Quantum Many-Body systems.
A crucial milestone in the field of quantum simulation and computation is to demonstrate that a quantum device can compute certain tasks that are nearly impossible to reproduce by a classical computer.
So, this study is to exhibit quantum supremacy which can be implemented in generic quantum many-body systems.
As, full control of many-body systems is a key towards the future quantum technologies and attaining quantum supremacy or quantum control over these quantum systems will enable to let any environment (be noisy etc) or even for long range interactions for a part of quantum computer.
The interactions between the particles of the quantum many-body systems create quantum correlations or entanglement.
In a study by Jirawat Tangpanitan of Centre for Quantum Technologies, National University of Singapore, among others in achieving Quantum Supremacy in driven quantum-many body systems issued on February 28, 2020, in which they analyzed on the eigenstate thermalization hypothesis in complexity theory by giving examples of simple disordered Ising chains driven by magnetic fields. Analog quantum simulators are controllable quantum platforms specifically built to implement complex quantum many body models [1]. In this work, they have provided evidence that generic isolated periodically-driven interacting quantum systems, when thermalized, cannot be efficiently simulated on a classical computer. These constitute a large class of quantum simulators.
The mathematical descriptions behind each step are discussed in Methods. Also, they have provided the exact parameters in the Ising Model for the dynamics, showing that the lattice and the field parameters are quasi-random numbers with no apparent structure.
The methods used by them are briefly mentioned as, Mapping pM(z) to the partition function of a classical complex Ising model. [*]
Their research opens the way for a large class of quantum platforms. Their results can be extended to a broader class of quantum many-body systems such as those with gauge fields, frustrated spin systems, and undriven systems, superconducting systems etc. [2]
This research essay is based on performing the direction of the results obtained by Jirawat Tangpanitan and team, in Boston sampling and random quantum circuits.
In a study by Masaki Owari, Koji Maruyama, Takeji Takui and Go Kato on November 21, 2018 in probing untouchable environment as a source for quantum computing where the manipulation of a quantum system and it’s surrounding environment is performed by probing and controlling a part of this environment as it is nearly hopeless to have full control of the infinitely large environment.
Also, as many experimental efforts are made towards achieving quantum supremacy for superconducting circuits.
In this paper, a hybrid system of a superconducting qubit and nitrogen-vacancy centers in diamond is directly controlled and measured. In this hybrid system, the small quantum device is finite dimensional, that is a superconducting qubit surrounded by finite coherently coupled trapped nitrogen-vacancy centers is studied by identifying the dynamical structure of the total system. [*]
In this section, I would like to throw light on my idea of implementing the method used by Jirawat Tangpanitan and team, in which they have provided justifications of the diagrammatic recipes to map the quantum gates which contains both diagonal and not diagonal gates.
Starting with a single qubit system, so according to my idea, their single qubit systems results can be implemented for the real time protocol of a single superconducting system surrounded by the finite coherently coupled nitrogen-vacancy electron spins in the study by Masaki Owari, Koji Maruyama and team in probing untouchable environment as a source for quantum computing
As, for the identification method they presented state-steering protocol to establish entanglement between the quantum system & it’s environment, and an ancillary or additional system.
By preparing a maximally entangled state between the additional systems as (|00i+|11i)/√2) and then trying different ways of swapping between the quantum system and these additional systems for transferring entanglement between the additional system and the quantum system.
While on the other hand, Jirawat Tangpanitan and team on starting with the single qubit system and random gates, also used a similar approach but here they inserted an identity between their unitary matrix and the random gate, Σ zn∈ {0,1} |znihzn.
Here, it was observed that diagonal gates in the circuits allow the reduction of the number of classical spins.
Similarly, they have analyzed for 2-qubit systems too.
Also, the COE Dynamics can be expressed in terms of quasi-random quantum circuit, so here the same procedure of single qubit can be applied.
The same method can be devised or can be tried for the single qubit superconducting qubit in probing the untouchable environment study.
As, also mentioned in the latter paper, that any quantum operations can be applied to the quantum system coupled by the coherent nitrogen-vacancy spins, here the outline of the quantum supremacy can be proved by considering a computational task of approximating the output probability. In this case, random quantum circuit has been showed the hard prove for at least once instance.
