How is a quantum computer simulated?

[TriKri]

Hi, after reading this article, I was left wondering how the heck a quantum computer can be simulated. To begin with, how is a quantum computer of 42 qubits built up? And the how could this computer possibly be simulated? I mean, the wave function of one qubit is a three dimensional scalar field, so 42 bits would be... a 3x42 = 126 dimensional scalar field?? That they have made a PDE out from which they are solving? Or have they succeeded to make a 2⁴² (only) variable ODE by considering the spins of the electrons only? Then if there is this 2⁴² (~ 4.4 trillion) variable ODE, what does it look like? How does each of these states of the system behave, and can two states affect each other?

 

[azntoon]

In order to simulate a quantum computer, scientists have developed a variety of mathematical approaches. The most successful approach is the Quantum Monte Carlo (QMC) method, which uses random numbers to create a simulation of the quantum system. This method can be used to accurately simulate a quantum system of up to 42 qubits. First, the quantum state of each qubit is represented by a three-dimensional scalar field. Each qubit has two states: spin up or spin down. When all the spins of the qubits are known, the QMC algorithm can generate a probability distribution which represents the total quantum state of the system. This probability distribution can then be used to calculate the expected value of any observable. The QMC method has been used to solve a variety of problems, including finding the ground state energy of a system and calculating entanglement properties of many-body systems. Additionally, the QMC method has been used to simulate quantum algorithms such as Shor’s algorithm and Grover’s algorithm. In addition to the QMC method, scientists have also developed other methods to simulate a quantum computer. These include the density matrix renormalization group (DMRG), tensor network methods, variational Monte Carlo, and matrix product states. All of these approaches are ultimately limited by the computational resources available, but they offer a good approximation of the quantum behavior of the system. Ultimately, simulating a quantum computer is a difficult task because of the complexity of the wavefunction describing the system. However, with the right algorithms and enough computational power, it is possible to accurately simulate a quantum system of up to 42 qubits.