Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session K40: Noisy Intermediate Scale Quantum Computers VIFocus Recordings Available

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Sponsoring Units: DQI DCOMP Chair: Nicholas Rubin, Google Room: McCormick Place W196B 
Tuesday, March 15, 2022 3:00PM  3:12PM 
K40.00001: Population dynamics theory for noisy random circuits: outoftime ordered correlators and circuit fidelity Kechedzhi Kostyantyn, Igor L Aleiner, Xiao Mi, Pedram Roushan, Chris Quintana, Salvatore Mandra, Jeffrey Marshall, Charles J Neill, Vadim Smelyanskiy, Yu Chen Random circuits were used to realize a quantum computation challenging the capacity of classical computers, Nature, 574, 505, (2019). Random circuits are also subsequently used as a metrology tool in NISQ devices. Both these applications rely on convergence to the universal unitary random matrix statistics and the associated PorterThomas distribution. However, depth of practically implemented circuits is often linear in system size and therefore convergence to PorterThomas needs to be analyzed carefully especially in presence of noise. In this work we address such intermediate depth dynamics theoretically. We developed a mapping of quantum dynamics in random unitary circuits to the classical random process akin to the population dynamics in biology. This population dynamics is defined by classical rules of propagation, creation and annihilation of "charges", invariants under rotations in the space of operators. These rules are derived from the entangling two qubit gate of the random circuit. Population dynamics predicts the dynamics at all time scales between an initial product state and the PorterThomas limit. It also accounts for the effect of noise and errors in the hardware. We predict dynamics of outoftime order correlators (OTOCs), Loschmidt echo (LE) and linear cross entropy (lXEB). Theoretical predictions for OTOCs demonstrate good agreement with 53qubit experiments. 
Tuesday, March 15, 2022 3:12PM  3:24PM 
K40.00002: Efficient approximation of experimental Gaussian boson sampling Benjamin Villalonga, Murphy Yuezhen Niu, Li Li, Hartmut Neven, John C Platt, Vadim Smelyanskiy, Sergio Boixo Recent landmark experiments have performed Gaussian boson sampling (GBS) with a nonprogrammable linear interferometer and threshold detectors on up to 144 output modes. We introduce a family of classical algorithms that approximately sample from the output of a GBS experiment at a cost polynomial in the number of modes. The quality of our mockup samplers increases with k, the “order” of the sampler, albeit at a cost exponential in k. Our numerical findings provide evidence that already at order k=2 (with cost quadratic in the number of modes) these algorithms approximate the ideal GBS distribution with lower statistical distance than current experiments, which suffer from experimental imperfections. This is a 2nd order approximation, with the uniform and thermal approximations corresponding to 0th and 1st order, respectively. The kth order approximation reproduces Ursell functions up to order k with a cost exponential in k and high precision, while experiments exhibit higher order Ursell functions with lower precision. Our approximations provide a family of strong classical contenders that experiments should be benchmarked against, as well as insight on the nature of the hardness of noisy GBS. Interestingly, the strategy we exploit does not apply to random circuit sampling. 
Tuesday, March 15, 2022 3:24PM  3:36PM 
K40.00003: Classical simulation of boson sampling using graph structure Changhun Oh, Youngrong Lim, Bill Fefferman, Liang Jiang Boson sampling is a fundamentally and practically important task that can be used to demonstrate quantum advantages using noisy intermediatescale quantum devices. We study the computational complexity for boson sampling depending on circuit depths. Specifically, we propose a classical algorithm that takes advantage of graph structure of a given circuit and analyze its complexity. A notable property of our algorithm is that its complexity increases exponentially as socalled treewidth of a graph, which is closely related to connectivity of a circuit. Focusing on typical linear optical circuits composed of local random beam splitters, we show that when a linearoptical circuit has a low depth, its outcomes can be characterized by a constanttreewidth graph so that the algorithm can implement the corresponding boson sampling efficiently. We then show that after the threshold for easy sampling, the complexity becomes subexponential and finally exponential for sufficiently deep circuits. The latter is consistent with a generic classical boson sampling algorithm. Finally, we numerically implement a validation test with a smaller size of a recent Gaussian boson sampling experiment and show that our algorithm can pass the test for the circuit having limited connectivity. 
Tuesday, March 15, 2022 3:36PM  3:48PM 
K40.00004: NonRandomness of Google's Quantum Supremacy Benchmark Sangchul Oh, Sabre Kais The first achievement of quantum supremacy has been claimed recently by Google for the random quantum circuit benchmark with 53 superconducting qubits. Here, we analyze the randomness of Google's quantum randombit sampling. The heat maps of Google's random bitstrings show stripe patterns at specific qubits in contrast to the Haarmeasure or classical randombit strings. Google's data contains more bit 0 than bit 1, i.e., about 2.8 % difference, and fail to pass the NIST random number tests, while the Haarmeasure or classical randombit samples pass. Their difference is also illustrated by the MarchenkoPastur distribution and the Girko circular law of random matrices of random bitstrings. The calculation of the Wasserstein distances shows that Google's random bitstrings are farther away from the Haarmeasure random bitstrings than the classical random bitstrings. Our results imply that random matrices and the Wasserstein distance could be new tools for analyzing the performance of quantum computers. 
Tuesday, March 15, 2022 3:48PM  4:00PM 
K40.00005: Using the MERA tensor network ansatz on Honeywell's QCCD chips Johannes Hauschild, Michael P Zaletel, Sajant Anand, Andrew C Potter One of the main applications for quantum computers will be the simulation of other strongly correlated quantum manybody systems. Tensor networks ansatz states are well established for simulations of such systems on classical hardware, where they drastically reduce the computational cost. Here, we show one example where a tensor network helps to reduce the required number of qubits on quantum hardware. The multiscale entanglement renormalization ansatz (MERA) is a tensor network specifically designed to accurately capture the longrange correlations in the ground states of critical spin chains. The ability of Honeywell's quantum charge coupled devices (QCCD) to measure and reset a qubit midcircuit, in combination with the MERA ansatz, allows to obtain expectation values of an $N$ site spin chain with only $O(log(N))$ qubits, at the price of a larger depth of the circuit. We demonstrate the measurement of longrange correlation functions on the quantum hardware. Further, we discuss the tradeoff how a larger depth of the MERA network leads to a more accurate wave function representation, but also more statistical noise due to the larger circuit depth. 
Tuesday, March 15, 2022 4:00PM  4:12PM 
K40.00006: Complexity of sampling bosonic atoms in the presence of weak interactions Gopikrishnan Muraleedharan, Adrian K Chapman, Sayonee Ray, Akimasa Miyake, Ivan Deutsch We study the complexity of sampling from the particle number distribution of interacting bosonic atoms described by the BoseHubbard model. In the noninteracting limit, the problem is equivalent to sampling from a linear optical network, whose complexity has been well studied in the framework of Boson Sampling. For neutral atoms trapped in an optical lattice, residual interactions may exist between the atoms, which could crucially alter the sampling complexity from the noninteracting case. When interactions are weak, we show that the sampling complexity is close to that of the noninteracting evolution in the total variation distance (TVD). Using Hubbard Stratonovich transformation, we express the transition amplitudes as an ensemble average of random permanents and show that TVD is upper bounded by a polynomial in interaction strength, evolution time, and particle number. Further, assuming that an efficient circuit implementation of the BoseHubbard evolution exists, we apply the worsttoaveragecase hardness reduction technique to show that sampling with random interaction strength is also equivalent to the noninteracting case. We numerically verify our bounds in the settings of random hopping on an alltoall geometry, and uniform nearestneighbor hopping on a linear chain. 
Tuesday, March 15, 2022 4:12PM  4:48PM 
K40.00007: NISQ: Error Correction, Mitigation, and Noise Simulation Invited Speaker: Bei Zeng Errorcorrecting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, may have a wider range of uses, including information transmission, quantum simulation/computation, and faulttolerance. These invite us to rethink QEC, in particular, about the role that quantum physics plays in terms of encoding and decoding. The fact that many quantum algorithms, especially nearterm hybrid quantumclassical algorithms, only use limited types of local measurements on quantum states, leads to various new techniques called Quantum Error Mitigation (QEM). This work addresses the differences and connections between QEC and QEM, by examining different application scenarios. We demonstrate that QEM protocols, which aim to recover the output density matrix, from a quantum circuit do not always preserve important quantum resources, such as entanglement with another party. We then discuss the implications of noise invertibility on the task of error mitigation, and give an explicit construction called quasiinverse for noninvertible noise, which is tracepreserving while the MoorePenrose pseudoinverse may not be. We also study the consequences of erroneously characterizing the noise channels, and derive conditions when a QEM protocol can reduce the noise. 
Tuesday, March 15, 2022 4:48PM  5:00PM 
K40.00008: Sampling Complexity of Noisy and Monitored Random Circuits Abhinav Deshpande, Bill Fefferman, Alexey V Gorshkov, Michael J Gullans, Pradeep Niroula, Oles Shtanko Noise is an unavoidable barrier to achieving quantum advantage in nearterm quantum experiments. Without faulttolerance, any noisy quantum circuit is rendered classically simulable at highenough depth. We study the tradeoff between circuit size and noise rates to identify regimes where a quantum advantage might be achieved, using sampling complexity as a proxy. We use a statistical mechanical mapping for random circuits to show that the distribution of noisy random circuits converges to uniform distribution exponentially fast. We do this by proving upper and lower bounds on the expected total variation distance with respect to the uniform distribution, which take the form $\exp[\tilde{\Theta}(d)]$. In addition, we show that noisy circuits anticoncentrate as fast as noiseless circuits, whereas both of them fail to anticoncentrate at sublogarithmic depth. Our results put an upper limit to circuit depth for which we might anticipate averagecase sampling hardness. We further consider sampling complexity of monitored random circuits where a certain fraction, $p$ of qubits are measured at each time. Using results from percolation theory, we find evidence of worstcase sampling hardness below $p=0.5$, coinciding with an entanglement phase transition in the Hartley entropy. 
Tuesday, March 15, 2022 5:00PM  5:12PM 
K40.00009: Faster stabilizerstate simulation based on graph states Tim Coopmans, Matthijs Rijlaarsdam, David Elkouss Classical simulation is a crucial element of the performance prediction and design of NoisyIntermediate Scale Quantum (NISQ) computers. Since it is wellknown that quantum circuits with only Clifford gates can be simulated in polynomial time in the number of gates, current research is mainly focused on speedups for nonClifford gates. However, many scenarios would still benefit greatly from faster Cliffordgate simulation. One example are quantum networks, since most quantum network protocols only contain Cliffords and current hardware can to a large extent be modelled by Clifford noise. Moreover, for e.g. design optimization and Monte Carlo methods, the simulation algorithm will be run many times, thus amplifying any runtime gains manifold. Our contributions regard improvement of existing Cliffordgate simulation based on a graph state formalism, which is in many cases faster than the conventional stabilizerbased simulation approach. Specifically, we focus on faster simulation of individual twoqubit gates, as well as scheduling algorithms for sequences of twoqubit gates. We also provide algorithms for fidelity and partial trace. Numerics confirm our approach yields significant runtime improvements in many situations. 
Tuesday, March 15, 2022 5:12PM  5:24PM 
K40.00010: Sequential generation of tensor network states ZhiYuan Wei, Daniel Malz, Alejandro GonzalezTudela, Juan I Cirac The sequential generation of tensor network states provides a way to deterministically prepare entangled states on both matterbased and photonbased quantum devices. In this talk, first, we discuss two implementations to sequentially generate photonic matrix product states, one based on a Rydberg atomic array [1], and another based on a microwave cavity dispersively coupled to a transmon [2]. We show both implementations can generate a large number of entangled photons. Then, we introduce plaquette projected entangledpair states (pPEPS)[3], a class of states in a lattice that can be generated by applying sequential unitaries acting on plaquettes of overlapping regions. They satisfy arealaw entanglement, possess longrange correlations, and naturally generalize other relevant classes of tensor network states. We identify a subclass that can be more efficiently prepared in a radial fashion and that contains the family of isometric tensor network states. We also show how such subclass can be efficiently prepared using an array of photon sources, and devise a physical realization by extending the above cavitytransmon setup [2]. 
Tuesday, March 15, 2022 5:24PM  5:36PM 
K40.00011: Efficient Classical Simulation of Lindblad Dynamics Michael Marthaler, Keith R Fratus, JanMichael Reiner While many proof of principle experiments have been performed the fundamental computational power of NISQ computers is unclear. One path to approach this problem is to investigate methods on classical computer that can efficently simulate noisy quantum systems. In limits where this is possible a NISQ computer can fundamentally not achive quantum advantage. Many quantum systems described by the Lindblad equation have properties which make them especially amenable to classical solution. Here we outline our approach to the classical simulation of such systems using a nonlinear approximation to the Lindblad equation. We will present our results regarding the systems we have been able to exclude as potential demonstrations of quantum advantage, and also discuss potential future applications of the classical method we have developed. 
Tuesday, March 15, 2022 5:36PM  5:48PM 
K40.00012: Quantum Tensor Networks for NISQ  Simualtion and Machine Learning James Dborin Tensor network methods permit efficient computation of 1D and 2D quantum systems by concentrating computing and entanglement resources into relevant regions of Hilbert Space. Quantum computing is an emerging technology which could provide great advances in simulations of quanutm systems. Currently available noisy quantum computers, socalled NISQ devices, are limited in the entanglement they can generate. Quantum tensor network methods provide a way of translating classical tensor network algorithms to NISQ devices, allowing them to use limited entanglement resources more effectively. Here I discuss how to translate tensor networks algorithms for time evolution and ground state optimisation onto NISQ devices, and show how these can be used to simulate quanutm systems that are much larger than the quanyum device. I discuss how the burgeoning field of machine learning with classical tensor networks can be used to improve the performance of machine learning and VQE tasks performed on NISQ devices. 
Tuesday, March 15, 2022 5:48PM  6:00PM 
K40.00013: Continuoustime dynamics of noisy quantum circuits with arbitrary neuralnetwork ansätze Kaelan Donatella, Zakari Denis, Alexandre Le Boité, Cristiano Ciuti We present a numerical method to simulate the dynamics of lowentropy open quantum systems. The method is based on compressing the Hilbert space to a timedependent ``corner" subspace that supports faithful representations of the density matrix. We show that this compression enables one to efficiently simulate systems with moderate entropy irrespective of the quantum state's degree of entanglement. In addition, we propose a second compression step, which consists in representing each state of the corner subspace with a neuralnetwork ansatz. This enables the use of a wider class of ansätze for the dynamics of open quantum systems and for noisy quantum circuit simulation. We present benchmarks of the method using different ansätze. We then apply the method to (i) dissipative spin models and (ii) to noisy quantum circuits. 
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