Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session B40: Noisy Intermediate Scale Quantum Computers IIFocus Recordings Available

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Sponsoring Units: DQI DCOMP Chair: PierreLuc DallaireDemers, Pauli Group Room: McCormick Place W196B 
Monday, March 14, 2022 11:30AM  11:42AM 
B40.00001: Quantum advantages for Pauli channel estimation Senrui Chen, Sisi Zhou, Alireza Seif, Liang Jiang An important challenge for the NISQ era is to demonstrate a practical quantum advantage. In this work, we show that quantum resources provide an exponential advantage in sample complexity for Pauli channel estimation, which is both a fundamental problem and an important subroutine for benchmarking nearterm quantum devices. The specific task we consider is to simultaneously learn all the eigenvalues of an nqubit Pauli channel to ε precision. We give an estimation protocol with an nqubit ancilla that succeeds with high probability using only O(n/ε^{2}) copies of the Pauli channel, while proving that any ancillafree protocol (possibly with adaptive control and channel concatenation) would need at least Ω(2^{n/3}) rounds of measurement. We further study the advantages provided by a small amount of ancilla: For the case that a kqubit ancilla (k≤n) is available, we obtain a sample complexity lower bound of Ω(2^{(nk)/3}) for any nonconcatenating protocol, and a stronger lower bound of Ω(2^{nk}) for any nonadaptive nonconcatenating protocol, which is shown to be tight. We then show how to apply the ancillaassisted protocol to a practical quantum device characterization task in a noiseresilient and sampleefficient manner. Our results provide a practically interesting example for quantum advantages in learning, and also bring new insight for quantum device characterization. 
Monday, March 14, 2022 11:42AM  11:54AM 
B40.00002: Pushing the Limit of Quantum Chemistry Simulations with IonTrap Hardware Luning Zhao, Sonika Johri, Jacek Jakowski, Titus Morris, Raphael Pooser, Daiwei Zhu The variational quantum eigensolver (VQE) is a promising approach to simulate molecular systems in the NISQ era, as it requires much shallower quantum circuits than quantum phase estimation. However, the low gate fidelity of currently available quantum computers severely limits its quantum chemistry application. In this work, we aim to push the limit of VQE chemistry simulations using the highfidelity, 11qubit iontrap quantum computers provided by IonQ. By testing the IonQ quantum computer with 2electron, 4qubit problems with error mitigation techniques, we have obtained results with improved accuracy compared to previous demonstration of benchmarks. As we shall show in our latest results for 2electron, 6qubit metal hydrides simulations, ion trap quantum computer's alltoall connectivity offers a great deal of flexibility to optimize the VQE circuits by reducing the number of twoqubit entangling gates. Pairing the optimized circuit with error detection techniques based on symmetry verification, hidden inverse, and density matrix purification, we simulate small molecular systems such as metal hydrides with a 2electron, 6qubit active space and beyond to chemical accuracy. 
Monday, March 14, 2022 11:54AM  12:06PM 
B40.00003: A QubitEfficient Encoding Scheme for Quantum Simulations of Electronic Structure PeiKai Tsai, Shee Yu, ChengLin Hong, HaoChung Cheng, HsiSheng Goan Simulating electronic structure on a quantum computer requires encoding of fermionic systems onto qubits. Common encoding methods transform a fermionic system of N spinorbitals into an Nqubit system, but many of the fermionic configurations do not respect the required conditions and symmetries of the system so the qubit Hilbert space in this case may have unphysical states and thus can not be fully utilized. We propose a generalized qubitefficient encoding (QEE) scheme that requires the qubit number to be only logarithmic in the number of configurations that satisfy the required conditions and symmetries. For the case of considering only the particleconserving and singlet configurations, we reduce the qubit count to O(mlog_{2}N), where m is the number of particles. This QEE scheme is demonstrated on an H_{2} molecule in the 631G basis set and a LiH molecule in the STO3G basis set using fewer qubits than the common encoding methods. We calculate the groundstate energy surfaces using a variational quantum eigensolver algorithm with a hardwareefficient ansatz circuit. We choose to use a hardwareefficient ansatz since most of the Hilbert space in our scheme is spanned by desired configurations so a heuristic search for an eigenstate is sensible. The simulations are performed on the Qiskit simulator with a noise model implemented from a real IBM Quantum machine. Using the methods of measurement error mitigation and errorfree linear extrapolation, we demonstrate that most of the distributions of the extrapolated energies using our QEE scheme agree with the exact results obtained by Hamiltonian diagonalization in the given basis sets within chemical accuracy. Our proposed scheme and results show the feasibility of quantum simulations for larger molecular systems in the noisy intermediatescale quantum (NISQ) era. 
Monday, March 14, 2022 12:06PM  12:18PM 
B40.00004: Simulating the Mott transition on a noisy digital quantum computer via Cartanbased fastforwarding circuits Thomas M Steckmann, Trevor A Keen, Alexander F Kemper, Eugene F Dumitrescu, Yan Wang Dynamical meanfield theory (DMFT) maps the local Green's function of the Hubbard to that of the Anderson impurity model. Quantum algorithms have been proposed to speed up solving the impurity model by preparing and evolving the ground state under the impurity Hamiltonian, which is the most expensive part of the calculation for DMFT. To improve existing quantum algorithms for the twosite DMFT problem and obtain quantitatively accurate results on noisy quantum hardware, we propose a highly optimized fastforwarding quantum circuit. Our Cartan decomposition based algorithm introduces no timediscretization errors and uses a fixed depth quantum circuit to evolve an initial state over any time. By exploiting the structure of the fastforwarding circuits, we sufficiently reduce the gate cost to simulate the dynamics of, and extract frequencies from, the Anderson impurity model on noisy quantum hardware and demonstrate the Mott transition. Especially near the Mott phase transition when the quasiparticle resonance frequency approaches zero and evolving the system over longtime scales is necessary, our method maintains accuracy where Trotter error would otherwise dominate. 
Monday, March 14, 2022 12:18PM  12:30PM 
B40.00005: Simulation of the Hubbard Model as an Open Quantum system on Nearterm Quantum Computers Brian W Rost Open quantum systems are everywhere in real life, whether it is systems exposed to temperature, electric field, or anything that causes dissipation and/or driving. I will be describing a couple of such systems that we have run on quantum hardware [1], which turns out to be an excellent platform for such simulations, being inherently robust against quantum hardware errors even with deep circuits. We give two examples: 1) we simulate one thousand steps of time evolution for the noninteracting limit of the infinite drivendissipative Hubbard model and calculate the current through the system; and 2) we prepare a thermal state of the atomic limit of the Hubbard model in a magnetic field. These problems were solved using circuits containing up to two thousand entangling gates on quantum computers made available by IBM, showing no signs of decreasing fidelity at long times. Our results demonstrate that algorithms for simulating dissipative problems are able to far outperform similarly complex nondissipative algorithms on noisy hardware. Our two examples are the basic building blocks of many condensed matter physics systems, and we anticipate their demonstrated robustness to hold with increasing complexity of drivendissipative problems. 
Monday, March 14, 2022 12:30PM  12:42PM 
B40.00006: Quantum Computation of Molecular Green's Functions in the Frequency Domain Using MultiControlled Gates ShiNing Sun, Brian Marinelli, Yosep Kim, Long B Nguyen, Jin Ming Koh, Irfan Siddiqi, Austin J Minnich The Green's function provides fundamental information about the response properties and correlation effects of a physical system and has been a primary target in quantum simulation of manybody physics. Several protocols of computing Green's functions in the frequency domain on quantum computers have been proposed, but their experimental demonstrations are hindered by the lack of efficient implementation of multicontrolled gates present in these protocols. In this work, we employ a recently proposed hardwareefficient implementation of a Toffoliclass gate on fixedfrequency transmons to calculate frequencydomain Green's functions of diatomic molecules. We obtain quasiparticle spectra and correlation energies of the diatomic molecules from the computed frequencydomain Green's functions. Our work demonstrates practical usage of multicontrolled gates for simulating quantum manybody physics on nearterm quantum hardware. 
Monday, March 14, 2022 12:42PM  1:18PM 
B40.00007: Accurately computing the electronic properties of a quantum ring Invited Speaker: Charles Neil A promising approach to study condensedmatter systems is to simulate them on an engineered quantum platform. However, achieving the accuracy needed to outperform classical methods has been an outstanding challenge. Here, using eighteen superconducting qubits, we provide an experimental blueprint for an accurate condensedmatter simulator and demonstrate how to probe fundamental electronic properties. We benchmark the underlying method by reconstructing the singleparticle bandstructure of a onedimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors and arrive at an accuracy in measuring energy eigenvalues of this wire with an error of ~0.01 radians. Insight into this unprecedented algorithm fidelity is gained by highlighting robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 1e4 radians. Furthermore, we synthesize magnetic flux and disordered local potentials, two key tenets of a condensedmatter system. When sweeping the magnetic flux, we observe avoided level crossings in the spectrum, a detailed fingerprint of the spatial distribution of local disorder. Combining these methods, we reconstruct electronic properties of the eigenstates where we observe persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation and paves the way to study novel quantum materials with superconducting qubits. 
Monday, March 14, 2022 1:18PM  1:30PM 
B40.00008: Finding excited states on a quantum computer using unitary block optimization with VQE Faisal Alam, Lucas Slattery, Bryan K Clark The variational quantum eigensolver (VQE) is a well studied quantum algorithm for finding ground states of quantum systems. Significantly less work has been dedicated to finding excited states. In this presentation we describe a DMRG inspired framework called the unitary block optimization scheme to optimize and find excited states on a quantum computer. We describe our algorithm and benchmark and compare it against other approaches in finding low lying excited states of spin models. 
Monday, March 14, 2022 1:30PM  1:42PM 
B40.00009: Quantum computation of molecular structure using data from challengingtoclassicallysimulate nuclear magnetic resonance experiments Thomas E O'Brien, Lev B Ioffe, Yuan Su, David Fushman, Hartmut Neven, Ryan Babbush, Vadim Smelyanskiy We propose a quantum algorithm for inferring the molecular nuclear spin Hamiltonian from timeresolved measurements of spinspin correlators, which can be obtained via nuclear magnetic resonance (NMR). We focus on learning the anisotropic dipolar term of the Hamiltonian, which generates dynamics that are challengingtoclassicallysimulate in some contexts. We demonstrate the ability to directly estimate the Jacobian and Hessian of the corresponding learning problem on a quantum computer. We develop algorithms for performing this computation on both noisy nearterm and future faulttolerant quantum computers. We argue that the former is promising as an early beyondclassical quantum application since it only requires evolution of a local spin Hamiltonian. We isolate small spin clusters in a protein example (ubiquitin), demonstrate the convergence of our learning algorithm on one such example, and then investigate the learnability of these clusters as we cross the ergodic to nonergodic phase transition by suppressing the dipolar interaction. We see a clear correspondence between a drop in the multifractal dimension measured across manybody eigenstates of these clusters, and a transition in the structure of the Hessian of the learning costfunction (from degenerate to learnable). 
Monday, March 14, 2022 1:42PM  1:54PM 
B40.00010: Quantumclassical hybrid algorithms for computing imaginarytime response functions on noisy intermediatescale quantum devices Rihito Sakurai, Wataru Mizukami, Hiroshi Shinaoka Quantum embedding methods are theoretical approaches to study strongly correlated systems, formulated in terms of correlated electrons coupled to an effective environment. The dynamic meanfield theory (DMFT) is a representative example [1,2], where the effective environment is represented by a quantum impurity problem. The biggest bottleneck in DMFT calculations is solving the quantum impurity model numerically, i.e., computing the Green's function. 
Monday, March 14, 2022 1:54PM  2:06PM 
B40.00011: Calculating the ground state energy of benzene under spatial deformations with noisy quantum computing. Wassil Sennane, Marko J Rančić In this manuscript, we calculate the ground state energy of benzene under spatial deformations by using the variational quantum eigensolver (VQE). The ultimate goal of the study is estimating the feasibility of using quantum computing ansatze on nearterm devices for solving problems with large number of orbitals in regions where classical methods are known to fail. The center of our study are the hardware efficient and quantum unitary coupled cluster ansatz (qUCC). Our advanced simulation platform allows us to incorporate a realistic idle noise model  describing noise in quantum devices with a full Krauss operator formalism. We find that the hardware efficient ansatz in the presence of realistic noise outperforms mean fieldmethods and fullconfiguration interaction with orbital freezing for extreme deformations of benzene. On the other hand the qUCC ansatz has deeper circuits and thus the effect of noise is so extreme that the energies obtained with that method do not outperform meanfield theories. We therefore foresee that the qUCC method will remain a method for simulators of quantum computers in the preerrorcorrection era, while the hardware efficient ansatz can be utilized on current day hardware. 
Monday, March 14, 2022 2:06PM  2:18PM 
B40.00012: Variational Hamiltonian Ansatz for 1D Hubbard chains Baptiste ANSELME MARTIN, Pascal SIMON, Marko RANCIC To circumvent noise limitations of current day quantum hardware, hybrid quantumclassical methods have been proposed. Among those, the Variational Quantum Eigensolver (VQE) has been implemented on intermediate size quantum computers. Here, the quantum computer produces a parametrized state, whose energy is minimized in a classicalquantum optimization loop. In this work we investigate the simulation of the strongly correlated ground states of the 1D Hubbard model on a quantum computer using the Variational Hamiltonian Ansatz. We quantify how short circuit depth affects the quality of optimized states in terms of fidelity and physical properties. We show that short VHA ansätze are still able to capture qualitatively the main features of the 1D Hubbard model with strong Coulomb repulsion such like the decreasing number of doubly occupied sites or spin correlations, indicating that the variational states lie in a physically relevant subspace of the total Hilbert space. We perform simulations of the algorithm including noise models for small size Hubbard chains. Although performance was greatly affected by hardware noise, zeronoise extrapolation techniques such as Richardson extrapolation allowed the partial mitigation of noise from our calculation. 
Monday, March 14, 2022 2:18PM  2:30PM 
B40.00013: Dynamical mean field theory algorithms for quantum computers Francois Jamet We present quantum algorithms to perform calculations for condensed matter systems on currently available quantum computers. Recent developments of noisy intermediate scale quantum (NISQ) computers open a new route for materials simulations that have exponential scaling with system size on classical computers. Quantum embedding approaches, such as dynamical meanfield theory (DMFT), provide corrections to firstprinciples calculations for strongly correlated materials, which are poorly described at lower levels of theory. Such embedding approaches are computationally demanding on classical computing architectures and hence remain restricted to small systems, limiting the scope of their applicability. Here we present the Krylov variational quantum algorithm (KVQA) with improved scaling properties, which allows to perform simulations for real material systems on quantum computing emulators (arXiv:2105.13298). We then present a method based on the maximally localised dynamical embedding (MLDE), and show how it allows to reduce the number of qubits required for DMFT simulations (Nature Comp. Sci. 1, 410 (2021)). 
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