Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session J32: Noisy Intermediate Scale Quantum Computers IIFocus Live

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Sponsoring Units: DQI DCOMP Chair: Nathan EarnestNoble 
Tuesday, March 16, 2021 3:00PM  3:12PM Live 
J32.00001: LargeScale Simulation of Quantum Circuits via Tensor Network Contraction Cupjin Huang, Fang Zhang, Michael Newman, Junjie Cai, Xun Gao, Zhengxiong Tian, Junyin Wu, Haihong Xu, Huanjun Yu, Bo Yuan, Mario Szegedy, Yaoyun Shi, Jianxin Chen In this work, we present a parallel tensor network contraction algorithm for quantum circuit simulations. The key ingredient for the efficient parallelization, called index slicing, reduces the space complexity and enables embarrassing parallelism with little total overhead. To benchmark the performance of the algorithm, we experiment on the Google Sycamore Random Circuit Sampling task performed by Arute et al. (Nature, 574, 505510 (2019)), which was initially estimated to require Summit, the world's most powerful supercomputer today, approximately 10,000 years. We estimate that our simulator can perform this task in less than 20 days on a Summitcomparable cluster. These estimates are based on explicit simulations of parallel subtasks, and leave no room for hidden costs. We further apply our algorithm to simulate quantum error correction under more realistic error models, as well as nearterm quantum algorithms. An implementation of the algorithm is now open sourced as Alibaba Cloud Quantum Development Platform. 
Tuesday, March 16, 2021 3:12PM  3:24PM Live 
J32.00002: NoiseInduced Barren Plateaus in Variational Quantum Algorithms Samson Wang, Enrico Fontana, Marco Cerezo, Kunal Sharma, Akira Sone, Lukasz Cincio, Patrick Coles Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy IntermediateScale Quantum (NISQ) computers. A natural question is whether the noise on NISQ devices places any fundamental limitations on the performance of VQAs. In this work, we rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of layers L. This implies exponential decay in the number of qubits n when L scales as poly(n), for sufficiently large coefficients in the polynomial. These noiseinduced barren plateaus (NIBPs) are conceptually different from noisefree barren plateaus, which are linked to random parameter initialization. Our result is formulated for an abstract ansatz that includes as special cases the Quantum Alternating Operator Ansatz (QAOA) and the Unitary Coupled Cluster Ansatz, among others. In the case of the QAOA, we implement numerical heuristics that confirm the NIBP phenomenon for a realistic hardware noise model. 
Tuesday, March 16, 2021 3:24PM  3:36PM Live 
J32.00003: Absence of Barren Plateaus in Quantum Convolutional Neural Networks Arthur Pesah, Marco Cerezo de la Roca, Samson Wang, Tyler Volkoff, Andrew Sornborger, Patrick Coles Quantum neural networks (QNNs) have generated excitement around the possibility of efficiently analyzing quantum data. But this excitement has been tempered by the existence of exponentially vanishing gradients, known as barren plateau landscapes, for many QNN architectures. Recently, Quantum Convolutional Neural Networks (QCNNs) have been proposed, involving a sequence of convolutional and pooling layers that reduce the number of qubits while preserving information about relevant data features. In this work, we rigorously analyze the gradient scaling for the parameters in the QCNN architecture. We find that the variance of the gradient vanishes no faster than polynomially, implying that QCNNs do not exhibit barren plateaus. This provides an analytical guarantee for the trainability of randomly initialized QCNNs, which singles out QCNNs as being trainable, unlike many other QNN architectures. To derive our results we introduce a novel graphbased method to compute expectation values over Haardistributed unitaries, which will likely be useful in other contexts. Finally, we perform numerical simulations to verify our analytical results. 
Tuesday, March 16, 2021 3:36PM  3:48PM Live 
J32.00004: Numerical Simulation of Large Scrambling Quantum Circuits Salvatore Mandra, Jeffrey Marshall, Kostyantyn Kechedzhi As Noisy IntermediateScale Quantum (NISQ) devices are becoming more available, it is important to identify meaningful physics inspired problems beyond randomized quantum circuits. In my talk I will present our latest large scale simulations of quantum scrambling circuits, with the goal to understand how quantum correlation propagates between qubits. As part of my talk, I will introduce the scrambling circuits used in our simulations and the numerical techniques (both exact and approximate) used to verify and benchmark the Sycamore@Google quantum chip. 
Tuesday, March 16, 2021 3:48PM  4:00PM Live 
J32.00005: Fermionic partial tomography via classical shadows Andrew Zhao, Nicholas Rubin, Akimasa Miyake We propose a tomographic protocol for estimating any kbody reduced density matrix (kRDM) of a fermionic state, a ubiquitous step in nearterm quantum algorithms for simulating manybody physics, chemistry, and materials. Our approach extends the framework of classical shadows, a randomized approach to learning a collection of quantum state properties, to the fermionic setting. Our sampling protocol employs randomized measurements generated by a discrete group of fermionic Gaussian unitaries, implementable with lineardepth circuits, to achieve nearoptimal scaling in the number of repeated state preparations required of fermionic RDM tomography. We also numerically demonstrate that our protocol offers a substantial improvement in constant overheads over prior stateoftheart for estimating 2, 3, and 4RDMs. 
Tuesday, March 16, 2021 4:00PM  4:36PM Live 
J32.00006: Classical algorithms for quantum mean values Invited Speaker: David Gosset We consider the task of estimating the expectation value of an nqubit tensor product observable in the output state of a shallow quantum circuit. This task is a cornerstone of variational quantum algorithms for optimization, machine learning, and the simulation of quantum manybody systems. Here we study its computational complexity for constantdepth quantum circuits and tensor products of singlequbit observables which are (a) close to the identity, (b) positive semidefinite, (c) arbitrary. We show that the mean value problem admits a classical approximation algorithm with polynomial runtime in case (a) and subexponential runtime in case (b). In case (c) we give a lineartime algorithm for geometrically local circuits on a twodimensional grid, which is based on a Monte Carlo method combined with Matrix Product State techniques. 
Tuesday, March 16, 2021 4:36PM  4:48PM Live 
J32.00007: Quantumenhanced analysis of discrete stochastic processes Carsten Blank, Kyungdeock Daniel Park, Francesco Petruccione Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have wide applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number of realizations increases exponentially with the number of time steps, and importance sampling is often required to reduce the variance. We propose a quantum algorithm for calculating the characteristic function of a DSP using the number of quantum circuit elements that grows only linearly with the number of time steps. The quantum algorithm reduces the sampling to a Bernoulli trial while taking all realizations into account. This approach guarantees the optimal variance without the need of importance sampling. The algorithm can be furnished with quantum amplitude estimation to provide additional speedup. The Fourier approximation can be used to estimate an expectation value of any integrable function of the random variable. We present an application in finance, and demonstrate the proofofprinciple using a IBM quantum device. 
Tuesday, March 16, 2021 4:48PM  5:00PM Live 
J32.00008: How efficiently can we simulate the open system dynamics of Ising models? Anupam Mitra, Tameem Albash, Akimasa Miyake, Ivan Deutsch A nearterm goal for Noisy Intermediate Scale Quantum (NISQ) devices is quantum simulation of nonequilibrium dynamics in manybody systems [Preskill Quantum 2, 79 (2018)]. While the exact unitary dynamics of a closed manybody quantum systems is generally intractable, recent work has shown that approximate simulations of NISQ devices are tractable [Zhou, et al, arXiv:2002.07730; Noh, et al, arXiv:2003.13163; Chen et al arXiv:2004.02388]. Inspired by experiments using arrays of Rydberg atoms and trapped ions, we study the quantum simulation of nonequilibrium dynamics of Ising spin chains in 1D. We assume open quantum system dynamics with local decoherence given by a Lindblad master equation, which we solve using quantum trajectories and tensor networks. We explore how decoherence and approximation using a truncated matrix product state representation effects the long range order observed in the nonequilibrium dynamics. We find that decoherence permits more aggressive truncation of matrix product states, suggesting that classical simulation of certain quantum observables may be tractable above a certain level of decoherence. 
Tuesday, March 16, 2021 5:00PM  5:12PM Live 
J32.00009: Simulating Noisy Quantum Circuits with Matrix Product Density Operators Bei Zeng Simulating quantum circuits with classical computers requires resources growing exponentially in terms of system size. Real quantum computer with noise, however, may be simulated polynomially with various methods considering different noise models. In this work, we simulate random quantum circuits in 1D with Matrix Product Density Operators (MPDO), for different noise models such as dephasing, depolarizing, and amplitude damping. We show that the method based on Matrix Product States (MPS) fails to approximate the noisy output quantum states for any of the noise models considered, while the MPDO method approximates them well. Compared with the method of Matrix Product Operators (MPO), the MPDO method reflects a clear physical picture of noise (with inner indices taking care of the noise simulation) and quantum entanglement (with bond indices taking care of twoqubit gate simulation). Consequently, in case of weak system noise, the resource cost of MPDO will be significantly less than that of the MPO due to a relatively small inner dimension needed for the simulation. In case of strong system noise, a relatively small bond dimension may be sufficient to simulate the noisy circuits, indicating a regime that the noise is large enough for an `easy' classical simulation. 
Tuesday, March 16, 2021 5:12PM  5:24PM Live 
J32.00010: TranslationInvariant FreeFermionSolvable Spin Models Adrian Chapman, Steven Flammia, Alicia Kollar We give an efficient algorithm for recognizing a freefermion solution in translationinvariant spin models using graph theory. When such a mapping does exist, the associated freefermion model may not itself be translationinvariant, but describes fermions coupled to a static gauge field whose configuration is captured by the orientation of a graph. This correspondence allows us to analyze the lowenergy behavior of these models using the socalled skewenergy of oriented graphs. We numerically investigate our characterization as applied to a variety of translationinvariant freefermion models. We expect these results to inform the design of freefermionsolvable subsystem codes with favorable spectra for error suppression. 
Tuesday, March 16, 2021 5:24PM  5:36PM Live 
J32.00011: Identification of SymmetryProtected Topological States on Noisy Quantum Computers Daniel Azses, Rafael Haenel, Yehuda Naveh, Robert Raussendorf, Eran Sela, Emanuele Dalla Torre Identifying topological properties is a major challenge because, by definition, topological states do not have a local order parameter. While a generic solution to this challenge is not available yet, a broad class of topological states, namely, symmetryprotected topological (SPT) states, can be identified by distinctive degeneracies in their entanglement spectrum. Here, we propose and realize two complementary protocols to probe these degeneracies based on, respectively, symmetryresolved entanglement entropies and measurementbased computational algorithms. The two protocols link quantum information processing to the classification of SPT phases of matter. They invoke the creation of a cluster state and are implemented on an IBM quantum computer. The experimental findings are compared to noisy simulations, allowing us to study the stability of topological states to perturbations and noise. 
Tuesday, March 16, 2021 5:36PM  5:48PM Live 
J32.00012: Computing Partition Functions on Limited Quantum Devices Andrew Jackson, Theodoros Kapourniotis, Animesh Datta We showcase an algorithm for approximating partition functions at (potentially) complex inverse temperatures. Compared to other partition function approximation algorithms, it is better suited for execution on near term devices due to significant reductions in the circuit depth, required number of qubits, and/or required number of measurements. All of which reduce the effect of noise on the computation. The key improvement is that the depth of the circuits required is independent of the real component of inverse temperature, hence low temperature physics (which for a stronglycorrelated system is classically much harder to study) are more accessible and can tolerate a greater error rate. 
Tuesday, March 16, 2021 5:48PM  6:00PM Live 
J32.00013: Stochastic simulation of open quantum systems on NISQ Computers Francesco Petruccione, Kyungdeock Daniel Park, JuneKoo(KEVIN) RHEE, Ilya Sinayskiy The unravelling of the quantum master equation (QME) based on quantum forking is proposed. Through the entanglement with log2(d) index qubits prepared in a superposition state, an initial quantum state can follow d quantum trajectories in superposition. An expectation value measurement on the target qubit at the end of the simulation yields the convex combination of the results from all possible paths, providing the ensembleaveraged solution of the QME. Regardless of the number of independent quantum trajectories needed in the unravelling, our method uses only a constant number of quantum circuit executions as well as the initial wave function. To simulate a generic stochastic SchrÃ¶dinger equation, one needs to be able to perform an arbitrary nonHermitian evolution. We also describe how this can be done systematically using projective measurement and postselection. As proof of concept, we demonstrate the parallel unravelling using IBMQ hardware. We implement unravelling of various singlequbit and twoqubit master equations. 
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