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1. 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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2. 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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3. TimeStitch: Exploiting Slack to Mitigate Decoherence in Quantum Circuits

   https://doi.org/10.1145/3548778  

   Smith, Kaitlin N. ; Ravi, Gokul Subramanian ; Murali, Prakash ; Baker, Jonathan M. ; Earnest, Nathan ; Javadi-Cabhari, Ali ; Chong, Frederic T. ( March 2023 , ACM Transactions on Quantum Computing)

   Quantum systems have the potential to demonstrate significant computational advantage, but current quantum devices suffer from the rapid accumulation of error that prevents the storage of quantum information over extended periods. The unintentional coupling of qubits to their environment and each other adds significant noise to computation, and improved methods to combat decoherence are required to boost the performance of quantum algorithms on real machines. While many existing techniques for mitigating error rely on adding extra gates to the circuit [ 13 , 20 , 56 ], calibrating new gates [ 50 ], or extending a circuit’s runtime [ 32 ], this article’s primary contribution leverages the gates already present in a quantum program without extending circuit duration. We exploit circuit slack for single-qubit gates that occur in idle windows, scheduling the gates such that their timing can counteract some errors. Spin-echo corrections that mitigate decoherence on idling qubits act as inspiration for this work. Theoretical models, however, fail to capture all sources of noise in Noisy Intermediate Scale Quantum devices, making practical solutions necessary that better minimize the impact of unpredictable errors in quantum machines. This article presents TimeStitch: a novel framework that pinpoints the optimum execution schedules for single-qubit gates within quantum circuits. TimeStitch, implemented as a compilation pass, leverages the reversible nature of quantum computation to boost the success of circuits on real quantum machines. Unlike past approaches that apply reversibility properties to improve quantum circuit execution [ 35 ], TimeStitch amplifies fidelity without violating critical path frontiers in either the slack tuning procedures or the final rescheduled circuit. On average, compared to a state-of-the-art baseline, a practically constrained TimeStitch achieves a mean 38% relative improvement in success rates, with a maximum of 106%, while observing bounds on circuit depth. When unconstrained by depth criteria, TimeStitch produces a mean relative fidelity increase of 50% with a maximum of 256%. Finally, when TimeStitch intelligently leverages periodic dynamical decoupling within its scheduling framework, a mean 64% improvement is observed over the baseline, relatively outperforming stand-alone dynamical decoupling by 19%, with a maximum of 287%. 

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4. Efficient classical simulation of noisy random quantum circuits in one dimension

   https://doi.org/10.22331/q-2020-09-11-318  

   Noh, Kyungjoo ; Jiang, Liang ; Fefferman, Bill ( September 2020 , Quantum)

   Understanding the computational power of noisy intermediate-scale quantum (NISQ) devices is of both fundamental and practical importance to quantum information science. Here, we address the question of whether error-uncorrected noisy quantum computers can provide computational advantage over classical computers. Specifically, we study noisy random circuit sampling in one dimension (or 1D noisy RCS) as a simple model for exploring the effects of noise on the computational power of a noisy quantum device. In particular, we simulate the real-time dynamics of 1D noisy random quantum circuits via matrix product operators (MPOs) and characterize the computational power of the 1D noisy quantum system by using a metric we call MPO entanglement entropy. The latter metric is chosen because it determines the cost of classical MPO simulation. We numerically demonstrate that for the two-qubit gate error rates we considered, there exists a characteristic system size above which adding more qubits does not bring about an exponential growth of the cost of classical MPO simulation of 1D noisy systems. Specifically, we show that above the characteristic system size, there is an optimal circuit depth, independent of the system size, where the MPO entanglement entropy is maximized. Most importantly, the maximum achievable MPO entanglement entropy is bounded by a constant that depends only on the gate error rate, not on the system size. We also provide a heuristic analysis to get the scaling of the maximum achievable MPO entanglement entropy as a function of the gate error rate. The obtained scaling suggests that although the cost of MPO simulation does not increase exponentially in the system size above a certain characteristic system size, it does increase exponentially as the gate error rate decreases, possibly making classical simulation practically not feasible even with state-of-the-art supercomputers. 

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5. 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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