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Quantum Computing

We use a truncated (regularized) Hamiltonian for the matrix quantum mechanics models. This Hamiltonian is constructed by considering a truncated Hilbert space in the Fock basis.

The truncated Hilbert space is constructed starting from the individual matrix degrees of freedom.

We consider two types of matrix quantum mechanics models:

  • a bosonic 2-matrix model with SU(2) gauge group, which has 6 bosonic degrees of freedom in total.
  • a supersymmetric 2-matrix model with SU(2) gauge group which corresponds to the BMN model with the minimal number of degrees of freedom (minimal BMN), 6 bosons and 3 fermions.

Software

QuTiP

The calculation of the spectrum of the truncated Hamiltonian for the matrix quantum mechanics models is done using qutip.

The annihilation operators are created for the states in a truncated Hilbert space with a cutoff \(\Lambda\) on the number of modes. We can study systems up to \(\Lambda=14\) with this method.

The code for the bosonic matrix model and the minimal BMN model is available in this repository.

QISKIT

We compute the ground state of the truncated Hamiltonian using a hybrid quantum-classical algorithm that is useful on current NISQ (Noisy Intermediate Scale Quantum) devices: the Variational Quantum Eigensolver (VQE).

We use the IBM qiskit library which allows users to directly access quantum hardware in the cloud.

Due to the limited number of qubits in current quantum hardware, we can study the truncated Hamiltonian with cutoff \(\Lambda\) up to 4.

The code is available in this repository.

Results

Under construction.