Practical Quantum computing hinges on the ability to control large numbers of qubits with high fidelity. Quantum dots define a promising platform due to their compatibility with semiconductor manufacturing. Moreover, high-fidelity operations above 99.9% have been realized with individual qubits, though their performance has been limited to 98.67% when driving two qubits simultaneously. Here we present single-qubit randomized benchmarking in a two-dimensional array of spin qubits, finding native gate fidelities as high as 99.992(1)%. Furthermore, we benchmark single qubit gate performance while simultaneously driving two and four qubits, utilizing a novel benchmarking technique called N-copy randomized benchmarking, designed for simple experimental implementation and accurate simultaneous gate fidelity estimation. We find two- and four-copy randomized benchmarking fidelities of 99.905(8)% and 99.34(4)% respectively, and that next-nearest neighbor pairs are highly robust to cross-talk errors. These characterizations of single-qubit gate quality are crucial for scaling up quantum information technology.

@en

We consider the task of spectral estimation of local quantum Hamiltonians. The spectral estimation is performed by estimating the oscillation frequencies or decay rates of signals representing the time evolution of states. We present a classical Monte Carlo (MC) scheme which efficiently estimates an imaginary-time, decaying signal for stoquastic (i.e. sign-problem-free) local Hamiltonians. The decay rates in this signal correspond to Hamiltonian eigenvalues (with associated eigenstates present in an input state) and can be extracted using a classical signal processing method like ESPRIT. We compare the efficiency of this MC scheme to its quantum counterpart in which one extracts eigenvalues of a general local Hamiltonian from a real-time, oscillatory signal obtained through quantum phase estimation circuits, again using the ESPRIT method. We prove that the ESPRIT method can resolve S = poly(n) eigenvalues, assuming a 1/poly(n) gap between them, with poly(n) quantum and classical effort through the quantum phase estimation (QPE) circuits, assuming efficient preparation of the input state. We prove that our MC scheme plus the ESPRIT method can resolve S = O(1) eigenvalues, assuming a 1/poly(n) gap between them, with poly(n) purely classical effort for stoquastic Hamiltonians, requiring some access structure to the input state. However, we also show that under these assumptions, i.e. S = O(1) eigenvalues, assuming a 1/poly(n) gap between them and some access structure to the input state, one can achieve this with poly(n) purely classical effort for general local Hamiltonians. These results thus quantify some opportunities and limitations of MC methods for spectral estimation of Hamiltonians. We numerically compare the MC eigenvalue estimation scheme (for stoquastic Hamiltonians) and the quantum-phase-estimation-based eigenvalue estimation scheme by implementing them for an archetypal stoquastic Hamiltonian system: the transverse field Ising chain.

@en

The bio-based industry is striving to replace refined sugars by much cheaper secondary feedstocks for the production of bio-fuels and chemicals. However, due to their higher complexity, a number of technological challenges need to be overcome. One example are the high concentrations of sodium and potassium present in the biomass hydrolysates that inhibit fermentation and hence need to be reduced. Previous research demonstrated the technical feasibility of membrane capacitive deionization (MCDI) for biomass hydrolysate desalination as a chemical/waste free alternative compared to the commonly used ion-exchange process (IEX). In this paper, the economic viability of MCDI was investigated for a production capacity of 500 ton sugar day 1 and a target Na removal from 3 to 0.1 g kg 1 hydrolysate. Although capital costs were higher for MCDI than for IEX due to the expensive MCDI cells and power supplies, operating costs were lower because less water and chemicals are used and less wastewater is generated. Cost calculations for different initial feed concentrations indicated that IEX was only preferential over MCDI when the feed Na+ concentration was below 0.4 g kg 1 hydrolysate. Then the higher chemical, water and wastewater treatment costs for IEX no longer outweighed the higher cost of MCDI cells compared to IEX resins.@en