A hardware-efficient leakage-reduction scheme for quantum error correction with superconducting transmon qubits

Leakage outside of the qubit computational subspace poses a threatening challenge to quantum error correction (QEC). We propose a scheme using two leakage-reduction units (LRUs) that mitigate these issues for a transmon-based surface code, without requiring an overhead in terms of hardware or QEC-cycle time as in previous proposals. For data qubits we consider a microwave drive to transfer leakage to the readout resonator, where it quickly decays, ensuring that this negligibly affects the coherence within the computational subspace for realistic system parameters. For ancilla qubits we apply a $|1\rangle\leftrightarrow|2\rangle$ $\pi$ pulse conditioned on the measurement outcome. Using density-matrix simulations of the distance-3 surface code we show that the average leakage lifetime is reduced to almost 1 QEC cycle, even when the LRUs are implemented with limited fidelity. Furthermore, we show that this leads to a significant reduction of the logical error rate. This LRU scheme opens the prospect for near-term scalable QEC demonstrations

DRUGS AND LABORATORY TESTS: I. INTERACTION OF PHENAMIN AND ACETYSAL WITH DETERMINATION OF FREE FATTY ACIDS

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Neural network decoder for near-term surface-code experiments

Neural-network decoders can achieve a lower logical error rate compared to conventional decoders, like minimum-weight perfect matching, when decoding the surface code. Furthermore, these decoders require no prior information about the physical error rates, making them highly adaptable. In this study, we investigate the performance of such a decoder using both simulated and experimental data obtained from a transmon-qubit processor, focusing on small-distance surface codes. We first show that the neural network typically outperforms the matching decoder due to better handling errors leading to multiple correlated syndrome defects, such as $Y$ errors. When applied to the experimental data of [Google Quantum AI, Nature 614, 676 (2023)], the neural network decoder achieves logical error rates approximately $25\%$ lower than minimum-weight perfect matching, approaching the performance of a maximum-likelihood decoder. To demonstrate the flexibility of this decoder, we incorporate the soft information available in the analog readout of transmon qubits and evaluate the performance of this decoder in simulation using a symmetric Gaussian-noise model. Considering the soft information leads to an approximately $10\%$ lower logical error rate, depending on the probability of a measurement error. The good logical performance, flexibility, and computational efficiency make neural network decoders well-suited for near-term demonstrations of quantum memories.Comment: 15 pages, 8 figures, 1 tabl

Decomposing generalized measurements into continuous stochastic processes

One of the broadest concepts of measurement in quantum theory is the generalized measurement. Another paradigm of measurement--arising naturally in quantum optics, among other fields--is that of continuous-time measurements, which can be seen as the limit of a consecutive sequence of weak measurements. They are naturally described in terms of stochastic processes, or time-dependent random variables. We show that any generalized measurement can be decomposed as a sequence of weak measurements with a mathematical limit as a continuous stochastic process. We give an explicit construction for any generalized measurement, and prove that the resulting continuous evolution, in the long-time limit, collapses the state of the quantum system to one of the final states generated by the generalized measurement, being decomposed, with the correct probabilities. A prominent feature of the construction is the presence of a feedback mechanism--the instantaneous choice weak measurement at a given time depends on the outcomes of earlier measurements. For a generalized measurement with $n$ outcomes, this information is captured by a real $n$-vector on an $n$-simplex, which obeys a simple classical stochastic evolution.Comment: 9 pages, LaTeX, name changed, typos correcte

Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements

Protecting quantum information from errors is essential for large-scale quantum computation. Quantum error correction (QEC) encodes information in entangled states of many qubits, and performs parity measurements to identify errors without destroying the encoded information. However, traditional QEC cannot handle leakage from the qubit computational space. Leakage affects leading experimental platforms, based on trapped ions and superconducting circuits, which use effective qubits within many-level physical systems. We investigate how two-transmon entangled states evolve under repeated parity measurements, and demonstrate the use of hidden Markov models to detect leakage using only the record of parity measurement outcomes required for QEC. We show the stabilization of Bell states over up to 26 parity measurements by mitigating leakage using postselection, and correcting qubit errors using Pauli-frame transformations. Our leakage identification method is computationally efficient and thus compatible with real-time leakage tracking and correction in larger quantum processors.Comment: 22 pages, 15 figure

Microwave-activated gates between a fluxonium and a transmon qubit

We propose and analyze two types of microwave-activated gates between a fluxonium and a transmon qubit, namely a cross-resonance (CR) and a CPHASE gate. The large frequency difference between a transmon and a fluxonium makes the realization of a two-qubit gate challenging. For a medium-frequency fluxonium qubit, the transmon-fluxonium system allows for a cross-resonance effect mediated by the higher levels of the fluxonium over a wide range of transmon frequencies. This allows one to realize the cross-resonance gate by driving the fluxonium at the transmon frequency, mitigating typical problems of the cross-resonance gate in transmon-transmon chips related to frequency targeting and residual ZZ coupling. However, when the fundamental frequency of the fluxonium enters the low-frequency regime below 100 MHz, the cross-resonance effect decreases leading to long gate times. For this range of parameters, a fast microwave CPHASE gate can be implemented using the higher levels of the fluxonium. In both cases, we perform numerical simulations of the gate showing that a gate fidelity above 99% can be obtained with gate times between 100 and 300 ns. Next to a detailed gate analysis, we perform a study of chip yield for a surface code lattice of fluxonia and transmons interacting via the proposed cross-resonance gate. We find a much better yield as compared to a transmon-only architecture with the cross-resonance gate as native two-qubit gate

Investigation of ultrasonic influence on the kinetics of extracting gold from electronic waste

In this paper the effect of ultrasonic treatment on the apparent activation energy of gold leaching from e-waste in aqueous thiourea solution was studied. The leaching was carried out under conventional conditions and under ultrasonic treatment. The leaching in both cases was carried out at 25 °C, 35 °C, 45 °C and 60 °C. The apparent activation energy using ultrasonic activation decreases. In both cases the process of gold leaching from e-waste proceeds in the diffusion region. Thus, ultrasonic intensification is a means of increasing the efficiency of hydrometallurgical processes of e-waste processing by reducing the activation energy of the process

Uranyl complexes formed with apara-t-butylcalix[4]arene bearing phosphinoyl pendant arms on the lower rim. Solid and solution studies

The current interest in functionalized calixarenes with phosphorylated pendant arms resides in their coordination ability towards f elements and capability towards actinide/rare earth separation. Uranyl cation forms 1:1 and 1:2 (M:L) complexes with atetra-phosphinoylated p-tert-butylcalix[4]arene, B4bL4: UO2(NO3)2(B4bL4)n· xH2O (n = 1, x = 2, 1; n = 2, x = 6, 2). Spectroscopic data point to the inner coordination sphere of 1 containing one monodentate nitrate anion, one water molecule and the four phosphinoylated arms bound to UO22+ while in 2, uranyl is only coordinated to calixarene ligands. In both cases the U(VI) ion is 8-coordinate. Uranyl complexes display enhanced metal-centred luminescence due to energy transfer from the calixarene ligands; the luminescence decays are bi-exponential with associated lifetimes in the ranges 220μs <τs <250μs and 630μs <τL < 640μs, pointing to the presence of two species with differently coordinated calixarene, as substantiated by aXPS study of U(4f5/2,7/2), O(1s) and P(2p) levels on solid state samples. The extraction study of UO22+ cation and trivalent rare-earth (Y, La, Eu) ions from acidic nitrate media by B4bL4 in chloroform shows the uranyl cation being much more extracted than rare earth