Quantum technology (QT) applies quantum mechanical properties such as quantum entanglement, quantum superposition, and No-cloning theorem to quantum systems such as atoms, ions, electrons, photons, or molecules. Quantum bit is the basic unit of quantum information. Whereas in a classical system, a bit is either in one state or the another. However, quantum qubits can exist in large number of states simultaneously, property called Superposition. Quantum entanglement is a phenomenon where entangled particles can stay connected in the sense that the actions performed on one of the particles affects the other no matter what’s the distance between them. No-cloning theorem tells us that quantum information (qubit) cannot be copied.

Quantum technology has many Quantum applications, one of the major class is Quantum computation and simulation. Quantum computers shall bring power of massive parallel processing, equivalent of supercomputer to a single chip. They can consider different possible solutions to a problem simultaneously, quickly converge on the correct solution without check each possibility individually. This dramatically speed up certain calculations, such as number factoring.

The power of quantum computers depends on the number of qubits and their quality measured by coherence, and gate fidelity. Qubit is very fragile, can be disrupted by things like tiny changes in temperature or very slight vibrations. Coherence measures the time during which quantum information is preserved. The gate fidelity uses distance from ideal gate to decide how noisy a quantum gate is.

We are now in era of Noisy intermediate-scale quantum (NISQ) in which quantum computers are composed of hundreds of noisy qubits that are not error-corrected. They Physical qubits are realized using superconducting Josephson junction qubits and the trapped-ion qubits. Other promising Qubits are Semiconductor based qubits; Topological qubits; and Photonic qubits.

Calculations using these noisy qubits can introduce errors and make long computations impossible. However, these computers still can demonstrate the advantages of quantum computing and various algorithms are being developed in disciplines such as machine learning, quantum chemistry and optimization.

One promising class of problems involves the simulation of quantum systems, with potential applications such as developing materials for batteries, industrial catalysis and nitrogen fixing.

Simulating models of the physical world is instrumental in advancing scientific knowledge and developing technologies. Unfortunately, simulation is not always easy. Many important problems in physics, especially low-temperature physics and many-body physics, remain poorly understood because the underlying quantum mechanics is vastly complex. These also include scientific research areas, from high-energy, nuclear, atomic and condensed matter physics to thermal rate constants and molecular energies in chemistry

Simulation of large quantum systems is a hard task even for today’s supercomputers. One difficulty is that the amount of computer memory needed to store a quantum state grows exponentially with the size of the quantum mechanical system. Conventional computers, including supercomputers, are inadequate for simulating quantum systems with as few as 30 particles.

Better computational tools are needed to understand and rationally design materials whose properties are believed to depend on the collective quantum behavior of hundreds of particles. Quantum simulators provide an alternative route to understanding the properties of these systems.

In 1982, the famous physicist Richard Feynman got an idea about how to overcome the difficulties: A controllable quantum system could be used to study another, less controllable or accessible quantum system. This is called quantum simulation. These simulators create clean realizations of specific systems of interest, which allows precise realizations of their properties. Precise control over and broad tunability of parameters of the system allows the influence of various parameters to be cleanly disentangled.

Quantum simulators can solve problems that are difficult to simulate on classical computers because they directly exploit the quantum properties of real particles. In particular, they exploit a property of quantum mechanics called superposition, wherein a quantum particle is made to be in two distinct states at the same time, for example, aligned and anti-aligned with an external magnetic field. Crucially, simulators also take advantage of a second quantum property called entanglement, allowing the behavior of even physically well-separated particles to be correlated.

Quantum simulators permit the study of quantum systems that are difficult to study in the laboratory and impossible to model with a supercomputer. In this instance, simulators are special-purpose devices designed to provide insight about specific physics problems. Quantum simulators may be contrasted with generally programmable “digital” quantum computers, which would be capable of solving a wider class of quantum problems.

Arguably, the most natural application of quantum computers is to the problem of simulating quantum dynamics. Quantum computers can simulate a wide variety of quantum systems, including fermionic lattice models, quantum chemistry, and quantum field theories. A quantum system of many particles could be simulated by a quantum computer using a number of quantum bits similar to the number of particles in the original system. This has been extended to much larger classes of quantum systems.

In addition to helping to identify new materials and drug substances, quantum simulation promises for example to solve routing and scheduling problems and to be very useful in advancing research in many fields of physics, quantum chemistry, and cosmology.

They have strong potential to address problems of societal importance, ranging from understanding vital chemical processes to enabling the design of new materials with enhanced performance, to solving complex computational problems.

### Quantum Simulators

Quantum computers can be many types. First is Digital quantum computer (also called a gate-level quantum computer), that is universal, programmable computer that can execute all quantum algorithms and have numerous applications. Another type of quantum computer is **quantum simulator** which is a non-programmable quantum circuit and built for single purpose. Quantum simulator is used to reproduce the behavior of other quantum systems that generally are less accessible

Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms. Recent advances in several physical architectures promise a golden age of quantum simulators ranging from highly optimized special-purpose simulators to flexible programmable devices.

Quantum simulation could be implemented using quantum computers (so-called digital simulation), but also with simpler devices, so-called analog simulators, which would be easier to construct. Analog simulators are specifically designed to simulate a certain system or process and therefore have a limited scope of use, while quantum computers can be programmed to take on many types of problems.

In recent years, the field of quantum simulation has been developing rapidly, and there are now a number of different platforms in which quantum systems – such as neutral atoms, ions, superconducting circuits, nuclear spins, and photons – can be experimentally probed for quantum simulation.

The most dominant approaches are two: quantum-phase estimation and quantum variational techniques (VQE). Especially, the latter approach has the highest likelihood of success on NISQ computers. For example, in 2020, Google performed the biggest quantum chemical simulation up to date (of H12 molecule using the VQE).

The algorithms for quantum chemistry simulations are being developed. They can be applied to more complex simulations hand in hand with the number of qubits. Therefore, even in this early stage of quantum computing, there is significant interest from the chemical and pharmaceutical industry. In general, such simulations allow the discovery and design of new drugs, chemicals, and materials. The recent, considered topics are, for instance, high-temperature superconducting, better batteries, protein folding, nitrogen fixation or peptides research.

To overcome the limitations of current quantum computers, scientists at Pacific Northwest National Laboratory (PNNL) are developing simulations that provide a glimpse into how quantum computers work. The simulations will offer them a glimpse of the behavior of quantum systems, like qubits, their quantum states will collapse.

PNNL Computer Scientist Ang Li said, “Testing quantum algorithms on quantum devices is slow and costly. Also, some algorithms are too advanced for current quantum devices. Our quantum simulators can help us look beyond the limitations of existing devices and test algorithms for more sophisticated systems.” Nathan Wiebe, a PNNL joint appointee from the University of Toronto, said, “Noisy quantum circuits produce errors in calculations. The more qubits needed for a calculation, the more error-prone it is.”

“This work provides a cheaper and faster way to perform quantum error correction. It potentially brings us closer to demonstrating a computationally useful example of a quantum simulation for quantum field theory on near-term quantum hardware.” Physicist Ben Loer and his colleagues look to the environment to manage external noise sources, whereas Wiebe works to limit noise by developing algorithms for error correction.

Quantum simulators could prove useful for a number of practical problems, and both neutral atom groups have launched spinoff businesses: Pasqal for the Paris team, and QuEra Computing in Cambridge, which earlier this month announced that it raised $17 million from investors, including the Japanese communications and e-commerce giant Rakuten.

Longer term, the companies hope to turn their simulators into universal quantum computers capable of handling any quantum calculation. That would require complete control over individual atoms to use them as full-blown qubits. While not as mature in this regard as the superconducting quantum computers from Google and IBM — which recently announced a 127-qubit universal quantum processor — neutral atoms may yet catch up. “Sometimes I start to get skeptical,” said Greiner. “Then at the same time I look into our lab, and I see that even with a handful of atoms we can do things that no supercomputer can calculate.”

The paper, published in *Nature*, explores near- and medium-term possibilities for quantum simulation on analogue and digital platforms to help evaluate the potential of this area. It has been co-written by researchers from Strathclyde, the Max Planck Institute of Quantum Optics, Ludwig Maximilians University in Munich, Munich Center for Quantum Science and Technology, the University of Innsbruck, the Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, and Microsoft Corporation.

Professor Andrew Daley, of Strathclyde’s Department of Physics, is lead author of the paper. He said: “There has been a great deal of exciting progress in analogue and digital quantum simulation in recent years, and quantum simulation is one of the most promising fields of quantum information processing. It is already quite mature, both in terms of algorithm development, and in the availability of significantly advanced analogue quantum simulation experiments internationally.

“In computing history, classical analogue and digital computing co-existed for more than half a century, with a gradual transition towards digital computing, and we expect the same thing to happen with the emergence of quantum simulation.

“As a next step along the development of this technology, it is now important to discuss ‘practical quantum advantage,’ the point at which quantum devices will solve problems of practical interest that are not tractable for traditional supercomputers.

“Many of the most promising short-term applications of quantum computers fall under the umbrella of quantum simulation: modelling the quantum properties of microscopic particles that are directly relevant to understanding modern materials science, high-energy physics and quantum chemistry.

“Quantum simulation should be possible in the future on fault-tolerant digital quantum computers with more flexibility and precision, but it can also already be done today for specific models through special-purpose analogue quantum simulators. This happens in an analogous way to the study of aerodynamics, which can be conducted either in a wind tunnel or through simulations on a digital computer. Where aerodynamics often use a smaller scale model to understand something big, analogue quantum simulators often take a larger scale model to understand something even smaller.

“Analogue quantum simulators are now moving from providing qualitative demonstrations of physical phenomena to providing quantitative solutions for native problems. A particularly exciting way forward in the near term is the development of a range of programmable quantum simulators hybridising digital and analogue techniques. This holds great potential because it combines the best advantages of both sides by making use of the native analogue operations to produce highly entangled states.”

### Highly programmable quantum simulator operates with up to 256 qubits, reported in July 2021

Physicists have demonstrated a large-scale, programmable quantum simulator, featuring a precisely-arranged two-dimensional array of 256 quantum bits (qubits). Designed by a team headed up at Harvard University, the system uses arrays of highly focused laser beams to trap individual atoms and drag them into desirable arrangements. The design, which the researchers describe in Nature, marks a key step forward in the global race to design larger, more reliable quantum computers, and could significantly improve their applicability in the near future.

Through the latest advances in quantum computing, researchers have recently demonstrated the potential for programmable quantum systems, capable of performing deeply complex simulations and computations. A promising platform for this technology can be found in arrangements of neutral, ultracold atoms individually trapped within arrays of optical tweezers. As their quantum states interact, these atoms can be used in operations including large-scale entanglement, quantum logic gates and realizing optical atomic clocks.

In 2017, the team developed a platform containing 51 ultracold rubidium atoms, arranged in a specific order using a one-dimensional array of optical tweezers. Building on this achievement, in their latest study the researchers aimed to develop a far more powerful two-dimensional arrangement of qubits. Although large numbers of atoms have already been trapped and rearranged in both two- and three-dimensional arrays, the coherent manipulation of programmable, strongly interacting systems containing over 100 qubits has remained far more challenging.

To overcome these difficulties, lead author Sepehr Ebadi and colleagues used a spatial light modulator to shape an optical two-dimensional wavefront, transforming the light into a uniform, two-dimensional array of highly focused laser beams that act as optical tweezers. After loading the beams with a random arrangement of ultracold rubidium atoms, they then used a second set of adjustable optical tweezers to drag the atoms into a defect-free antiferromagnetic arrangement – where the magnetic moment of each atom was exactly opposite to that of each of its neighbours.

Finally, the researchers used coherent optical beams to excite the atoms into their Rydberg states. In these states, the outer electron of the atom orbits at a large distance from its host nuclei, ensuring strong, highly tuneable interactions between individual qubits. In addition, they arranged the atoms in arrays of several different shapes, including square, honeycomb and triangular lattices. Each of these configurations featured a different type of interaction between qubits.

Altogether, the technique allowed the team to produce a highly programmable quantum simulator, containing up to 256 qubits – which together could occupy a vast number of possible quantum states. In their future research, the physicists will aim to upgrade their setup even further, through a better control over each individual tweezer beam and making the system more programmable. These improvements could pave the way for a diverse range of applications: including advanced new ways to study strongly-correlated quantum matter, designing hardware suitable for running efficient quantum algorithms, and solving challenging real-world problems in computation and measurement.

### IBM Scientists double the size of quantum simulations with entanglement forging, reported in Jan 2022

A team of IBM researchers has been looking for a new way to give quantum simulation technology a boost, but their goal isn’t to enhance the hardware, itself. Instead, they’re developing new techniques for combining quantum and classical computing resources to tackle simulation problems that are too hard for today’s noisy quantum hardware. The results of these efforts could represent a major step forward in the quest towards quantum advantage.

This isn’t the first time that researchers have thought to incorporate classical computing resources in quantum simulation. In fact, classical computing powers many techniques that are widely used in quantum simulation today, including variational quantum eigensolver (VQE) methods and error mitigation. Now, with a newly published paper1 in PRX Quantum, the IBM team has introduced a new method of quantum simulation called entanglement forging, which enables researchers to simulate a given quantum system using only half as many qubits on a quantum computer.

In their paper, the IBM team demonstrate this by using entanglement forging to create a remarkably accurate simulation of the ground state energy of a Under most circumstances, if researchers wanted to simulate 10 spin-orbitals of a water molecule, they would need to do so using a quantum computer with at least 10 qubits. That’s because most quantum simulation techniques require one qubit for each relevant “feature” of the systems they simulate.

With entanglement forging, IBM Quantum researchers were able to effectively split the problem in half. This means they separated the 10 spin-orbitals into two groups of five, and then processed each grouping using just five qubits.water molecule, successfully representing 10 spin-orbitals on just five qubits of IBM’s 27-qubit Falcon quantum processor. Given its scalability and broad application across a variety of problem structures, entanglement forging could markedly expand the computational power of quantum systems, especially when combined with new programming models like IBM Quantum’s quantum serverless — a new programming model that takes advantage of quantum and classical resources.

“We demonstrated a method that in many cases will allow you to run larger problems on your quantum processor than you otherwise could,” said Andrew Eddins, IBM Quantum researcher and lead author on the recent paper. “Entanglement forging provides an efficient method of bringing classical computational resources to bear on quantum problems in a way that, in one respect, doubles your capability. It effectively increases your qubit number by a factor of two, which is really remarkable.

### Quantum Simulators Create a Totally New Phase of Matter, reported in Dec 2021

Over the past few years, groups in Paris and Cambridge, Massachusetts, have made great progress to this end using a dark-horse type of quantum simulator. They have made a series of simulations that would take months or more to replicate on a classical computer.

“They’ve been exploring some of the frontiers of physics,” said Ivan Deutsch, a pioneer of the technology, currently at the University of New Mexico.

Today the Cambridge group unveiled their most significant discovery yet: the detection of an elusive state of matter known as a quantum spin liquid, which exists outside the century-old paradigm outlining the ways in which matter can organize. It confirms a nearly 50-year-old theory predicting the exotic state. It also marks a step toward the dream of building a truly useful universal quantum computer.

In 1973, Philip Anderson, a condensed matter pioneer and eventual Nobel laureate, predicted that matter might enter a bizarre state called a quantum spin liquid. Many atoms have a quantum property known as “spin,” which defines a direction. Spins interact magnetically, which can make them tend to point in opposite directions, especially at low temperatures. But if three atoms are arranged in a triangle, only two of the three can point in opposite directions. Therefore a trianglelike lattice of atoms can’t “freeze” into a tidy pattern of spins. Even at absolute zero, spins continue to fluctuate, analogous to how atoms slosh in a liquid.

Quantum spin liquids experience a lot of entanglement. That feature leads to “topological” order, because individual particles can sense the system’s overall topology — or geometry. Punch a hole in an ice cube and it stays frozen, but remove the atoms at the center of a quantum spin liquid and the system’s properties could change. That puts quantum spin liquids in a novel class of matter.

The Cambridge group used the quantum simulator to get a bird’s-eye view. They first programmed their neutral atoms to act like the atoms in Herbertsmithite, with the on-off Rydberg state standing in for spin. They then measured the Rydberg states throughout loops and strings of atoms to get nonlocal observations involving entanglement. The result is the first direct measurement of the topological order of a quantum spin liquid.

“If I take the entire history of ultracold atomic experiments, it probably was one of the most impressive and groundbreaking experiments in the field,” said Ehud Altman, a condensed matter theorist at the University of California, Berkeley.

### References and Resources also include:

https://physicsworld.com/a/highly-programmable-quantum-simulator-operates-with-up-to-256-qubits/

https://www.techexplorist.com/developing-next-generation-quantum-algorithms-materials/47960/

https://research.ibm.com/blog/quantum-entanglement-forging

https://www.sciencedaily.com/releases/2022/07/220729173217.htm

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