The implementation of a quantum-controlled full adder-subtractor of two binary digits and of a "carry in" or a "borrow in" is simulated by encoding four qubits in the vibrational eigenstates of a tetra-atomic molecule (trans-HONO). The laser field of the gate is computed using optimal control theory by treating dynamics in full dimensionality. A controlled qubit enforces the addition or the subtraction. The global unitary transformation that connects the inputs to the outputs is driven by a single laser pulse. This decreases the duration of the operation and allows for a better use of the optical resources and for an improvement of the fidelity (>97%). Initialization and reading out are discussed. The timescale of the sequence initialization, gate and read out is<100 ps.
A controlled full addition or subtraction can be realized by a unitary transformation on a register of four qubits. The fourth qubit is then used as a control qubit to enforce the addition or the subtraction of two binary digits and a carry or a borrow. The transformation can be decomposed into six elementary gates. The network differs from the adder network of four elementary gates by including two new controlled-NOT gates. The scheme is general and its implementation using vibrational computing has the advantage that the single global transformation that connects the inputs to the outputs can be driven in one step by a single laser shot. This decreases the time of operation and allows for a better use of the optical resources and for an improvement of the fidelity. The laser pulses are optimized by optimal control theory.
In digital circuits, a Flip-Flop (FF) is a circuit element that has two stable states which can be used to store and remember state information. The state of the circuit can be changed by applying signals to the control input. FFs are the basic building blocks of sequential logic circuits, as logic gates AND,OR, NOT are the basic building block for combinational logic circuits, and are therefore necessary for any computations involving memory. Consequently, the design and implementation of FFs can be considered as a pre-requisite for memory machine design. Here we present the design of an optical FFs in an atomic multi-level system, based on the optical manipulation of populations and coherences using stimulated Raman adiabatic passage. We first demonstrate that both populations and coherences can be transferred over multistate systems. We then propose the design of toggle-FFs, Delay-FFs, and Serial-in Serial-Out (SISO) shift registers using such systems. For the design of the filp-flops we use a three level
Λ-type system. In order to design SISO shift registers we concatenate two
Λ-type systems and construct an "M"-type scheme, and similarly concatenating three
Λ-type system we are able to obtain a seven level system. By concatenating we are able to use output of one three level
Λ-type system serve as input of another three level
Λ-type system. On top of using populations for design of logic gates, we uniquely exploit the coherences for logic machine, which provides an additional degree of freedom which can be used for the design of computing elements.
The Toffoli gate is an essential logic element, which permits implementation of a reversible processor. It is of relevance both for classical as well as quantum logics. We propose and theoretically study all-optical implementations of three-bit and four-bit Toffoli gates by application of adiabatic population transfer techniques. For a three-bit Toffoli gate we use variants of stimulated Raman adiabatic passage (STIRAP) processes in a
Λ-type level scheme, driven by two laser pulses at sufficiently large detunings. For the implementation of a four-bit Toffoli gate, we apply reversible adiabatic population transfer in five-level quantum systems, interacting with three laser pulses. We demonstrate correct all-optical implementation of the truth table of three-bit and four-bit Toffoli gates. Moreover, we derive conditions for adiabatic evolution of the population dynamics and robust operation of the gates.
Following the scheme recently proposed by Remacle and Levine [Phys. Rev. A 73, 033820 (2006)], we investigate the concrete implementation of a classical full adder on two electronic states (X 1A1 and C 1B2) of the SO2 molecule by optical pump-probe laser pulses using intuitive and counterintuitive (stimulated Raman adiabatic passage) excitation schemes. The resources needed for providing the inputs and reading out are discussed, as well as the conditions for achieving robustness in both the intuitive and counterintuitive pump-dump sequences. The fidelity of the scheme is analyzed with respect to experimental noise and two kinds of perturbations: The coupling to the neighboring rovibrational states and a finite rotational temperature that leads to a mixture for the initial state. It is shown that the logic processing of a full addition cycle can be realistically experimentally implemented on a picosecond time scale while the readout takes a few nanoseconds.