Quantum Simulation, Emulation & Annealing : Deep dive of Quantum Computing

In essence

Simulation is a method  of creating a model to represent the behavior of a system and normally used for analysis, prediction & training, 

Emulation is the act of replicating the behavior of one system on another often including hardware and software and used for running legacy software & testing hardware interaction etc.

Annealing is a heat treatment process that alters the physical properties of a material for specific use like reducing hardness and increasing ductility. In Annealing process material is heated up-to a specific temperature & after holding for specific time in that specific temperature, material is cooled slowly.

Quantum simulation, Quantum emulation and Quantum annealing :

Above mentioned Concepts are being used in Quantum Computing to achieve the targeted goals.

Quantum simulation, Quantum emulation and Quantum annealing are related concepts in Quantum Computing with quantum simulation using quantum systems to simulate other quantum systems, quantum emulation focusing on replicating the behavior of quantum hardware and quantum annealing leveraging quantum phenomena to find optimal solutions to optimization problems by finding the lowest energy state of a system using quantum effects like superposition and entanglement. 

Detailed description is given below.

1. Quantum Simulation :

Quantum simulators are a promising technology on the spectrum of quantum devices from specialized quantum experiments to universal quantum computers. These quantum devices utilize entanglement and many-particle behaviour to explore and solve hard scientific, engineering and computational problems. Rapid development over the last two decades has produced more than 300 quantum simulators in operation worldwide using a wide variety of experimental platforms.

Quantum simulation involves simulating a quantum system by quantum mechanical means  and there are generally two approaches. The first approach is known as digital quantum simulation and achieved by building a quantum computer from unitary gate components that are generated by a Hamiltonians of quantum processes. The second approach is known as analog quantum simulation and it involves building simpler analog devices that mimic other less accessible quantum systems.

Case Study - NIST's Super Quantum Simulator 'Entangles' Hundreds of Ions :

• NIST physicists have built a quantum simulator made of trapped beryllium ions (charged atoms) that are proven to be entangled, a quantum phenomenon linking the properties of all the particles. The spinning crystal, about 1 millimeter wide, can contain anywhere from 20 to several hundred ions.
• In the NIST quantum simulator, ions act as quantum bits (qubits) to store information. Trapped ions are naturally suited to studies of quantum physics phenomena such as magnetism.
• Quantum simulators with hundreds of qubits have been made of other materials such as neutral atoms and molecules. But trapped ions offer unique advantages such as reliable preparation and detection of quantum states, long-lived states, and strong couplings among qubits at a variety of distances.

Few Best Quantum Computer Simulators :

1. Intel Quantum Simulator (IQS, former qHiPSTER - The Quantum High-Performance Software Testing Environment) is a simulator of quantum circuits optimized to take maximum advantage of multi-core and multi-nodes architectures and available on GitHub.
2. STAQ (Quantum Computer Simulator) is a modern C++17 library for the synthesis, transformation, optimization and compilation of quantum circuits authored by softwareQ Inc. under the MIT License and available as a GitHub repository.
3. Other popular and well-regarded quantum simulator examples include IBM Quantum Experience (Qiskit : a cloud-based simulator with an intuitive interface), Google Cirq (an open-source framework for designing quantum circuits) and the Microsoft Quantum Development Kit (QDK). These simulators offer varying levels of flexibility and power, suitable for different needs in the field of quantum computing. 

2. Quantum Emulation :

Quantum simulation uses quantum systems to simulate other quantum systems while Quantum Emulation uses classical systems to simulate quantum hardware. 

Quantum emulators, though distinct from quantum computers, leverage classical resources to simulate quantum phenomena i.e. they can emulate the behavior of quantum bits (qubits - the basic units of quantum information ) , the entanglement of qubits ( a quantum feature that allows them to share states and correlations) , the implementation of quantum logic gates ( the operations that manipulate qubits ) or quantum circuits (the sequences of gates that perform quantum functions ) etc. Quantum emulators can run on various platforms such as personal computers, servers, clusters or cloud services.

Quantum Emulators advantages over Quantum Computers :

Quantum emulators allow testing and refining quantum algorithms and systems without use of a full-scale quantum computer. Quantum Emulators have several advantages over quantum computers.

• Quantum emulators are more accessible and cost-effective, as they do not require specialized hardware or facilities.
• Quantum emulators are more scalable and flexible also, as they can handle larger numbers of qubits and gates and adjust to different architectures and parameters.
• Quantum emulators are more reliable and accurate also because they do not suffer from noise, decoherence or errors that affect quantum systems.
• Quantum emulators are more compatible and interoperable, as they can use standard software tools and languages and communicate with other classical devices.

Quantum Emulators working Process :

Quantum emulators work by mapping quantum states and operations to classical data and algorithms. Like a qubit can be represented by a two-dimensional vector and a quantum gate by a matrix. A quantum circuit can be represented by a series of matrix multiplications and a quantum measurement can be represented by a probabilistic sampling. Quantum emulators can use different techniques to optimize the simulation process, such as parallel computing, distributed computing or tensor network methods.

Quantum Emulators Limitations and Challenges :

In Quantum emulators the main limitation is the exponential growth of the computational resources needed to simulate quantum systems. Like to simulate a system of n qubits, there is need of  2^n bits of memory and 2^n x 2^n operations hence even a moderate number of qubits can quickly exceed the capacity of classical hardware.  Further the fidelity of the simulation or how well the quantum emulator reproduces the quantum behaviour is the other major challenge. For example, some quantum effects, such as interference or randomness, may be hard to capture or verify by classical means.

Uses of Quantum Emulators :

Quantum emulators are used as various applications in quantum computing as quantum cryptography, quantum machine learning or quantum optimization and in accelerating the research and development process in quantum computing.

Case Study - MIT’s Quantum Emulator Recreates Electromagnetic Fields for Innovative Electronics Development :

Electromagnetic fields shape the behavior of electrons within materials, influencing properties like conductivity, magnetism, and even the transition between insulators and superconductors.

• In a recent study MIT researchers have developed a method to emulate electromagnetic fields on a 16-qubit superconducting quantum processor, allowing new ways to explore material properties like conductivity and magnetism.

• By using microwave signals to control qubit energy levels, they simulate electron movement in magnetic fields, providing insights into material behaviours that are otherwise hard to replicate.

• This flexible quantum emulator enables material scientists to investigate a range of conditions without needing new hardware for each experiment, simplifying studies on phenomena such as electron hopping and phase transitions.
• Although faced challenges with qubit calibration and coupling persist, this could drive future research in high-performance materials, advancing our understanding of superconductivity and other complex material properties.

Thus creating new possibilities for studying materials with the potential to inform high-performance electronics and illustrating how quantum simulation can be used as a tool to explore complex material properties.

3. Quantum Annealing :

Quantum annealing is a specific technique used to solve optimization problems, while quantum simulation and emulation are broader approaches to studying and developing quantum technologies. 

Annealing Process ( Working ) :  

The quantum bits ( qubits ) are the lowest energy states of the superconducting loops corresponding to a circulating current and resulted magnetic field. As with classical bits, a qubit can be in state of 0 or 1 and as a quantum object the qubit can also be in a superposition of the 0 state and the 1 state at the same time. At the end of the quantum annealing process, each qubit collapses from a superposition state into either 0 or 1 (a classical state).

Annealing process is illustrated by drawn energy diagram, in which at the start of the annealing , the qubit is in a superposition state, which can be represented as a single valley with a single minimum energy. As the quantum annealing process runs, an energy barrier is raised which separates the single minimum energy into two valleys ( double -well potential ). In the annealing process energy diagram  a single qubit that results in two valleys of equal energy minima; thus the qubit has a 50/50 chance of being in either valley at the end of the anneal that is in the classical state of either 0 or 1.

The probability of the qubit falling into the 0 or 1 state can be controlled by applying an external magnetic field to bias the qubit to end in one state over the other; the magnetic field is programmatically controlled via a qubit bias & the magnetic field tilts the valleys in a preferred direction, increasing the probability of the qubit ending up in the valley with the lower energy minimum here the classical state of 1. 

Quantum annealing and adiabatic quantum computation :

The space of energy states of a physical system resembles a landscape formed by mountains and valleys. Each valley is an energy minimum and all are separated each other by peaks that represent energy maxima. The solution corresponds to one of these valleys, the lowest one.

Let’s prepare the system in a quantum superposition of many possible solutions of the problem. The quantum tunnelling effect allows to “pass” the high energy “peaks” through tunnels instead of climbing them as in simulated annealing. Quantum annealing is driven with an external magnetic field which plays the role of the temperature in simulated annealing: the quantum annealing starts with high magnetic field (high temperature) and ends up with a low magnetic field (low temperature).

In adiabatic quantum computation, Start from Ground State of System with Hamilton H0 to adiabatically transform up to Hamilton H1 , Mathematically  Hamiltonian H is given as

If the algorithm is performed slowly enough, the adiabatic theorem guarantees that the ground state at the end of the computation is the optimal solution.

The term “quantum annealing" is used indistinctly to describe the quantum annealing process that we have explained above, adiabatic quantum computation or some process that involves annealing and adiabatic both.

Hardware: Quantum annealers are a type of quantum computer designed for optimization problems, while gate-based quantum computers are more general-purpose. 

Applications: Quantum annealing is particularly well-suited for problems that can be mapped to an Ising model or a similar optimization landscape. 

Quantum-Classical Hybrid: AI Multiple notes that quantum annealing can be used in conjunction with classical algorithms to solve problems more efficiently. 

Simulated Annealing and Quantum Annealing : Simulated Annealing and Quantum Annealing are algorithms for combinatorial optimization problems. Simulated Annealing brings solutions using thermal fluctuations and through classical dynamics while Quantum Annealing does using quantum fluctuations and through quantum dynamics.

Topics “Quantum Computers : Facts and Specs" , “Quantum Computers : Reality and Future" and "Advances in Quantum Computing" are covered in Next Sections of this Quantum Computing deep dive Series.