Quantum computers that are based on technologies like superconducting and quantum dots impose a physical constraint that requires interacting qubits to be adjacent. The initial placement of qubits and the swap gate insertion techniques affect the circuit cost. The authors proposed a global qubit ordering technique that considers fewer permutations for the number of interactions a qubit does with other qubits of its circuit. They also performed the local re‐ordering of qubits by attempting to reduce the cost as much as possible; the cost is estimated by defining a window with weights assigned in such a way that nearby gates to the current gate in question are given higher weightage. Experiments have been conducted on NCV benchmarks, and results have been compared with those of recent state‐of‐the‐art techniques. When compared with the existing works, the proposed method shows improvements of up to 53.3% for smaller benchmarks and up to 51.61% for larger benchmarks.
To run an algorithm on a quantum computer, one must choose an assignment from logical qubits in a circuit to physical qubits on quantum hardware. This task of initial qubit placement, or qubit allocation, is especially important on present-day quantum computers which have a limited number of qubits, connectivity constraints, and varying gate fidelities. In this work we formulate and implement the qubit placement problem as a quadratic, unconstrained binary optimization (QUBO) problem and solve it using simulated annealing to obtain a spectrum of initial placements. Compared to contemporary allocation methods available in t|ket$\rangle $ and Qiskit, the QUBO method yields allocations with improved circuit depth for $>$50% of a large set of benchmark circuits, with many also requiring fewer CX gates.
We present a concrete oracle construction for bilinear Diophantine equations of the form
f(x,y)=Axy+Bx+Cy+D, together with its application as a scalable, hardware-agnostic benchmark for digital quantum computers. The oracle can be used in a Grover search algorithm in two variants suitable for both noisy-intermediate scale quantum devices and early fault-tolerant quantum processors. Applied to integer factoring via a residue-class encoding, the circuit requires
2n−5 qubits or fewer to factor an
n-bit biprime
N=pq; for
N=143 requiring as few as 7 qubits and 135 two-qubit gates compared to 19 qubits and 51,048 two-qubit gates for a qubit-efficient variant of Shor's algorithm. Large-scale simulations confirm a success probability approaching 100\% for $>$800 randomly selected biprimes with
5≤n≤35. The circuit family provides a scalable, deterministically convergent and easily verifiable benchmark in a range accessible to near term quantum hardware.