Quantum Computing Simplifies Arithmetic with Reduced Qubit Requirements.

Researchers demonstrate reversible half and full adder circuits utilising a novel Hamiltonian coding (QHC) technique, compressing standard designs from three to five qubits into a two qubit system within a four by four Hilbert space. This approach minimises qubit and gate resources for truth table evaluation, potentially advancing field programmable gate array capabilities.

The efficient execution of arithmetic operations represents a persistent challenge in quantum computation, frequently demanding substantial qubit resources to maintain reversibility. Researchers now propose a method to significantly reduce this overhead, potentially streamlining quantum circuits for practical applications. Omid Faizy, from Laboratoire de Chimie de la Matière Condensée de Paris, Sorbonne Université, alongside Norbert Wehn, Paul Lukowicz, and Maximilian Kiefer-Emmanouilidis, all from the Department of Computer Science and Research Initiative QC-AI at RPTU Kaiserslautern-Landau, with Kiefer-Emmanouilidis also affiliated with the German Research Center for Artificial Intelligence (DFKI), detail their approach in the article, “No Scratch Quantum Computing by Reducing Qubit Overhead for Efficient Arithmetics”. Their work introduces a Hamiltonian Quantum Computing (QHC) technique, encoding input states within a rotating gate, thereby compressing the qubit requirements for arithmetic circuits. This innovation allows for the construction of half-adder and full-adder circuits utilising a two-qubit Hilbert space, a considerable reduction from existing designs that typically require three to five qubits. The team demonstrate the potential for this scheme to optimise classical logic evaluation on quantum hardware, potentially circumventing energy limitations inherent in conventional CMOS technology.

Conventional quantum computation typically relies on sequences of quantum gates to manipulate qubits, but Quantum Hamiltonian Computing (QHC) represents a departure from this established paradigm, investigating a novel approach to digital logic. This research demonstrates a reversible half-adder circuit, a fundamental component in digital systems, implemented using QHC and showcases a reduction in complexity compared to standard implementations. By encoding Boolean inputs directly into the energy levels of a quantum system, defined by its Hamiltonian, computation proceeds through the natural evolution of the system itself, offering a pathway towards more compact and potentially more energy-efficient quantum logic.

Traditional reversible quantum computation necessitates a qubit register size equivalent to the larger of the input or output registers, due to the requirements of state encoding, creating significant overhead in qubit resources. QHC, conversely, reduces this requirement to the size of the output states, offering a potential advantage in qubit efficiency and enabling the construction of a half-adder within a two-qubit, 4×4 Hilbert space. The Hilbert space defines all possible states of the quantum system. This compression stems from encoding the inputs into the Hamiltonian, rather than using traditional gates.

The study successfully implements a reversible half-adder circuit within this two-qubit Hilbert space, a reduction in complexity compared to standard three and four-qubit implementations, and highlights the potential for QHC to bypass certain energy limitations inherent in classical Complementary Metal-Oxide-Semiconductor (CMOS) circuits. By leveraging the principles of unitary evolution, which governs quantum systems and ensures energy conservation during transformations, QHC offers a pathway towards more compact and potentially more energy-efficient quantum logic. The successful implementation of a half-adder serves as a proof-of-concept, suggesting the broader applicability of this approach to more complex digital circuits and computational tasks.

The research highlights the potential for QHC to bypass certain energy limitations inherent in classical CMOS circuits, due to the principles of unitary evolution, and positions QHC as a promising candidate for advancing Field Programmable Gate Array (FPGA) capabilities through integrated circuits or photonics. While the current manuscript avoids superposition of input and output states, the authors note this remains a feasible extension, suggesting future work could explore harnessing quantum superposition – where a qubit exists in multiple states simultaneously – to further enhance computational power and efficiency.

Future research focuses on exploring the scalability of QHC to more complex circuits and investigating the potential for implementing other quantum algorithms using this approach. Additionally, the authors plan to investigate the use of different Hamiltonian designs to optimise the performance of QHC circuits and reduce the required quantum resources. They also aim to develop a software framework for designing and simulating QHC circuits, facilitating exploration of this promising new paradigm for quantum computation.