Qubit gate and producing a generalized controlled-not quantum gate

A process for producing a generalized controlled-not quantum gate, the process comprising:

• providing a plurality of atoms, wherein the atoms comprise:
• a set of control atoms;
• and
• a set of target atoms,
• wherein each atom comprises an initial quantum state, such that the initial quantum state consists essentially of a first state |0 and a second state |1 in a ground state manifold;
• subjecting the target atoms to a single-qubit Hadamard gate;
• for each atom:
• making a control Rydberg state |c by applying a π-polarized microwave drive and a σ-polarized microwave drive, such that the control Rydberg state |c comprises a superposition of three or more initial Rydberg states;
• and
• making a target Rydberg state |t by applying the π-polarized microwave drive and the σ-polarized microwave drive, such that the target Rydberg state |t comprises a different superposition of the three or more initial Rydberg states, wherein:
• the control Rydberg state |c is orthogonal to the target Rydberg state |t;
• control Rydberg states of different atoms do not interact via dipole-dipole interactions;
• target Rydberg states of different atoms do not interact via dipole-dipole interactions;
• and
• among different atoms, control Rydberg states interact with target Rydberg states via dipole-dipole interactions;
• subjecting control atoms to a π pulse, such that the π pulse transitions the first state |0 of the initial quantum state to the control Rydberg state |c in the control atoms;
• subjecting the first state |0 of the target atoms to a 2π pulse via the target Rydberg state |t of the target atoms, such that the 2π pulse:
• for all control atoms in the second state |1, changes the phase of the first state |0;
• and
• otherwise, for at least one control atom in the control Rydberg state |c, conserves the phase of the first state |0;
• and
• subjecting the control atoms to a second π pulse, such that the second π pulse transitions the control Rydberg state |c back to the first state |0 in the control atoms to produce a multi-control and multi-target Z gate;
• and
• subjecting the target atoms in the multi-control and multi-target Z gate to a second single-qubit Hadamard gate to produce the generalized controlled-not quantum gate.

A process for preparing a metrologically-relevant entangled state, the process comprising:

• providing a plurality of atoms arranged in a regular lattice, wherein each atom comprises an initial quantum state, such that the initial quantum state consists essentially of a first state |0 in a ground state manifold;
• initializing a central atom of the atoms in the regular lattice to a (|0+|1)/√{square root over (2)} state, such that all other atoms remain in the first state |0 as remaining atoms;
• and
• proceeding, starting with the central atom, to propagate preparation of Greenberger-Horne-Zeilinger (GHZ) states in a nonlinear progression by increasing a number of GHZ states in each iteration through the remaining atoms in a recursive manner, to produce an intermediate GHZ state, such that the intermediate GHZ state acts as an initial GHZ state for a next iteration, until a final GHZ state is formed to prepare the metrologically-relevant entangled state of the atoms.

A process for preparing a metrologically-relevant entangled state, the process comprising:

• providing a plurality of atoms arranged in a regular lattice, wherein each atom comprises an initial quantum state, such that the initial quantum state consists essentially of a first state |0 in a ground state manifold;
• initializing a central atom of the atoms in the regular lattice to a (|0+|1)/√{square root over (2)} state to produce a GHZ state that includes the central atom, such that:
• all other atoms remain in the first state |0 as remaining atoms;
• the central atom is a control atom;
• and
• the nearest neighbor atoms to control atom are target atoms;
• subjecting the target atoms to a Hadamard gate, such that target atoms are configured to (|0+|1)/√{square root over (2)} state;
• subjecting the control atom and the target atoms to a Ck=1Zm gate;
• subjecting the target atoms to another Hadamard gate to increase the number of atoms in the GHZ state;
• and
• repetitively increasing the size of the GHZ state, wherein during each repetition the outermost atoms of the GHZ state are used as control atoms while the nearest neighbor atoms to the control atoms outside of the GHZ state are used as target atoms, by performing the following GHZ-increasing steps:
• subjecting the target atoms to a Hadamard gate, such that target atoms are configured to (|0+|1)/√{square root over (2)} state;
• subjecting the control atoms and the target atoms to a CkZm gate;
• subjecting the target atoms to another Hadamard gate to increase the number of atoms in the GHZ state to prepare the metrologically-relevant entangled state;
• and
• repeating the GHZ-increasing steps.