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1. Just-in-time Quantum Circuit Transpilation Reduces Noise

   Ellis Wilson, Sudhakar Singh ( October 2020 , International Conference on Quantum Computing and Engineering (QCE))

   Running quantum programs is fraught with challenges on on today’s noisy intermediate scale quantum (NISQ) devices. Many of these challenges originate from the error characteristics that stem from rapid decoherence and noise during measurement, qubit connections, crosstalk, the qubits themselves, and transformations of qubit state via gates. Not only are qubits not “created equal”, but their noise level also changes over time. IBM is said to calibrate their quantum systems once per day and reports noise levels (errors) at the time of such calibration. This information is subsequently used to map circuits to higher quality qubits and connections up to the next calibration point. This work provides evidence that there is room for improvement over this daily calibration cycle. It contributes a technique to measure noise levels (errors) related to qubits immediately before executing one or more sensitive circuits and shows that just-in-time noise measurements can benefit late physical qubit mappings. With this just-in-time recalibrated transpilation, the fidelity of results is improved over IBM’s default mappings, which only uses their daily calibrations. The framework assess two major sources of noise, namely readout errors (measurement errors) and two-qubit gate/connection errors. Experiments indicate that the accuracy of circuit results improves by 3-304% on average and up to 400% with on-the-fly circuit mappings based on error measurements just prior to application execution. 

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2. Extending the Frontier of Quantum Computers with Qutrits

   https://doi.org/10.1109/MM.2020.2985976  

   Gokhale, Pranav ; Baker, Jonathan M. ; Duckering, Casey ; Brown, Natalie C. ; Brown, Kenneth R. ; Chong, Fred ( April 2020 , IEEE Micro)

   We advocate for a fundamentally different way to perform quantum computation by using three-level qutrits instead of qubits. In particular, we substantially reduce the resource requirements of quantum computations by exploiting a third state for temporary variables (ancilla) in quantum circuits. Past work with qutrits has demonstrated only constant factor improvements, owing to the lg(3) binary-to-ternary compression factor. We present a novel technique using qutrits to achieve a logarithmic runtime decomposition of the Generalized Toffoli gate using no ancilla - an exponential improvement over the best qubit-only equivalent. Our approach features a 70× improvement in total two-qudit gate count over the qubit-only decomposition. This results in improvements for important algorithms for arithmetic and QRAM. Simulation results under realistic noise models indicate over 90% mean reliability (fidelity) for our circuit, versus under 30% for the qubit-only baseline. These results suggest that qutrits offer a promising path toward extending the frontier of quantum computers. 

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3. VAQEM: A Variational Approach to Quantum Error Mitigation

   https://doi.org/10.1109/HPCA53966.2022.00029  

   Ravi, Gokul Subramanian ; Smith, Kaitlin N. ; Gokhale, Pranav ; Mari, Andrea ; Earnest, Nathan ; Javadi-Abhari, Ali ; Chong, Frederic T. ( April 2022 , 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA))

   Variational Quantum Algorithms (VQA) are one of the most promising candidates for near-term quantum advantage. Traditionally, these algorithms are parameterized by rotational gate angles whose values are tuned over iterative execution on quantum machines. The iterative tuning of these gate angle parameters make VQAs more robust to a quantum machine’s noise profile. However, the effect of noise is still a significant detriment to VQA’s target estimations on real quantum machines — they are far from ideal. Thus, it is imperative to employ effective error mitigation strategies to improve the fidelity of these quantum algorithms on near-term machines.While existing error mitigation techniques built from theory do provide substantial gains, the disconnect between theory and real machine execution characteristics limit the scope of these improvements. Thus, it is critical to optimize mitigation techniques to explicitly suit the target application as well as the noise characteristics of the target machine.We propose VAQEM, which dynamically tailors existing error mitigation techniques to the actual, dynamic noisy execution characteristics of VQAs on a target quantum machine. We do so by tuning specific features of these mitigation techniques similar to the traditional rotation angle parameters -by targeting improvements towards a specific objective function which represents the VQA problem at hand. In this paper, we target two types of error mitigation techniques which are suited to idle times in quantum circuits: single qubit gate scheduling and the insertion of dynamical decoupling sequences. We gain substantial improvements to VQA objective measurements — a mean of over 3x across a variety of VQA applications, run on IBM Quantum machines.More importantly, while we study two specific error mitigation techniques, the proposed variational approach is general and can be extended to many other error mitigation techniques whose specific configurations are hard to select a priori. Integrating more mitigation techniques into the VAQEM framework in the future can lead to further formidable gains, potentially realizing practically useful VQA benefits on today’s noisy quantum machines. 

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4. Mitigating CNOT Errors via Noise-aware Token Swapping

   https://doi.org/10.1109/QCE57702.2023.00044  

   Sharma, Asim ; Banerjee, Avah ( September 2023 , 2023 IEEE International Conference on Quantum Computing and Engineering (QCE))

   Due to the limited decoherence time of qubits in the Noisy Intermediate-Scale Quantum (NISQ) era, optimizing the size and depth of logical quantum circuits for efficient implementation on sparsely connected physical architectures is crucial. In this work, we extend the Approximate Token Swapping (ATS) algorithm by incorporating qubit priority and the size of permutation cycles to be routed. We refer to this algorithm as Priority-ATS (PATS), which also considers CNOT gate errors while constructing the routing schedule for the qubits. We provide theoretical justification for the superior effectiveness of PATS over ATS and experimentally demonstrate its ability to improve the fidelity of the output state. Furthermore, we use depolarizing error channels to model the noisy CNOT gates, where each adjacent qubit pair has a distinct error rate. By employing realistic error rates, we showcase the robust improvement in output fidelity when using PATS as opposed to a noise-oblivious ATS routing scheme. 

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5. Random Quantum Circuits Transform Local Noise into Global White Noise

   https://doi.org/10.1007/s00220-024-04958-z  

   Dalzell, Alexander M. ; Hunter-Jones, Nicholas ; Brandão, Fernando G. S. L. ( March 2024 , Communications in Mathematical Physics)

   We study the distribution over measurement outcomes of noisy random quantum circuits in the regime of low fidelity, which corresponds to the setting where the computation experiences at least one gate-level error with probability close to one. We model noise by adding a pair of weak, unital, single-qubit noise channels after each two-qubit gate, and we show that for typical random circuit instances, correlations between the noisy output distribution$$p_{\text {noisy}}$$$p_{\text{noisy}}$and the corresponding noiseless output distribution$$p_{\text {ideal}}$$$p_{\text{ideal}}$shrink exponentially with the expected number of gate-level errors. Specifically, the linear cross-entropy benchmarkFthat measures this correlation behaves as$$F=\text {exp}(-2s\epsilon \pm O(s\epsilon ^2))$$$F=\text{exp}(-2sϵ\pm O\left(s{ϵ}^2\right))$, where$$\epsilon $$$ϵ$is the probability of error per circuit location andsis the number of two-qubit gates. Furthermore, if the noise is incoherent—for example, depolarizing or dephasing noise—the total variation distance between the noisy output distribution$$p_{\text {noisy}}$$$p_{\text{noisy}}$and the uniform distribution$$p_{\text {unif}}$$$p_{\text{unif}}$decays at precisely the same rate. Consequently, the noisy output distribution can be approximated as$$p_{\text {noisy}}\approx Fp_{\text {ideal}}+ (1-F)p_{\text {unif}}$$$p_{\text{noisy}}\approx F{p}_{\text{ideal}}+(1-F)p_{\text{unif}}$. In other words, although at least one local error occurs with probability$$1-F$$$1-F$, the errors are scrambled by the random quantum circuit and can be treated as global white noise, contributing completely uniform output. Importantly, we upper bound the average total variation error in this approximation by$$O(F\epsilon \sqrt{s})$$$O\left(Fϵ\sqrt{s}\right)$. Thus, the “white-noise approximation” is meaningful when$$\epsilon \sqrt{s} \ll 1$$$ϵ\sqrt{s}\ll 1$, a quadratically weaker condition than the$$\epsilon s\ll 1$$$ϵs\ll 1$requirement to maintain high fidelity. The bound applies if the circuit size satisfies$$s \ge \Omega (n\log (n))$$$s\ge \Omega (nlog(n\left)\right)$, which corresponds to onlylogarithmic depthcircuits, and if, additionally, the inverse error rate satisfies$$\epsilon ^{-1} \ge {\tilde{\Omega }}(n)$$${ϵ}^{-1}\ge \tilde{\Omega }\left(n\right)$, which is needed to ensure errors are scrambled faster thanFdecays. The white-noise approximation is useful for salvaging the signal from a noisy quantum computation; for example, it was an underlying assumption in complexity-theoretic arguments that noisy random quantum circuits cannot be efficiently sampled classically, even when the fidelity is low. Our method is based on a map from second-moment quantities in random quantum circuits to expectation values of certain stochastic processes for which we compute upper and lower bounds.

    

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