Quantum annealing and the variational quantum eigensolver are two promising quantum algorithms to find the ground state of complicated Hamiltonians on near-term quantum devices. However, it is necessary to limit the evolution time or the circuit depth as much as possible since otherwise decoherence will degrade the computation. Even when this is done, there always exists a non-negligible estimation error in the ground state energy. Here we propose a scalable extrapolation approach to mitigate this error. With an appropriate regression, we can significantly improve the estimation accuracy for quantum annealing and variational quantum eigensolver for fixed quantum resources. The inference is achieved by extrapolating the annealing time to infinity or extrapolating the variance to zero. The only additional overhead is an increase in the number of measurements by a constant factor. We verified the validity of our method with the transverse-field Ising model. The method is robust to noise, and the techniques are applicable to other physics problems. Analytic derivations for the quadratic convergence feature of the residual energy in quantum annealing and the linear convergence feature of energy variance are given.
SpinQ Gemini is a commercial desktop quantum computer designed and manufactured by SpinQ Technology. It is an integrated hardware-software system. The first generation product with two qubits was launched in January 2020. The hardware is based on NMR spectrometer, with permanent magnets providing $sim 1$ T magnetic field. SpinQ Gemini operates under room temperature ($0$-$30^{circ}$C), highlighting its lightweight (55 kg with a volume of $70times 40 times 80$ cm$^3$), cost-effective (under $50$k USD), and maintenance-free. SpinQ Gemini aims to provide real-device experience for quantum computing education for K-12 and at the college level. It also features quantum control design capabilities that benefit the researchers studying quantum control and quantum noise. Since its first launch, SpinQ Gemini has been shipped to institutions in Canada, Taiwan and Mainland China. This paper introduces the system of design of SpinQ Gemini, from hardware to software. We also demonstrate examples for performing quantum computing tasks on SpinQ Gemini, including one task for a variational quantum eigensolver of a two-qubit Heisenberg model. The next generations of SpinQ quantum computing devices will adopt models of more qubits, advanced control functions for researchers with comparable cost, as well as simplified models for much lower cost (under $5$k USD) for K-12 education. We believe that low-cost portable quantum computer products will facilitate hands-on experience for teaching quantum computing at all levels, well-prepare younger generations of students and researchers for the future of quantum technologies.
Variational quantum eigensolver (VQE) is promising to show quantum advantage on near-term noisy-intermediate-scale quantum (NISQ) computers. One central problem of VQE is the effect of noise, especially the physical noise on realistic quantum computers. We study systematically the effect of noise for the VQE algorithm, by performing numerical simulations with various local noise models, including the amplitude damping, dephasing, and depolarizing noise. We show that the ground state energy will deviate from the exact value as the noise probability increase and normally noise will accumulate as the circuit depth increase. We build a noise model to capture the noise in a real quantum computer. Our numerical simulation is consistent with the quantum experiment results on IBM Quantum computers through Cloud. Our work sheds new light on the practical research of noisy VQE. The deep understanding of the noise effect of VQE may help to develop quantum error mitigation techniques on near team quantum computers.
