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1. Gleipnir: toward practical error analysis for Quantum programs

   https://doi.org/10.1145/3453483.3454029  

   Tao, Runzhou ; Shi, Yunong ; Yao, Jianan ; Hui, John ; Chong, Frederic T. ; Gu, Ronghui ( June 2021 , Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation)

   null (Ed.)

   Practical error analysis is essential for the design, optimization, and evaluation of Noisy Intermediate-Scale Quantum(NISQ) computing. However, bounding errors in quantum programs is a grand challenge, because the effects of quantum errors depend on exponentially large quantum states. In this work, we present Gleipnir, a novel methodology toward practically computing verified error bounds in quantum programs. Gleipnir introduces the (ρ,δ)-diamond norm, an error metric constrained by a quantum predicate consisting of the approximate state ρ and its distance δ to the ideal state ρ. This predicate (ρ,δ) can be computed adaptively using tensor networks based on the Matrix Product States. Gleipnir features a lightweight logic for reasoning about error bounds in noisy quantum programs, based on the (ρ,δ)-diamond norm metric. Our experimental results show that Gleipnir is able to efficiently generate tight error bounds for real-world quantum programs with 10 to 100 qubits, and can be used to evaluate the error mitigation performance of quantum compiler transformations. 

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2. Error metric for non-trace-preserving quantum operations

   https://doi.org/10.1103/PhysRevA.108.032609  

   Shi, Yu ; Waks, Edo ( September 2023 , Physical Review A)

   We study the problem of measuring errors in non-trace-preserving quantum operations, with a focus on their impact on quantum computing. We propose an error metric that efficiently provides an upper bound on the trace distance between the normalized output states from imperfect and ideal operations, while remaining compatible with the diamond distance. As a demonstration of its application, we apply our metric in the analysis of a lossy beam splitter and a nondeterministic conditional sign-flip gate, two primary non-trace-preserving operations in the Knill-Laflamme-Milburn protocol. We then turn to the leakage errors of neutral-atom quantum computers, finding that these errors scale worse than previously anticipated, implying a more stringent fault-tolerant threshold. We also assess the quantum Zeno gate's error using our metric. In a broader context, we discuss the potential of our metric to analyze general postselected protocols, where it can be employed to study error propagation and estimate thresholds in fault-tolerant quantum computing. The results highlight the critical role of our proposed error metric in understanding and addressing challenges in practical quantum information processing. 

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3. Generation of arbitrary all-photonic graph states from quantum emitters

   https://doi.org/10.1088/1367-2630/ab193d  

   Russo, Antonio ; Barnes, Edwin ; Economou, Sophia E. ( May 2019 , New Journal of Physics)

   We present protocols to generate arbitrary photonic graph states from quantum emitters that are in principle deterministic. We focus primarily on two-dimensional cluster states of arbitrary size due to their importance for measurement-based quantum computing. Our protocols for these and many other types of two-dimensional graph states require a linear array of emitters in which each emitter can be controllably pumped, rotated about certain axes, and entangled with its nearest neighbors. We show that an error on one emitter produces a localized region of errors in the resulting graph state, where the size of the region is determined by the coordination number of the graph. We describe how these protocols can be implemented for different types of emitters, including trapped ions, quantum dots, and nitrogen-vacancy centers in diamond.

    

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4. Adiabatic quantum state transfer in a semiconductor quantum-dot spin chain

   https://doi.org/10.1038/s41467-021-22416-5  

   Kandel, Yadav P. ; Qiao, Haifeng ; Fallahi, Saeed ; Gardner, Geoffrey C. ; Manfra, Michael J. ; Nichol, John M. ( December 2021 , Nature Communications)

   null (Ed.)

   Abstract Semiconductor quantum-dot spin qubits are a promising platform for quantum computation, because they are scalable and possess long coherence times. In order to realize this full potential, however, high-fidelity information transfer mechanisms are required for quantum error correction and efficient algorithms. Here, we present evidence of adiabatic quantum-state transfer in a chain of semiconductor quantum-dot electron spins. By adiabatically modifying exchange couplings, we transfer single- and two-spin states between distant electrons in less than 127 ns. We also show that this method can be cascaded for spin-state transfer in long spin chains. Based on simulations, we estimate that the probability to correctly transfer single-spin eigenstates and two-spin singlet states can exceed 0.95 for the experimental parameters studied here. In the future, state and process tomography will be required to verify the transfer of arbitrary single qubit states with a fidelity exceeding the classical bound. Adiabatic quantum-state transfer is robust to noise and pulse-timing errors. This method will be useful for initialization, state distribution, and readout in large spin-qubit arrays for gate-based quantum computing. It also opens up the possibility of universal adiabatic quantum computing in semiconductor quantum-dot spin qubits. 

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5. Spin coherent quantum transport of electrons between defects in diamond

   https://doi.org/10.1515/nanoph-2019-0144  

   Oberg, Lachlan M. ; Huang, Eric ; Reddy, Prithvi M. ; Alkauskas, Audrius ; Greentree, Andrew D. ; Cole, Jared H. ; Manson, Neil B. ; Meriles, Carlos A. ; Doherty, Marcus W. ( August 2019 , Nanophotonics)

   Abstract The nitrogen-vacancy (NV) color center in diamond has rapidly emerged as an important solid-state system for quantum information processing. Whereas individual spin registers have been used to implement small-scale diamond quantum computing, the realization of a large-scale device requires the development of an on-chip quantum bus for transporting information between distant qubits. Here, we propose a method for coherent quantum transport of an electron and its spin state between distant NV centers. Transport is achieved by the implementation of spatial stimulated adiabatic Raman passage through the optical control of the NV center charge states and the confined conduction states of a diamond nanostructure. Our models show that, for two NV centers in a diamond nanowire, high-fidelity transport can be achieved over distances of order hundreds of nanometers in timescales of order hundreds of nanoseconds. Spatial adiabatic passage is therefore a promising option for realizing an on-chip spin quantum bus. 

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