Bulletin of the American Physical Society
APS March Meeting 2023
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session F64: Quantum Simulation II: Estimating Ground StatesFocus
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Sponsoring Units: DQI Chair: Yanzhu Chen, Virginia Tech Room: Room 415 |
Tuesday, March 7, 2023 8:00AM - 8:12AM |
F64.00001: Accurate quantum chemistry calculations on near-term quantum computers enabled by the transcorrelated method Werner Dobrautz, Igor O Sokolov, Martin Rahm, Ali Alavi, Ivano Tavernelli Quantum computing has the potential to provide an exponential speedup compared to classical computers, but the practical implementation is still in its infancy. Two central questions are: (1) in which field the current noisy intermediate-scale quantum (NISQ) hardware can provide benefits compared to classical computers and (2) which methods and algorithms enable this advantage? |
Tuesday, March 7, 2023 8:12AM - 8:24AM |
F64.00002: Angular momentum entanglement of molecular interactions for quantum computing using solid harmonic Gaussian orbitals Anguang Hu, Hang Hu, Hsu Kiang (James) Ooi For quantum chemistry simulations, its molecular integral package is a crucial part of any quantum chemistry program. Unfortunately, efficient calculations of molecular integrals using quantum computers remain a big challenge. Solid harmonic Gaussian orbitals (SHGOs) are angular momentum eigenfunctions and can apply to calculate angular momentum entanglement of molecular integrals using quantum computers. Vector-coupling and vector-uncoupling schemes of quantum angular momenta correspond to unitary Clebsch-Gordan transformations to manipulate angular momentum entanglement of molecular interactions. The addition of quantum angular momentum and the product of Gaussian orbitals simultaneously apply to transform molecular multi-center interactions to one-center interactions, reducing the degree of entanglement using the orthonormality of SHGOs. This transformation also leads to simple analytical molecular integrals, revealing angular momentum entanglement interactions under nuclear and electron Coulomb fields. The molecular angular momentum entanglement provides quantum constraint to limit multipole interactions of Coulomb fields, resulting in highly efficient calculations of molecular integrals using quantum circuits of unitary and cascading Clebsch-Gordan transformations in quantum computers. |
Tuesday, March 7, 2023 8:24AM - 8:36AM |
F64.00003: Adaptive variational ground state preparation of spin-1 models with multiple spin-qubit encodings Joao C Getelina, Yong-Xin Yao, Peter P Orth, Thomas Iadecola Recent advances in quantum computing hardware have stimulated the search for efficient quantum algorithms tailored for current noisy devices. One of the main targets of these algorithms are quantum spin models that cannot be solved efficiently on classical computers. Here, we focus on interacting spin-1 models, which are known to exhibit rich phase diagrams as they can contain local anisotropy terms, modeling crystal field effects of higher-S spin materials such as rare-earth magnets, including much sought-after quantum spin liquids. We investigate the optimal spin-to-qubit encoding scheme and apply it to use adaptive variational quantum imaginary time evolution to determine the ground state of a general XXZ spin-1 Hamiltonian in a transverse field. We compare the required CNOT gates of four different binary encodings: the standard binary, the triplet-singlet representation, the Gray code, and the unary. Our results show that the triplet-singlet and the Gray encoding are comparable and perform much better than the unary encoding. |
Tuesday, March 7, 2023 8:36AM - 9:12AM |
F64.00004: Ground-state energy estimation on early fault-tolerant quantum computers Invited Speaker: Lin Lin The problem of estimating the ground-state energy of a quantum Hamiltonian is one of the most important and promising applications of early fault-tolerant quantum computers, which are expected to have a very limited number of logical qubits and may have difficulty in handling circuit beyond a certain maximal depth. We argue that algorithms based on the Hamiltonian evolution input model are suitable in the early-fault tolerant regime, can be as efficient as those based on the block encoding input model, and can achieve near-optimal complexities for estimating the ground-state energy and for preparing the ground state. We will also introduce new techniques to significantly reduce the preconstant of circuit depth, while maintaining Heisenberg-limited scaling. |
Tuesday, March 7, 2023 9:12AM - 9:24AM |
F64.00005: Quantum Gaussian filter for exploring ground-state properties Min-Quan He, Dan-Bo Zhang, Z. D. Wang Filter methods realize a projection from a superposed quantum state onto a target state, which can be efficient if two states have sufficient overlap. Here we propose a quantum Gaussian filter (QGF) with the filter operator being a Gaussian function of the system Hamiltonian. A hybrid quantum-classical algorithm feasible on near-term quantum computers is developed, which implements the quantum Gaussian filter as a linear combination of Hamiltonian evolution at various times. Remarkably, the linear combination coefficients are determined classically and can be optimized in the postprocessing procedure. Compared to the existing filter algorithms whose coefficients are given in advance, our method is more flexible in practice under given quantum resources with the help of postprocessing on classical computers. We demonstrate the quantum Gaussian filter algorithm for the quantum Ising model with numeral simulations under noises. We also propose an alternative full quantum approach that implements a QGF with an ancillary continuous-variable mode. |
Tuesday, March 7, 2023 9:24AM - 9:36AM |
F64.00006: Accurate quantum chemistry calculations using NISQ era quantum computers Ashutosh Kumar, Ayush Asthana, Vibin Abraham, Thomas D Crawford, Nicholas Mayhall, Yu Zhang, Lukasz Cincio, Sergei Tretiak, Pavel A Dub Accurate quantum simulation of molecular excited states is necessary to realize the quantum advantage in describing complex chemical phenomena. In this regard, we have developed an equation of motion (EOM) based quantum algorithm which is theoretically rigorous, requires fewer quantum resources and is expected to be more robust to noise than the current state-of-the art methods We demonstrate the usefulness of our approach by calculating ionization potentials, electron affinities and excitation energies of small molecular systems. Based on the insights developed from the EOM work, we recently developed an efficient quantum version of linear response theory (qLR) to calculate response properties like polarizabilities, specific rotation, etc. We illustrate the advantages associated with qLR theory by comparing it against the classical approaches. However, a quantitative description of these properties requires large number of basis functions or qubits. This is clearly a major bottleneck due to the limited qubit connectivity, short coherence times and sizable gate error rates associated with the contemporary quantum hardware. To overcome this, we have developed a transcorrelated Hamiltonian approach where we downfold the effects of a large basis set into a Hamiltonian in the space of a much smaller basis set. Thus, the transcorrelated Hamiltonian can provide desired quantitative accuracies with a much smaller Hilbert space, resulting in a massive reduction in the required quantum resources. |
Tuesday, March 7, 2023 9:36AM - 9:48AM Author not Attending |
F64.00007: Quantum algorithm for downfolding quantum chemistry Hamiltonians Anirban Mukherjee We develop a quantum computing approach to construct an effective Hamiltonian acting on the reduced subspace of orbitals starting from the parent electronic Hamiltonian that acts upon the complete active space. The effective Hamiltonian is constructed via systematically downfolding the core/virtual orbitals and counting inwards towards the orbitals in the energy neighbourhood of the HOMO-LUMO orbitals. The downfolding is carried out by a sequence of similarity transformations that are block-encoded via the qubitization algorithm in the quantum circuit. The parameters of the similarity transformation are optimised by the variational quantum-classical hybrid algorithm, by choosing an appropriate cost function. |
Tuesday, March 7, 2023 9:48AM - 10:00AM |
F64.00008: When is better ground state preparation worthwhile for energy estimation? Shivesh Pathak, Antonio E Russo, Stefan Seritan, Andrew D Baczewski Many quantum simulation tasks require preparing a state with overlap γ relative to the ground state of a Hamiltonian of interest, such that the probability of computing the associated energy eigenvalue is upper bounded by γ2. |
Tuesday, March 7, 2023 10:00AM - 10:12AM |
F64.00009: Quantum algorithm for ground state energy estimation using circuit depth with exponentially improved dependence on precision Ruizhe Zhang, Guoming Wang, Daniel Stilck França, Shuchen Zhu, Peter D Johnson A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving a quantum advantage in this area will require some degree of error correction. While hardware is improving towards this milestone, optimizing quantum algorithms also brings it closer to the present. Existing methods for ground state energy estimation require circuit depths that scale as O(1/ε · polylog(1/ε)) to reach accuracy ε. In this work, we develop and analyze ground state energy estimation algorithms that use just one auxiliary qubit and for which the circuit depths scale as O(1/Δ · polylog(Δ/ε)), where Δ ≥ ε is a lower bound on the energy gap of the Hamiltonian. With this tilde{O}(Δ/ε) reduction in circuit depth, relative to recent resource estimates of ground state energy estimation for the industrially-relevant molecules of ethylene-carbonate and PF-6, the estimated gate count and circuit depth are reduced by a factor of 43 and 78, respectively. Furthermore, the algorithm can take advantage of larger available circuit depths to reduce the total runtime. By setting a ∈ [0, 1] and using depth proportional to ε-aΔtrue -1+a, the resulting total runtime is tilde{O}(ε-2+aΔtrue 1-a), where Δtrue is the true energy gap of the Hamiltonian. These features make our algorithm a promising candidate for realizing quantum advantage in the era of early fault-tolerant quantum computing. |
Tuesday, March 7, 2023 10:12AM - 10:24AM |
F64.00010: Training variational quantum circuits with CoVaR: covariance root finding with classical shadows Balint Koczor, Gregory Boyd Exploiting near-term quantum computers and achieving practical value is a considerable and exciting challenge. Most prominent candidates as variational algorithms typically aim to find the ground state of a Hamiltonian by minimising a single classical (energy) surface which is sampled from by a quantum computer. Here we introduce a method we call CoVaR, an alternative means to exploit the power of variational circuits: We find eigenstates by finding joint roots of a polynomially growing number of properties of the quantum state as covariance functions between the Hamiltonian and an operator pool of our choice. The most remarkable feature of our CoVaR approach is that it allows us to fully exploit the extremely powerful classical shadow techniques, i.e., we simultaneously estimate a very large number >10^4 − 10^7 of covariances. We randomly select covariances and estimate analytical derivatives at each iteration applying a stochastic Levenberg-Marquardt step via a large but tractable linear system of equations that we solve with a classical computer. We prove that the cost in quantum resources per iteration is comparable to a standard gradient estimation, however, we observe in numerical simulations a very significant improvement by many orders of magnitude in convergence speed. CoVaR is directly analogous to stochastic gradient-based optimisations of paramount importance to classical machine learning while we also offload significant but tractable work onto the classical processor. This talk is based on [G Boyd, B Koczor, Phys Rev X (2022), arXiv:2204.08494]. |
Tuesday, March 7, 2023 10:24AM - 10:36AM |
F64.00011: Measurement based quantum algorithm for ground state preparation. Alessandro Baroni, Joseph A Carlson, Ionel Stetcu In this presentation we will present a quantum algorithm for state preparation that uses time evolution along with repeated measurement scheme to obtain the ground state of a Hamiltonian with known energies for the ground and first excited state. We show its implementation on current simulators for both the two-dimensional Heisenberg model and the phenomenological nuclear shell model and we compare its performance with other methods that make use of Linear Combination of Unitaries, previously developed in the literature. |
Tuesday, March 7, 2023 10:36AM - 10:48AM |
F64.00012: Bootstrap Embedding on a Quantum Computer Yuan Liu, Zachary E Chin, Oinam R Meitei, Arkopal Dutt, Max Tao, Troy Van Voorhis, Isaac L Chuang Finding the ground state of interacting fermionic systems is an outstanding challenge for quantum chemistry, material science, and condensed matter physics. However, numerically solving the time-independent Schrodinger equation of a meaningfully large many-electron system in an exact fashion is a daunting task because the dimension of the underlying Hilbert space grows exponentially as the number of electrons increases whereas any practically available computational resources will be finite. Extending bootstrap embedding methods for addressing this challenge, we present a quantum bootstrap embedding theory that formulates the electronic structure problem of the total system as a constraint optimization problem for a composite Lagrangian where the constraint is constructed from matching conditions on the qubit reduced density matrices. We present an iterative algorithm to solve the optimization problem using a quantum subroutine as an eigensolver to solve each fragment Hamiltonian. An adaptive sampling scheduling and a quantum coherent matching algorithm based on a quantum SWAP test are designed to dramatically improve the efficiency of the algorithm as compared to the usual exponentially costly method of measuring every qubit on the fragment edge to construct the reduced density matrix. Moreover, by using amplitude amplification and a binary search algorithm, an additional quadratic speedup could be realized. Current quantum computers are small, but quantum bootstrap embedding proves a potentially generalizable strategy for harnessing such small machines, since it enables the stitching together of fragment solutions to solve a quantum chemistry problem that is much larger than current quantum computer capacities. |
Tuesday, March 7, 2023 10:48AM - 11:00AM |
F64.00013: Quantum Computation for Periodic Solids in Second Quantization Christoph Sünderhauf, Aleksei V Ivanov, Nicole Holzmann, Tom Ellaby, Rachel Kerber, Glenn Jones, Joan Camps We present a quantum algorithm for ground-state energy calculations of periodic solids on error-corrected quantum computers. The algorithm is based on the sparse qubitization approach in second quantization and developed for Bloch and Wannier basis sets. We show that Wannier functions require less computational resources with respect to Bloch functions because: (i) the L1norm of the Hamiltonian is considerably lower and (ii) the translational symmetry of Wannier functions can be exploited in order to reduce the amount of classical data that must be loaded into the quantum computer. The resource requirements of the quantum algorithm are estimated for periodic solids such as NiO and PdO. These transition metal oxides are industrially relevant for their catalytic properties. We find that ground-state energy estimation of Hamiltonians approximated using 200-900 spin orbitals requires ca. 10^10-10^12 T gates and up to 3⋅10^8 physical qubits for a physical error rate of 0.1%. |
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