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.
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.
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.
Within the context of vibrational molecular quantum computing, we investigate the implementation of a full addition of two binary digits and a carry that provides the sum and the carry out. Four qubits are necessary and they are encoded into four different normal vibrational modes of a molecule. We choose the bromoacetyl chloride molecule because it possesses four bright infrared active modes. The ground and first excited states of each mode form the one-qubit computational basis set. Two approaches are proposed for the realization of the full addition. In the first one, we optimize a pulse that implements directly the entire addition by a single unitary transformation. In the second one, we decompose the full addition in elementary quantum gates, following a scheme proposed by Vedral et al. [Phys. Rev. A 54, 147 (1996)]. Four elementary quantum gates are necessary, two two-qubit CNOT gates (controlled NOT) and two three-qubit TOFFOLI gates (controlled-controlled NOT). All the logic operations consist in one-qubit flip. The logic implementation is therefore quasiclassical and the readout is based on a population analysis of the vibrational modes that does not take the phases into account. The fields are optimized by the multitarget extension of the optimal control theory involving all the transformations among the 2(4) qubit states. A single cycle of addition without considering the preparation or the measure or copy of the result can be carried out in a very competitive time, on a picosecond time scale.
Reversible logic is becoming increasingly important with the rise of technologies like quantum computing, as it retains information during computation and maintains a direct match between each input and its corresponding output. Quantum circuits are inherently reversible and the best computational model in quantum computing systems. Quantum computers require quantum processors. A critical component of any computer's processor is the arithmetic component, that handles binary operations like addition, subtraction, multiplication, and division. Notably, multiplication can be accomplished by repeatedly adding, while division can be carried out by repeatedly subtracting. This paper proposes a new design of quantum-controlled adder/subtractor (QCAS) with efficient quantum criteria like delay, quantum cost, number of ancilla and of garbage outputs. We propose a quantum reversible controlled full adder/subtractor block which is applied to construct an n-bit quantum adder/subtractor circuit. The proposed circuit is simulated using the Quirk online tool and the result confirms the accuracy of the design. This design achieves 28.5% and 61.3% improvement in delay and garbage outputs, and 14% and 41.2% increase in quantum cost and constant input, compared to its counterpart, respectively.
Quantum computing (Q-computing) is a revolutionary technology that applies quantum mechanics (QM) to implement calculations significantly quicker than traditional computers. Q-computing employs Q-bits (qubits) rather than classical bits, which can take on a superposition state, making it possible to represent both 0 and 1 at once. This distinctive property allows qubits to perform multiple calculations simultaneously, making Q computers exponentially more powerful as more qubits are added, compared to the linear scaling of classical computers. However, challenges such as qubit instability and error rates remain significant obstacles to fully realizing this potential. A vital aspect of this technology is the development of Q arithmetic circuits, which act as the foundational blocks for efficiently executing Q algorithms. Q half-adder and full-adder circuits are integral to performing fundamental arithmetic operations within Q computers. In contrast to classical adders, Q adders rely on Q gates such as Controlled NOT (CNOT) and Toffoli gates. These gates exploit Q phenomena like entanglement and superposition, allowing for more efficient computations. The Q half-adder consists of two qubits and adds two single bits, producing a carry and sum output. It utilizes the CNOT gate to compute the sum and the Toffoli gate (controlled-controlled-NOT [CCNOT]) to compute the carry. The Q full-adder builds on this, adding three qubits to produce a sum and a carry output, further increasing computational capacity. Through the entanglement of qubits, these circuits allow for more parallelism and speed compared to classical adders. Q carry-look-ahead adders (QCLAs) and Q ripple-carry adders (QRCAs) are used to perform more complex arithmetic operations based on these half-adder and full-adder structures. Q arithmetic circuits have broad applications, boosting secure key generation in cryptography, speeding up matrix operations for faster model training in machine learning, and enabling more precise, efficient image transformations in Q image processing, benefiting fields like medical imaging and computer vision.
The quantum adder is an essential attribute of a quantum computer, just as classical adder is needed for operation of a digital computer. We model the quantum full adder as a realistic complex algorithm on a large number of qubits in an Ising spin quantum computer. Our results are an important step toward effective modeling of the quantum modular adder which is needed for Shor's and other quantum algorithms. Our full adder has the following features. (i) The near-resonant transitions with small detunings are completely suppressed, which allows us to decrease errors by several orders of magnitude and to model a 1000-qubit full adder. (We add a 1000-bit number using 2001 spins.) (ii) We construct the full adder gates directly as sequences of radio-frequency pulses, rather than breaking them down into generalized logical gates, such as Control-Not and one qubit gates. This substantially reduces the number of pulses needed to implement the full adder. (The maximum number of pulses required to add one bit (F-gate) is 15.) (iii) Full adder is realized in a homogeneous spin chain. (iv) The phase error is minimized: the F-gates generate approximately the same phase for different states of the superposition. (v) Modeling of the full adder is performed using quantum maps instead of differential equations. This allows us to reduce the calculation time to a reasonable value.
The combination of quantum computing and DNA computing is a new creation that is introduced in this book with multi-valued logic. This is actually the combination of quantum physics and molecular biology. So, it can be said that the combination is actually quantum molecular biology. In the multiple-valued logic system, the general organization of the Quantum-DNA cross-platform for the multiple-valued logic system is depicted. A Multi-Valued half adder is a type of adder or electronic circuit that performs ternary number addition. A Multiple-Valued Quantum-DNA full adder removes the drawback of a Multiple-Valued Quantum-DNA half adder as it includes carry bit in the addition operation. A ternary half subtractor is a type of subtractor, an electronic circuit that performs the subtractions of ternary numbers. Multi-Valued full subtractor performs subtraction operation taking borrow qubit in consideration, thus it solves the problem that half subtractor cannot overcome.