Abstract: A method and a quantum circuit to be utilised for performing a multi-step quantum basis state shift. For a state vector space having the size of 2N+1, a full shift register includes N+1 qubits. A last qubit (qN+1) of the full shift register is a superposition qubit, which allows for defining a superposition of substates. The superposition qubit is used to determine which substates are to be incremented and which substates are to be decremented. Even substates to be incremented can be incremented by simply applying a step of inverting an i+1th qubit (qi+1), namely a step qubit. Similarly, odd substates to be decremented can be decremented by applying the same step of inverting. Remaining steps of the quantum circuit are employed to perform a rearrangement of the even substates to be incremented, the even substates to be decremented, the odd substates to be incremented, and the odd substates to be decremented, such that applying the step of inverting performs the multi-step quantum basis state shift in one go.

Abstract: A quantum circuit for a lattice gas automata simulation includes an initialization step performed by setting up, for the quantum circuit, a position register, a channel register and a first ancilla register. To the position register, the channel register and the first ancilla register are applied in a sequential order: (i) a collision step constructed using a first set of multi-controlled gates, a second set of multi-controlled gates, and four CX gates arranged between the first set and the second set, the collision step being applied to the channel register and the first ancilla register; (ii) a mapping step constructed using two Hadamard gates and four multi-controlled SWAP gates, the mapping step being applied to the channel register and the first ancilla register; and (iii) a propagation step being applied to the position register and the first ancilla register.

Abstract: Disclosed is a method for setting up a quantum circuit (300, 400) utilizing a lattice Boltzmann method. An initialization step (302, 402) is performed by setting up for the quantum circuit, a first quantum register (f1), a second quantum register (f2) and at least a first ancilla register (a, a1). The quantum circuit is applied to the first quantum register (f1), the second quantum register (f2) and the first ancilla register (a, a1), wherein the quantum circuit comprises in a sequential order: (i) a collision step (304, 404) constructed using a first set of quantum gates; (ii) a propagation step (306, 406) constructed using a second set of quantum gates; and (iii) a macroscopic variables calculation step (308, 408) constructed using a third set of quantum gates.

Abstract: A method of setting up a quantum circuit for computational basis state shift. For the quantum circuit, a first quantum register, a second quantum register and a first ancilla register are set up. The first quantum register includes four qubits and the second quantum register includes N?4 qubits. To the first quantum register, the second quantum register and the first ancilla register are applied in a sequential order: (i) an initial step including three CX gates and a first X gate; (ii) a first segment including seven multi-controlled gates; (iii) a second segment comprising a first set of CX gates, a second set of CX gates and a cascade of gates arranged between the first set and the second set; and (iv) a third segment comprising two CX gates and a second X gate.