The spin-vortex-induced loop current (SVILC) is a nano-sized loop current predicted to exist in the CuO 2 plane in the bulk of hole-doped cuprate superconductors. It is a persistent loop current protected by the topological winding number associated with the wave function. It exists around a spin-vortex created by the itinerant electrons with a doped hole at its center. The direction of each SVILC can be either clockwise (winding number −1) or counterclockwise (winding number +1); and the currentless winding number zero is forbidden by the single-valued requirement of the wave function with respect to the electron coordinates. Recently, it has been demonstrated, theoretically, that this degree-of-freedom can be used for qubits. The gate-operation time by the Rabi oscillation using an electromagnetic field with electric field intensity 10 5 V m –1 is estimated to be several nanoseconds. This is comparable or shorter than the existing superconducting qubits. Since SVILCs do not require Cooper pairs, the SVILC qubit is free from the relaxation caused by broken Cooper pair electrons that is speculated to limit the qubit coherence time in the existing superconducting qubits. Thus, the coherence time for the SVILC qubit may exceed the value achieved by the superconducting qubit (about 100 μ s). Further, since the stabilization temperature of SVILCs is expected to be the superconducting transition temperature of the cuprates, a much higher operation temperature may be possible for the SVILC qubits compared to the existing superconducting qubits, which requires the operation temperature of about 10 mK. In the present work, we show, theoretically, that coupling of two SVILC qubits can be achieved by external current feeding. This enables the construction of nano-sized qubit-couplers, and may provide a scalability that is needed in the construction of a fully fault-tolerant quantum computer.
Quantum computers open up new possibilities for faster and more efficient solutions to real-world, large-scale optimization problems that currently pose a challenge for classical computer systems. One such problem is searching very large neighborhoods, with an exponential number of elements, in local search algorithms for solving NP-hard problems. Currently, the only barrier to the effective use of quantum computers in optimization is the limited number of available qubits. Therefore, the main challenge today, given the limited number of qubits, is to formulate the problem to be solved in a form that minimizes the number of variables and, consequently, the number of necessary qubits. To meet these expectations, we propose a new solution representation used to generate neighborhoods with an exponential number of elements. We prove that for n -element permutations, the number of elements in this neighborhood is the n -th Fibonacci number. Permutations are commonly represented by binary matrices with
n2 elements. We propose a new, cost-effective method for representing solutions using
n−1 element binary sequences. For an
n=50 element permutation, the former requires 2500 qubits, while the latter requires only 49. Computational experiments for a certain NP-hard single-machine scheduling problem were performed on a D-Wave quantum computer. The obtained results clearly indicate the high effectiveness of the presented method. With a limited number of qubits, it is possible to search neighborhoods for much larger permutations. By examining the capabilities and limitations of current quantum annealers, we can more precisely identify them and then use them in the construction of new algorithms better suited to current and future quantum computers.
Quantum computers, which process qubits, offer the promise of spectacular performance improvement over ordinary computers that deal only with classical bits, but there are obstacles to this vision. First, current quantum technology only allows a small number of qubits, and these are susceptible to noise. Second, quantum algorithms must be reversible, which often requires ancillary data that consume precious qubits. Third, interesting algorithms amenable to quantum implementation, such as chemistry simulation, require representing real numbers. Although quantum integer arithmetic has been studied extensively, the few works on quantum floating point demand more ancillary qubits than input data making floating point impractical for current quantum hardware. This paper suggests an alternative to floating point, known as the Logarithmic Number System (LNS), which has proven effective for approximate arithmetic with classical hardware. Reversible LNS multiplication and division are easy and exact with one ancillary qubit. Here we explore the quantum cost of difficult LNS operations (addition and subtraction). LNS offers implementation tradeoffs between accuracy and qubit cost that suggest highly-approximate LNS will be practical on quantum hardware sooner than when quantum technology has improved enough for floating-point to be practical.