 NSFPAR ID:
 10426580
 Publisher / Repository:
 American Physical Society
 Date Published:
 Journal Name:
 PRX Quantum
 Volume:
 3
 Issue:
 4
 ISSN:
 26913399
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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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 singlequbit gates that occur in idle windows, scheduling the gates such that their timing can counteract some errors. Spinecho 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 singlequbit 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 stateoftheart 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 standalone dynamical decoupling by 19%, with a maximum of 287%.more » « less

Abstract 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 gatelevel error with probability close to one. We model noise by adding a pair of weak, unital, singlequbit noise channels after each twoqubit gate, and we show that for typical random circuit instances, correlations between the noisy output distribution
and the corresponding noiseless output distribution$$p_{\text {noisy}}$$ ${p}_{\text{noisy}}$ shrink exponentially with the expected number of gatelevel errors. Specifically, the linear crossentropy benchmark$$p_{\text {ideal}}$$ ${p}_{\text{ideal}}$F that measures this correlation behaves as , where$$F=\text {exp}(2s\epsilon \pm O(s\epsilon ^2))$$ $F=\text{exp}(2s\u03f5\pm O\left(s{\u03f5}^{2}\right))$ is the probability of error per circuit location and$$\epsilon $$ $\u03f5$s is the number of twoqubit gates. Furthermore, if the noise is incoherent—for example, depolarizing or dephasing noise—the total variation distance between the noisy output distribution and the uniform distribution$$p_{\text {noisy}}$$ ${p}_{\text{noisy}}$ decays at precisely the same rate. Consequently, the noisy output distribution can be approximated as$$p_{\text {unif}}$$ ${p}_{\text{unif}}$ . In other words, although at least one local error occurs with probability$$p_{\text {noisy}}\approx Fp_{\text {ideal}}+ (1F)p_{\text {unif}}$$ ${p}_{\text{noisy}}\approx F{p}_{\text{ideal}}+(1F){p}_{\text{unif}}$ , 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$$1F$$ $1F$ . Thus, the “whitenoise approximation” is meaningful when$$O(F\epsilon \sqrt{s})$$ $O\left(F\u03f5\sqrt{s}\right)$ , a quadratically weaker condition than the$$\epsilon \sqrt{s} \ll 1$$ $\u03f5\sqrt{s}\ll 1$ requirement to maintain high fidelity. The bound applies if the circuit size satisfies$$\epsilon s\ll 1$$ $\u03f5s\ll 1$ , which corresponds to only$$s \ge \Omega (n\log (n))$$ $s\ge \Omega (nlog(n\left)\right)$logarithmic depth circuits, and if, additionally, the inverse error rate satisfies , which is needed to ensure errors are scrambled faster than$$\epsilon ^{1} \ge {\tilde{\Omega }}(n)$$ ${\u03f5}^{1}\ge \stackrel{~}{\Omega}\left(n\right)$F decays. The whitenoise approximation is useful for salvaging the signal from a noisy quantum computation; for example, it was an underlying assumption in complexitytheoretic 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 secondmoment quantities in random quantum circuits to expectation values of certain stochastic processes for which we compute upper and lower bounds. 
Instruction scheduling is a key compiler optimization in quantum computing, just as it is for classical computing. Current schedulers optimize for data parallelism by allowing simultaneous execution of instructions, as long as their qubits do not overlap. However, on many quantum hardware platforms, instructions on overlapping qubits can be executed simultaneously through global interactions. For example, while fanout in traditional quantum circuits can only be implemented sequentially when viewed at the logical level, global interactions at the physical level allow fanout to be achieved in one step. We leverage this simultaneous fanout primitive to optimize circuit synthesis for NISQ (Noisy IntermediateScale Quantum) workloads. In addition, we introduce novel quantum memory architectures based on fanout.Our work also addresses hardware implementation of the fanout primitive. We perform realistic simulations for trapped ion quantum computers. We also demonstrate experimental proofofconcept of fanout with superconducting qubits. We perform depth (runtime) and fidelity estimation for NISQ application circuits and quantum memory architectures under realistic noise models. Our simulations indicate promising results with an asymptotic advantage in runtime, as well as 7–24% reduction in error.more » « less

Understanding the computational power of noisy intermediatescale quantum (NISQ) devices is of both fundamental and practical importance to quantum information science. Here, we address the question of whether erroruncorrected 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 realtime 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 twoqubit 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 stateoftheart supercomputers.more » « less

Abstract The quantum approximate optimization algorithm (QAOA) is an approach for nearterm quantum computers to potentially demonstrate computational advantage in solving combinatorial optimization problems. However, the viability of the QAOA depends on how its performance and resource requirements scale with problem size and complexity for realistic hardware implementations. Here, we quantify scaling of the expected resource requirements by synthesizing optimized circuits for hardware architectures with varying levels of connectivity. Assuming noisy gate operations, we estimate the number of measurements needed to sample the output of the idealized QAOA circuit with high probability. We show the number of measurements, and hence total time to solution, grows exponentially in problem size and problem graph degree as well as depth of the QAOA ansatz, gate infidelities, and inverse hardware graph degree. These problems may be alleviated by increasing hardware connectivity or by recently proposed modifications to the QAOA that achieve higher performance with fewer circuit layers.more » « less