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 M32: Noisy Intermediate Scale Quantum Computers IVLive

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Sponsoring Units: DQI DCOMP Chair: Nicolas Sawaya, Intel Corp  Santa Clara 
Wednesday, March 17, 2021 11:30AM  11:42AM Live 
M32.00001: ManyBody Thermodynamics on Quantum Computers via Partition Function Zeros AKHIL FRANCIS, Daiwei Zhu, Cinthia Huerta Alderete, Sonika Johri, Xiao Xiao, James Freericks, Christopher Monroe, Norbert M Linke, Alexander F Kemper Partition functions are ubiquitous in physics: they are important in determining the thermodynamic properties of manybody systems, and in understanding their phase transitions. As shown by Lee and Yang, analytically continuing the partition function to the complex plane allows us to obtains its zeros and thus the entire function. Moreover, the scaling and nature of these zeros can elucidate phase transitions. Here we show how to find partition function zeros on noisy intermediatescale trapped ion quantum computers in a scalable manner, using the XXZ model as a prototype. We illustrate the transition from XYlike behavior to Isinglike behavior as a function of the anisotropy. While quantum computers cannot yet scale to the thermodynamic limit, our work provides a pathway to do so as hardware improves, allowing the determination of critical phenomena for systems that cannot be solved otherwise. 
Wednesday, March 17, 2021 11:42AM  11:54AM Live 
M32.00002: Quantum Algorithms for Open Lattice Field Theories Jay M. Hubisz, Bharath Sambasivam, Judah F UnmuthYockey Certain aspects of unitary quantum systems are welldescribed by nonHermitian effective Hamiltonians, as in the WignerWeisskopf (WW) theory for spontaneous decay. Conversely, any nonHermitian Hamiltonian can be embedded in a unital quantum channel via a generalization of the WW theory. This existence demonstrates the physical relevance of novel features like exceptional points in quantum dynamics and opens avenues for studying manybody systems in the complex plane of couplings. In the case of lattice field theory (LFT), locality/sparsity lends these channels the promise of efficient simulation on standard quantum hardware. We thus consider quantum operations that correspond to SuzukiLeeTrotter approximation of LFTs undergoing nonHermitian dynamics, with potential applicability to spin or gauge models at finite temperature, and/or chemical potential, to quantum phase transitions, and a class of theories with sign problems. We explore these channels on a benchmark, the 1D quantum transverse Ising model with an imaginary longitudinal magnetic field, showing that observables can probe the LeeYang edge singularity. Our channels can resolve this despite quantum jumps, and potentially other noise, making a coarse implementation viable for NISQ era technologies 
Wednesday, March 17, 2021 11:54AM  12:06PM Live 
M32.00003: Calculation of the Green's function on nearterm quantum computers Suguru Endo, Iori Kurata, Yuya O. Nakagawa The Green's function plays a crucial role when studying the nature of quantum manybody systems, especially strongly correlated systems. Although the development of quantum computers in the near future may enable us to compute energy spectra of classically intractable systems, methods to simulate the Green's function with nearterm quantum algorithms have not been proposed yet. Here, we propose two methods to calculate the Green's function of a given Hamiltonian on nearterm quantum computers. The first one makes use of a variational dynamics simulation of quantum systems and computes the dynamics of the Green's function in real time directly. The second one utilizes the Lehmann representation of the Green's function and a method which calculates excited states of the Hamiltonian. Both methods require shallow quantum circuits and are compatible with nearterm quantum computers. We numerically simulated the Green's function of the FermiHubbard model and demonstrated the validity of our proposals. 
Wednesday, March 17, 2021 12:06PM  12:18PM Live 
M32.00004: Digital quantum simulation of quantum synchronization dynamics on NISQ hardware Martin Koppenhoefer, Christoph Bruder, Alexandre Roulet Synchronization of nonlinear selfsustained oscillators is a widespread phenomenon in nonlinear dynamics, engineering, and biology. In the quantum regime, synchronization dynamics shows genuine quantum features, which stem from energy quantization and interference phenomena. Observing these effects experimentally is challenging because both coherent and dissipative dynamics of a nonlinear oscillator must be controlled in the quantum regime. However, recently, we demonstrated quantum synchronization effects by a digital quantum simulation of a spin1 limitcycle oscillator on the IBM Q system. In this talk, we will discuss how the perturbative structure of quantum synchronization dynamics can be used to simplify the wellknown algorithm of digital quantum simulation. This modification renders the circuit compatible with current noisy intermediatescale quantum hardware while it ensures that one can still observe quantum synchronization effects. 
Wednesday, March 17, 2021 12:18PM  12:30PM Live 
M32.00005: A flexible initializer for parametrized quantum circuits Frederic Sauvage, Alejandro PerdomoOrtiz Compared to faulttolerant quantum computing, variational quantum algorithms (VQAs) hold the hope for a quantum advantage of practical relevance in a not too distant future. However, optimization of circuit parameters remains arduous and is impeded by many obstacles such as the presence of barren plateaus and many local minima in the optimization landscape. Hence, developing more efficient strategies for training parametrized quantum circuits (PQCs) is needed to unlock the full potential offered by VQAs. Extending ideas from the field of metalearning, we address this task from an initialization perspective, and propose a FLexible Initializer for Parametrized quantum circuits (FLIP) scheme which can be applied to any family of PQCs. FLIP is tailored to learn the structure of successful parameters from a small number of related problems used as the training set. Once trained it can be used on similar problems and show a dramatic advantage over random initialization and also over more involved metalearning initialization strategies. Furthermore FLIP accommodates quantum circuits of arbitrary sizes and we show that it can be employed on circuits larger than the ones seen during training: a feature lacking in other metalearning parameter initializing strategies proposed to date. 
Wednesday, March 17, 2021 12:30PM  12:42PM Live 
M32.00006: Quantum optimization experiments with advanced mixers and controls M. Sohaib Alam, Shon Grabbe, Alexander Hill, Mark Hodson, Zoe Gonzalez Izquierdo, Ryan LaRose, Aaron Lott, Matt Reagor, Eleanor G Rieffel, James Sud, Davide Venturelli, Zhihui Wang, Filip Wudarski Modern quantum optimization methods feature quantum circuits with partiallyordered modular levels, such as the Quantum Alternating Operator Ansatz^{1}. For QAOA to work in practice on NISQ devices, it must extract value from quantum effects despite daunting fidelity degradation due to noise^{2}. Our experiments on a Rigetti processor, featuring these kind of algorithms, employ calibrated parametric CZ^{3} and XY^{4,5} gates, as well as analogcontrolled phases between qubit pairs programmed with a lowlevel pulse design language (Quilt). We show experimental benchmark results on a 32qubit chip for circuits related to hardconstrained scheduling problems as well as MaxCut. 
Wednesday, March 17, 2021 12:42PM  12:54PM Live 
M32.00007: Reducing circuit size in the variational quantum eigensolver  Part 1: Theory Tanvi Gujarati, Andrew Eddins, Sergey Bravyi, Charles Hadfield, Antonio Mezzacapo, Mario Motta, Sarah Sheldon The variational quantum eigensolver (VQE) is a promising technique for the nearterm application of quantum coherent processors to the study of chemical and physical systems. However, the maximum accessible problem size is limited by the number of qubits in a processor that can be mutually entangled with high fidelity. For instance, swap operations needed to distribute entanglement across a device with limited connectivity can quickly consume the available error budget. Here we discuss how to soften this limitation by leveraging the structure of certain simulation problems to reduce the required circuit size. In the first half of our twopart presentation, we will discuss the theoretical formulation of our approach, and applicability to problems of interest. In the second half, we will present data from quantum hardware demonstrating the viability of the approach, and discuss technical details of the experimental realization. 
Wednesday, March 17, 2021 12:54PM  1:06PM Live 
M32.00008: Reducing circuit size in the variational quantum eigensolver  Part 2: Experiment Andrew Eddins, Tanvi Gujarati, Sergey Bravyi, Charles Hadfield, Antonio Mezzacapo, Mario Motta, Sarah Sheldon The variational quantum eigensolver (VQE) is a promising technique for the nearterm application of quantum coherent processors to the study of chemical and physical systems. However, the maximum accessible problem size is limited by the number of qubits in a processor that can be mutually entangled with high fidelity. For instance, swap operations needed to distribute entanglement across a device with limited connectivity can quickly consume the available error budget. Here we discuss how to soften this limitation by leveraging the structure of certain simulation problems to reduce the required circuit size. In the first half of our twopart presentation, we will discuss the theoretical formulation of our approach, and applicability to problems of interest. In the second half, we will present data from quantum hardware demonstrating the viability of the approach, and discuss technical details of the experimental realization. 
Wednesday, March 17, 2021 1:06PM  1:18PM Live 
M32.00009: Mitigating global depolarizing noise with noise estimation circuits Miroslav Urbanek, Benjamin Nachman, Andre He, Christian W Bauer, Wibe A De Jong A significant problem for existing quantum computers is noise. While there are many distinct noise channels, the depolarizing noise model can often appropriately describe average noise for large circuits involving many qubits and gates. We present a method to mitigate the global depolarizing noise by first estimating its rate by executing a noise estimation circuit and then correcting the output of the target circuit using the estimated noise rate. A noise estimation circuit is a circuit that has a similar structure as the target circuit, has a welldefined output, and is classically simulable. We further utilize randomized compiling to convert incoherent noise to coherent noise. The method is experimentally validated on several test cases. 
Wednesday, March 17, 2021 1:18PM  1:30PM Live 
M32.00010: Error mitigation with Clifford quantumcircuit data Piotr Czarnik, Andrew Arrasmith, Patrick Coles, Lukasz Cincio Achieving nearterm quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable errormitigation method that applies to gatebased quantum computers [1]. The method generates training data {X_{i}^{noisy}, X_{i}^{exact} } via quantum circuits composed largely of Clifford gates, which can be efficiently simulated classically, where X_{i}^{noisy} and X_{i}^{exact} are noisy and noiseless observables respectively. Fitting a linear ansatz to this data then allows for the prediction of noisefree observables for arbitrary circuits. We analyze the performance of our method versus the number of qubits, circuit depth, and number of nonClifford gates. We obtain an orderofmagnitude error reduction for a groundstate energy problem on 16 qubits in an IBMQ quantum computer and on a 64qubit noisy simulator. 
Wednesday, March 17, 2021 1:30PM  1:42PM Live 
M32.00011: Filter functions for robust quantum control Tobias Hangleiter, Julian David Teske, Isabel NhÃ£ Minh Le, Pascal Cerfontaine, Hendrik Bluhm Correlated noise such as the 1/f noise found in many solidstate systems limits the improvement of gate fidelities in quantum information processors because it is unfeasibly expensive to simulate using conventional methods. This issue is exacerbated when considering algorithms in the presence of noise with correlation times larger than gate durations as gate errors may interfer. Previously, we have shown how filter functions can be used to compute the effect of such noise on gate sequences. Here, I will show how the effect can be efficiently mitigated in gradientbased robust quantum control by introducing analytical results for the derivatives of filter functions. Filter functions represent a spectrally resolved susceptibility to external perturbations and allow for computing complete quantum processes and hence also gate fidelities or leakage rates. Using the analytical expressions for the gradients, we can efficiently optimize control pulses for highfidelity gates. As an example, I show how one can obtain Rabi pulses that are robust against 1/f noise. I conclude by presenting the opensource filter_functions software framework (https://github.com/qutech/filter_functions), which facilitates computing filter functions and their derivatives for arbitrary quantum gates. 
Wednesday, March 17, 2021 1:42PM  1:54PM Live 
M32.00012: Energy gap calculation on nearterm quantum hardware with robust phase estimation Antonio Russo, Andrew D Baczewski, Benjamin C. A. Morrison, Kenneth Rudinger Can alternative approaches to phase estimation yield better results for chemical simulation on NISQ hardware? Robust phase estimation (RPE) calculates the difference in phases between two eigenstates of a unitary, provided oracular access to that unitary and the relevant eigenstates. In contrast to conventional phase estimation, it does not require a controlledU and is naturally resistant to state preparation and measurement errors. 
Wednesday, March 17, 2021 1:54PM  2:06PM Live 
M32.00013: Measuring global state properties with simple random singlequbit rotations Yariv Yanay, Charles Tahan State tomography and other measures of the global properties of a quantum state are indispensable tools in understanding many body physics through quantum simulators. Unfortunately, the number of measurements of the system required to estimate these global quantities scales exponentially with system size. The use of random rotations can greatly reduce the basis of this exponent. We focus on experimentally relevant protocols for state tomography and state purity measurement in superconducting qubits, relying on simple X/Y rotations only. We show a framework for evaluating such protocols, and analytically calculate the required number of measurements, finding significant improvement in the scaling behavior. 
Wednesday, March 17, 2021 2:06PM  2:18PM Live 
M32.00014: Unified approach to datadriven quantum error mitigation Angus Lowe, Max Hunter Gordon, Piotr Czarnik, Andrew Arrasmith, Patrick Coles, Lukasz Cincio

Wednesday, March 17, 2021 2:18PM  2:30PM Live 
M32.00015: Randomized Benchmarking for Continuosly Parametrized Entangling Gates Karl Mayer, Charles H Baldwin, David Hayes We present a variation of the randomized benchmarking (RB) protocol in which random sequences are drawn from a twirling group containing entangling gates with arbitrary rotation angles. Under standard RB assumptions, the average noise channel twirls to a sum of projectors onto the irreducible representations (irreps) of the group. The decay parameters associated with the irreps are isolated by measuring a suitable POVM and applying a transformation to the outcome distribution. We apply this technique to several groups, including the group generated by the twoqubit Pauli operators and continuously parametrized MolmerSorenson (MS) gates, which are realizable as the native entangling gates in a trapped ion architecture. The protocol estimates the average fidelity and determines the blockdiagonal components of the noise on the MS gates projected onto each irrep. We simulate this method and show that the precision of the noise estimates compares favorably to joint process and measurement tomography, indicating that the tomographic information can be extracted in a manner that is robust to state prep and measurement errors. 
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