger. Since the cost often depends on the dimension of the cut qubits, the cost increases exponentially in the cut size (since the Hilbert space dimension grows as 2^k for the number of cuts k).

Thus, we see that circuit cutting can be very powerful in special problem instances, in which it can e.g. reduce the required qubits roughly by half - this helps making circuits shallower and smaller. However, there are lots of limitation given by the set of suitable problem instances and the sampling overhead.

--- References

[1] Marvin Bechtold, Johanna Barzen, Frank Leymann, Alexander Mandl, Julian Obst, Felix Truger, Benjamin Weder. Investigating the effect of circuit cutting in QAOA for the MaxCut problem on NISQ devices. 2023. arXiv:2302.01792

[2] M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, Patrick J. Coles. Variational Quantum Algorithms. 2021. arXiv:2012.09265

[3] Christian Ufrecht, Maniraman Periyasamy, Sebastian Rietsch, Daniel D. Scherer, Axel Plinge, Christopher Mutschler. Cutting multi-control quantum gates with ZX calculus. 2023. arXiv:2302.00387

[4] Kosuke Mitarai, Keisuke Fujii. Constructing a virtual two-qubit gate by sampling single-qubit operations. 2019. arXiv:1909.07534

[5] Tianyi Peng, Aram Harrow, Maris Ozols, Xiaodi Wu. Simulating Large Quantum Circuits on a Small Quantum Computer. 2019. arXiv:1904.00102

[6] Angus Lowe, Matija Medvidović, Anthony Hayes, Lee J. O'Riordan, Thomas R. Bromley, Juan Miguel Arrazola, Nathan Killoran. Fast quantum circuit cutting with randomized measurements. 2022. arXiv:2207.14734

#mysteriousquantumphysics #physics #quantum physics #quantum computing #quantum circuit #education #women in science #science #science studyblr #quantum science #physicsblr #circuit cutting #qaoa #vqa #vqe #ibm

[roamnook]

NEW STUDY REVEALS 75% OF AMERICANS STRUGGLE WITH FINANCIAL LITERACY. Learn more about the shocking statistics and what you can do to improve your financial knowledge. Check out the full report now.

Welcome to the RoamNook blog! We aim to provide you with the most cutting-edge information, backed by concrete data and hard facts. In this article, we will dive deep into various technical, professional, and scientific concepts to bring you new information and insights. So let's get started!

The Fascinating World of Quantum Computing

Quantum computing, a revolutionary field in computer science, is gaining momentum and generating great excitement among researchers, scientists, and technology enthusiasts. With the potential to solve complex problems that are practically impossible for classical computers, quantum computing holds the key to unlocking new discoveries and advancements in various domains.

Before we delve into the practical applications of quantum computing, let's understand some fundamental concepts and terminology:

1. Quantum Bits (Qubits)

In classical computers, data is stored and manipulated using bits, which can represent either a 0 or a 1. In quantum computing, qubits are the fundamental units of information. Unlike classical bits, qubits can exist in multiple states simultaneously, thanks to a phenomenon called superposition.

Superposition allows qubits to be in a state that represents both 0 and 1 at the same time, exponentially increasing the computational power of quantum computers. This feature opens up a whole new world of possibilities and applications.

2. Qubit Entanglement

Another fascinating characteristic of qubits is entanglement. When qubits become entangled, the state of one qubit becomes linked or correlated to the state of another qubit, regardless of the distance between them. This phenomenon enables quantum computers to perform parallel computations and solve complex problems more efficiently.

3. Quantum Gates

Similar to classical logic gates that manipulate bits, quantum gates manipulate qubits to perform operations. Quantum gates are crucial for performing quantum computations, and they help in creating superpositions, entanglements, and transformations of qubit states.

4. Quantum Algorithms

With the foundation of qubits, entanglement, and quantum gates in place, researchers have developed various quantum algorithms that can solve problems exponentially faster than classical algorithms. Some prominent quantum algorithms include Shor's algorithm for prime factorization, Grover's algorithm for searching databases, and the Quantum Approximate Optimization Algorithm (QAOA) for optimization problems.

Now that we have covered the basics, let's explore the real-world applications of quantum computing:

1. Drug Discovery and Material Design

One of the most promising applications of quantum computing is in the field of drug discovery and material design. The computational power of quantum computers can accelerate the process of simulating and analyzing complex chemical reactions, enabling scientists to discover new drugs and materials with desired properties.

By utilizing quantum algorithms like the Variational Quantum Eigensolver (VQE) and the Quantum Monte Carlo (QMC) method, researchers can accurately model molecular behavior and predict their properties. This breakthrough can potentially revolutionize the healthcare industry by accelerating the development of new drugs and therapies.

2. Optimization and Logistics

Optimization problems are prevalent in various domains, including logistics, finance, and supply chain management. Quantum computing has the potential to greatly enhance optimization algorithms, allowing businesses to optimize routes, schedules, and resource allocation more efficiently.

With quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA), companies can solve complex optimization problems in near real-time. This capability can have a significant impact on industries such as transportation, manufacturing, and finance, where even small improvements in optimization can lead to substantial cost savings and increased efficiency.

3. Cryptography and Security

Cryptography is at the heart of modern communication systems, ensuring the security and privacy of sensitive data. However, as classical computers continue to advance, conventional cryptographic techniques are at risk of being compromised by quantum computers in the future.

Quantum computing offers a potential solution to this problem. Quantum cryptography, based on the principles of quantum mechanics, provides a new level of security by leveraging quantum properties like entanglement and the Heisenberg uncertainty principle.

Quantum key distribution (QKD) is one of the most well-known applications of quantum cryptography, which ensures provable secure communication channels. With the advent of quantum computers, quantum-resistant cryptographic algorithms are being developed to secure data in a post-quantum computing era.

4. Machine Learning and Data Analysis

As the volume of data continues to grow exponentially, classical machine learning algorithms struggle to handle complex datasets. Quantum machine learning (QML) aims to leverage the unique properties of quantum computing to accelerate and improve machine learning tasks.

Quantum computers can process and analyze massive amounts of data simultaneously, allowing for faster training and inference of machine learning models. Quantum algorithms like the Quantum Support Vector Machine (QSVM) and Quantum Neural Networks (QNN) have shown promising results in solving classification and optimization problems.

Furthermore, quantum computing can also enhance data analysis techniques, enabling researchers and data scientists to uncover hidden patterns and gain deeper insights into various domains, including finance, healthcare, and marketing.

Conclusion: Unlocking the Future with RoamNook

Quantum computing represents a paradigm shift in information processing and offers unparalleled computational power to tackle complex problems. The practical applications and potential advancements in various fields are truly awe-inspiring.

At RoamNook, we are passionate about fueling digital growth by helping businesses leverage cutting-edge technologies. Whether you need IT consultation, custom software development, or digital marketing services, our team of experts is ready to assist you in achieving your goals.

Explore our website [https://www.roamnook.com] to learn more about how RoamNook can collaborate with you to stay ahead of the technological curve. Embrace the power of innovation, and together we can unlock a world of possibilities.

Source: https://www.simplilearn.com/tutorials/python-tutorial&sa=U&ved=2ahUKEwjWn6bc-uWFAxUdFVkFHUv7ANUQxfQBegQIARAC&usg=AOvVaw0GzxPvxsUzsZ0uHs82GrFn

[infradapt]

Exploring the Potential of Quantum Computing

Quantum computing is an emerging field that holds the potential to revolutionize various aspects of technology and computation. Unlike classical computers that use bits to store and process information, quantum computers utilize quantum bits, or qubits, which exploit the principles of quantum mechanics. Let’s explore the potential of quantum computing and its impact on various domains.

1. Increased Computing Power

Quantum computing has the potential to dramatically increase computing power beyond the capabilities of classical computers. Quantum computers can solve certain complex problems exponentially faster than classical computers. This could have profound implications for fields such as cryptography, optimization, and simulation, where computations that are currently infeasible could be efficiently performed.

2. Cryptography and Security

Quantum computing has the potential to disrupt modern cryptographic systems. Quantum computers can efficiently factor large numbers, which poses a threat to widely used encryption algorithms such as RSA and ECC. However, quantum-resistant cryptographic algorithms are being developed to withstand attacks from quantum computers. These post-quantum cryptographic systems aim to ensure secure communication and protect sensitive data in a world with quantum computing.

3. Optimization and Machine Learning

Quantum computing can enhance optimization problems by providing faster and more efficient solutions. Optimization is a critical component in various fields, such as logistics, finance, and scheduling. Quantum algorithms, such as the Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing, show promise in solving optimization problems more effectively, enabling businesses to make better decisions and improve efficiency.

Quantum computing can also have an impact on machine learning. Quantum machine learning algorithms and techniques can be used to analyze large datasets, perform pattern recognition, and enhance predictive modeling. Quantum machine learning has the potential to unlock new insights and drive advancements in artificial intelligence.

4. Drug Discovery and Material Science

Quantum computing can revolutionize the fields of drug discovery and material science. Quantum computers can simulate complex molecular interactions and provide insights into the behavior of atoms and molecules. This capability can accelerate the discovery of new drugs, design more efficient catalysts, and optimize materials with desired properties. Quantum simulations can lead to significant advancements in areas such as healthcare, renewable energy, and materials engineering.

5. Financial Modeling and Risk Analysis

Quantum computing has the potential to improve financial modeling and risk analysis. Quantum algorithms can efficiently simulate and analyze complex financial systems, enabling better risk assessment, portfolio optimization, and pricing of derivatives. This can help financial institutions make more informed decisions, manage risks more effectively, and improve overall financial stability.

6. Quantum Communication and Networking

Quantum computing can enable secure and unbreakable quantum communication protocols. Quantum key distribution (QKD) protocols leverage the principles of quantum mechanics to ensure secure communication by detecting any attempt to intercept transmitted information. Quantum networks can provide unprecedented levels of security, ensuring the confidentiality and integrity of data transmission.

7. Scientific Research and Discovery

Quantum computing can greatly impact scientific research and discovery. It can help solve complex problems in fields such as physics, chemistry, biology, and astronomy. Quantum simulations can provide insights into fundamental physical processes, simulate chemical reactions, model biological systems, and aid in the discovery of new materials and compounds.

While quantum computing is still in its early stages, it has the potential to revolutionize various domains. Continued advancements in quantum hardware, algorithms, and error correction techniques will be crucial for unlocking the full potential of quantum computing and its practical applications.

Excited about the potential of quantum computing? Stay updated with the latest developments in quantum computing by visiting reputable research institutions and industry organizations. The future of quantum computing holds immense promise for transforming the way we solve complex problems and shape the future of technology.

https://www.infradapt.com/news/exploring-the-potential-of-quantum-computing/

[quantumlearningforpersonaluse]

量子こんぴゅーたの使い道 最適化系

量子コンピュータはたくさんのパターンを同時に計算して、最後にその中の1パターンの出力を取り出す、といった感じの動きらしいので、大量のパターンから最適な一つを見つける「組合せ最適化問題」というのが得意なのだそうです。

QAOAとか、アニーリングっていうアルゴリズムが使われるのだそうです。QAOAは問題を数式化してそれを細かく分割して計算、アニーリングは量子アニーリングマシンっていう専用のマシンで選択肢を量子ビットに割り当てて収束させていくような感じらしいです。

これらは問題が小さいと古典コンピュータでも解けてしまうそうなので、より大規模な問題で成果を発揮するかもしれません。ある意味良い制約かもしれませんね。

最適化の具体例は、職場のシフトや工場のロボットの制御、仕事のスケジュール、渋滞緩和とかいろいろあるそうです。コンピュータの計算によって、きつきつのスケジュールを組まれたらつらいですね。人間の体力を考慮して、かつ効率の良いスケジュールが自動で組まれたら嬉しいかもです。

-

-

-

参考

-

湊雄一郎

『いちばんやさしい量子コンピューターの教本　人気講師が教える世界が注目する最新テクノロジー「いちばんやさしい教本」シリーズ』

#量子コンピュータ #最適化 #QAOA #アニーリング

[cutecatpics]

Barn kitten still isn't comfortable around humans, so I wrapped her up in a towel and she calmed right down. Cat burritos work, and are super adorable! Source: QAoA on catpictures.

#cats #cute cats #cat #aww

[softwarily]

[massivelyscreechingcycle-blog]

#qaoa

[physics369]

Max-Cut Problem:--- Raju Rai

* Introduction:

Max-cut problem is one of important  graph partition problems, and it is  most difficult combinatorial optimization problem to solve. The main goal of max-cut problem is partition of set of vertices of graph  into two subsets, such that the sum of the weights of the edges having one endpoint in each of the subsets is maximum.  MAX-CUT is an important combinatorial problem and has applications in many fields including VLSI circuit design  and statistical physics, Data clustering that is Machine Learning.

“Protons give an atom its identity, electrons its personality.” ― Bill Bryson, A Short History of Nearly Everything

# QAOA:

The quantum approximate optimization algorithm (QAOA) is a general technique that can be used to find approximate solutions to combinatorial optimization problems, in particular problems that can be cast as searching for an optimal bit-string .

Steps of QAOA:

-  cost Hamiltonian.

-  mixer Hamiltonian.

-  Draw e−iγHCe−iγHC and e−iαHM.

-  Choose a parameter n≥1n≥1 and draw circuit.

- Prepare the initial state.

-  Measurement.

“Not only does God play dice but... he sometimes throws them where they cannot be seen.” ― Stephen Hawking

Note:  QAOA is the specification of cost and mixer Hamiltonians.

THANK YOU:

[sciencespies]

Scientists just simulated quantum technology on classical computing hardware

https://sciencespies.com/tech/scientists-just-simulated-quantum-technology-on-classical-computing-hardware/

Scientists just simulated quantum technology on classical computing hardware

Lurking in the background of the quest for true quantum supremacy hangs an awkward possibility – hyper-fast number crunching tasks based on quantum trickery might just be a load of hype.

Now, a pair of physicists from École Polytechnique Fédérale de Lausanne (EPFL) in Switzerland and Columbia University in the US have come up with a better way to judge the potential of near-term quantum devices – by simulating the quantum mechanics they rely upon on more traditional hardware.

Their study made use of a neural network developed by EPFL’s Giuseppe Carleo and his colleague Matthias Troyer back in 2016, using machine learning to come up with an approximation of a quantum system tasked with running a specific process.

Known as the Quantum Approximate Optimization Algorithm (QAOA), the process identifies optimal solutions to a problem on energy states from a list of possibilities, solutions that should produce the fewest errors when applied.

“There is a lot of interest in understanding what problems can be solved efficiently by a quantum computer, and QAOA is one of the more prominent candidates,” says Carleo.

The QAOA simulation developed by Carleo and Matija Medvidović, a graduate student from Columbia University, mimicked a 54 qubit device – sizeable, but well in line with the latest achievements in quantum tech. 

While it was an approximation of how the algorithm would run on an actual quantum computer, it did a good enough job to serve as the real deal.

Time will tell if physicists of the future will be quickly crunching out ground states in an afternoon of QAOA calculations on a bona fide machine, or take their time using tried-and-true binary code.

Engineers are still making incredible headway in harnessing the spinning wheel of probability trapped in quantum boxes. Whether current innovations will ever be enough to overcome the biggest hurdles in this generation’s attempt at quantum technology is the pressing question.

At the core of every quantum processor are units of calculation called qubits. Each represents a wave of probability, one without a single defined state but is robustly captured by a relatively straight-forward equation.

Link together enough qubits – what’s known as entanglement – and that equation becomes increasingly more complex.

As the linked qubits rise in number, from dozens to scores to thousands, the kinds of calculations its waves can represent will leave anything we can manage using classical bits of binary code in the dust.

But the whole process is like weaving a lace rug from spiderweb: Every wave is a breath away from entangling with its environment, resulting in catastrophic errors. While we can reduce the risk of such mistakes, there’s no easy way right now to eliminate them altogether.

However, we might be able to live with the errors if there’s a simple way to compensate for them. For now, the anticipated quantum speedup risks being a mirage physicists are desperately chasing.

“But the barrier of ‘quantum speedup’ is all but rigid and it is being continuously reshaped by new research, also thanks to the progress in the development of more efficient classical algorithms,” says Carleo.

As tempting as it might be to use simulations as a way to argue classical computing retains an advantage over quantum machines, Carleo and Medvidović insist the approximation’s ultimate benefit is to establish benchmarks in what could be achieved in the current era of newly emerging, imperfect quantum technologies.

Beyond that, who knows? Quantum technology is already enough of a gamble. So far, it’s one that seems to be paying off nicely.

This research was published in Nature Quantum Information.

#Tech

#Tech

[cloudtales]

Local classical MAX-CUT algorithm outperforms $p=2$ QAOA on high-girth regular graphs

Local classical MAX-CUT algorithm outperforms $p=2$ QAOA on high-girth regular graphs

Quantum 5, 437 (2021). https://doi.org/10.22331/q-2021-04-20-437 The $p$-stage Quantum Approximate Optimization Algorithm (QAOA$_p$) is a promising approach for combinatorial optimization on noisy intermediate-scale quantum (NISQ) devices, but its theoretical behavior is not well understood beyond $p=1$. We analyze QAOA$_2$ for the $textit{maximum cut problem}$ (MAX-CUT), deriving a…

View On WordPress

[cutecatpics]

He doesn't fit in the hammock so he spills over the edge Source: QAoA on catpictures.

#cats #cute cats #cat #aww

[rajamanickam]

Tiny Quantum Computer solves real optimisation problem | QAOA to solve T...

#computing #quantum #futurology

[solplparty]

[M/V] Grim Hilde(그림하일드) - Alone(혼자) https://youtu.be/t3gHzB-QAoA [M/V] Grim Hilde(그림하일드) - Alone(혼자) Grim Hilde's New Single Album [Hide N Seek] Now Available on : ▶Bugs : https://music.bugs.co.kr/album/4013630 SUPER SOUND, BUGS! http://www.bugs.co.kr SUPER SOUND Bugs!

#Bugs #벅스 #유통사 #YouTube

[basicpharma]

[milocamj]

Entropica releases QAOA package for Rigetti's Quantum Cloud Service - Quantaneo, the Quantum Computing Source http://dlvr.it/RGb4mh http://dlvr.it/RGb4mh

[mevaporat]

Meridianville, Alabama Consumer Credit Counseling Service | [phone]

Meridianville, Alabama Free Consumer Credit Counseling Service call [phone] Credit Repair, Bankruptcy Counseling, Foreclosure Prevention, Student Loan Debt Consolidation, Wage Garnishment and Vehicle Repossession solutions, Mortgage Loan Modification, and Debt Settlement through chapter 13. Meridianville, Alabama Credit counseling [phone] starts with the parent and may include intermediaries later in life empowered by the individual debtor to act on their behalf to negotiate with creditors and resolve debt that is beyond a debtor’s ability to pay. Credit counseling is a generic name and is not a brand name owned or controlled by any agency or company.

Meridianville, Alabama Consumer credit counseling services [phone] are provided by attorneys, accountants, finance and tax professionals, for-profit, and non-profit credit counseling companies. Regulations on credit counseling and credit counseling agencies varies by country and sometimes within regions of the countries themselves. In Meridianville, Alabama individuals filing Chapter 13 bankruptcy are required to receive counseling from a designated credit counseling agency.

https://endlessvideo.com/watch?v=Li3m1-qAOas

  https://youtu.be/zp5nk4acaDo

      https://www.youtube.com/channel/UCkA8O5tUotNOwTbBikDQ1ag/about

    https://www.youtube.com/channel/UCIwT5lGtnEb6ck6wpXeDGEQ/about

  https://youtu.be/zp5nk4acaDo

    copyright © 2016 Privacy Policyzp5nk4acaDo

from Meridianville, Alabama Consumer Credit Counseling Service | [phone] via Meridianville, Alabama Consumer Credit Counseling Service | [phone] September 18, 2019 at 06:03AM Copyright © September 18, 2019 at 06:03AM

#Meridianville #Alabama Consumer Credit Counseling Service | [phone]