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 A64: Algorithms for Hamiltionian SimulationsFocus
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Sponsoring Units: DQI Chair: William Munizzi, Arizona State University Room: Room 415 |
Monday, March 6, 2023 8:00AM - 8:12AM |
A64.00001: Simple and high-precision Hamiltonian simulation by compensating Trotter errors with linear combination of unitary operations Pei Zeng, jinzhao sun, Liang Jiang, Qi Zhao Trotter and linear-combination-of-unitary (LCU) methods are two popular Hamiltonian simulation algorithms. The Trotter method is easy to implement and enjoys good system-size dependence endowed by commutator scaling, while the LCU method admits high accuracy simulation with smaller gate cost. |
Monday, March 6, 2023 8:12AM - 8:24AM |
A64.00002: Improved Trotter formula for time-dependent Hamiltonians SHO SUGIURA, Asir Abrar, Isaac L Chuang, Tatsuhiko N Ikeda Hamiltonian simulations of time-dependent systems are important for a variety of applications, from chemical reactions to optimization problems. Various simulation algorithms have been proposed for time-independent systems, but far less work has been done on algorithms for time-dependent systems. |
Monday, March 6, 2023 8:24AM - 8:36AM |
A64.00003: Rapid quantum approximate solvers for combinatorial optimisation problems inspired by Hamiltonians for optimal state-transfer Robert J Banks, Dan E Browne, Paul A Warburton Designing and developing quantum algorithms remains a formidable challenge without mature hardware to test ideas on. Here we suggest a new design heuristic to tackle combinatorial optimisation problems, inspired by Hamiltonians for optimal state-transfer. The result is a rapid approximate optimisation algorithm. We provide numerical evidence of the success of this new design heuristic. We find this new approach gives a better approximation ratio than the Quantum Approximate Optimisation Algorithm at lowest depth on the majority of problem instances considered, while utilising comparable resources. This opens the door to investigating new approaches for tackling combinatorial optimisation problems, away from adiabatic inspired approaches. |
Monday, March 6, 2023 8:36AM - 9:12AM |
A64.00004: Quantum dynamics simulation and its application to Hamiltonian learning Invited Speaker: Di Fang Recent years have witnessed tremendous progress in developing and analyzing quantum algorithms for quantum dynamics simulation (Hamiltonian simulation). The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on the operator norm of the Hamiltonian. However, the operator norm measures the worst-case scenario, while practical simulation concerns the error with respect to a given initial vector or given observables at hand. In this talk, we will discuss a few ways to weaken the strong operator norm dependence in quantum simulation tasks by taking into account the the initial condition and observables. We then discuss how such analysis can be applied in the setting of Hamiltonian learning. Using a Hamiltonian reshaping technique, we propose a first learning algorithm to achieve the Heisenberg limit for efficiently learning an interacting N-qubit local Hamiltonian. |
Monday, March 6, 2023 9:12AM - 9:24AM |
A64.00005: SQuISH: self-consistent quantum iteratively sparsified Hamiltonian Diana Chamaki, Stuart Hadfield, Katherine Klymko, Bryan A O'Gorman, Norm M Tubman Due to coherence time limitations, reducing the resources required to run quantum algorithms and simulate physical systems on a quantum computer is crucial. With regards to Hamiltonian simulation, a significant effort has focused on building efficient algorithms using various factorizations and truncations, typically derived from the Hamiltonian alone. We introduce a new paradigm for improving Hamiltonian simulation and reducing the cost of ground state problems based on ideas recently developed for classical chemistry simulations. The key idea is that one can find efficient ways to reduce resources needed by quantum algorithms by making use of two key pieces of information: the Hamiltonian operator and an approximate ground state wavefunction. We refer to our algorithm as the self-consistent quantum iteratively sparsified Hamiltonian (SQuISH). By performing our scheme iteratively, one can drive SQuISH to create an accurate wavefunction using a truncated, resource-efficient Hamiltonian. By utilizing this more compact Hamiltonian, our algorithm provides an approach to reduce the gate complexity of ground state calculations on quantum hardware. As proof of principle, we implement SQuISH using configuration interaction for small molecules and coupled cluster for larger systems. Through our combination of approaches, we demonstrate how it performs on a range of systems, the largest of which would require more than 200 qubits to run on quantum hardware. |
Monday, March 6, 2023 9:24AM - 9:36AM |
A64.00006: A variational quantum algorithm for Hamiltonian diagonalization ZHANG CHAO Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those can be implemented on near-term quantum devices. In this work, we propose a variational algorithm for Hamiltonians diagonalization (VQHD) of quantum systems, which explores the important physical properties, such as temperature, locality, and correlation, of the system. The key idea is that the thermal states of the system encode the information of eigenvalues and eigenstates of the system Hamiltonian. To obtain the full spectrum of the Hamiltonian, we use a quantum imaginary time evolution algorithm with high temperature, which prepares a thermal state with a small correlation length. With Trotterization, this then allows us to implement each step of imaginary time evolution by a local unitary transformation on only a small number of sites. Diagonalizing these thermal states hence leads to a full knowledge of the Hamiltonian eigensystem. We apply our algorithm to diagonalize local Hamiltonians and return results with high precision. Our VQHD algorithm sheds new light on the applications of near-term quantum computers. |
Monday, March 6, 2023 9:36AM - 9:48AM |
A64.00007: Efficient calculation of energy derivatives on a Fault-Tolerant Quantum Computer Raffaele Santagati, Thomas E O'Brien, Michael Streif, Nicholas C Rubin, Yuan Su, William J Huggins, Joshua Goings, Nikolaj Moll, Elica Kyoseva, Matthias Degroote, Christofer Tautermann, Joonho Lee, Dominic W Berry, Nathan Wiebe, Ryan Babbush Energy derivatives underpin many fundamental properties of molecular systems, from the dipole moments to the hyperfine couplings and forces. |
Monday, March 6, 2023 9:48AM - 10:00AM |
A64.00008: Hamiltonian Simulation via Quantum Assisted Cartan Decomposition and Iterative Block Diagonalization Efekan Kökcü, Alexander F Kemper Generating an efficient time evolution circuit for a given many body Hamiltonian is crucial for simulation of quantum systems via quantum computation. Standard algorithms based on Trotter-Suzuki product formulas result in circuits that grow with increasing simulation time, which is incompatible with the noisy nature of current NISQ devices. Circuits whose depth is independent of simulation time can be generated by Cartan decomposition [1], but this involves finding a local minimum of a cost function, which requires efficient calculation of the cost function, and an efficient search through parameter space. In this work, we advance this method in two aspects. First, we propose a method to calculate the cost function on a quantum computer, which quadratically speeds up its calculation. Secondly, we present a method to partition the parameter space by exploiting the Lie algebraic properties of the cost function, and thus divide the optimization problem into a sequence of smaller optimization problems. With our developments, we are moving towards efficient synthesis of unitaries, in a way that leverages the power of quantum computers, rather than purely offloading the difficult work to classical computer. |
Monday, March 6, 2023 10:00AM - 10:12AM |
A64.00009: Quantum Hamiltonian Descent Jiaqi Leng, Ethan Hickman, Joseph Li, Xiaodi Wu Ubiquitous continuous optimization has been an active topic investigated for quantum speed-ups. The conventional approach relies on the quantum acceleration of intermediate steps of corresponding classical algorithms, whereas the trajectory of resultant quantum algorithms and the quality of the solutions are similar to classical ones. We propose Quantum Hamiltonian Descent (QHD) as a truly quantum counterpart of classical gradient methods for continuous optimization, which is derived by quantizing dynamical systems referring to the continuous-time limit of gradient methods through the path integral formulation of quantum mechanics. QHD's convergence to the global optimum is established in both convex and non-convex settings. More importantly, QHD is described as a time-dependent Hamiltonian evolution that can be efficiently simulated on both digital and analog quantum computers. By embedding QHD's Hamiltonian evolution into the evolution of the so-called Quantum Ising Machine (including DWave and others), we empirically observe that the DWave-implemented QHD outperforms a selection of the state-of-the-art gradient-based classical solvers and the standard quantum adiabatic algorithm, based on the time-to-solution metric, on non-convex constrained quadratic programming instances up to 75 dimensions. Finally, we propose a "three-phase picture" to explain the behavior of QHD, especially its difference from the quantum adiabatic algorithm. |
Monday, March 6, 2023 10:12AM - 10:24AM |
A64.00010: Optimal fermion-qubit mappings Mitchell Chiew, Sergii Strelchuk Simulating fermionic systems on a quantum computer requires a high-performing mapping of fermionic states to qubits. The key characteristic of an efficient mapping is its ability to translate local fermionic interactions into local qubit interactions, leading to easy-to-simulate qubit Hamiltonians. All fermion-qubit mappings must use a numbering scheme for the fermionic modes in order to make translation to qubit operations possible. We present a new way to design fermion-qubit mappings by making use of the extra degree of freedom – the choice of enumeration for the fermionic modes. This allows us to minimise the average number of Pauli matrices in each term of a mapping’s qubit Hamiltonian – its average Pauli weight. Finding the best enumeration scheme allows one to increase the locality of the target qubit Hamiltonian without expending any additional resources. |
Monday, March 6, 2023 10:24AM - 10:36AM |
A64.00011: Preparing quantum many-body scar states on quantum computers Erik Gustafson Quantum many-body scar states are highly excited eigenstates of many-body systems that exhibit atypical entanglement and correlation properties relative to other eigenstates at the same energy density. Scar states also give rise to infinitely long-lived coherent dynamics when the system is prepared in a special initial state having finite overlap with them. Many models with exact scar states have been constructed, but the fate of scarred eigenstates and dynamics when these models are perturbed is difficult to study with classical computational techniques. In this work, we propose state preparation protocols for individual scar states in a particular model, as well as superpositions of them that give rise to coherent dynamics. For superpositions of scar states, we propose both a linear depth unitary and a finite-depth nonunitary state preparation protocol, the latter of which uses measurement and postselection to reduce the circuit depth. For individual scarred eigenstates, we propose a circuit architecture with polynomial depth. We also provide proof of principle implementations of these protocols on superconducting quantum hardware. |
Monday, March 6, 2023 10:36AM - 10:48AM |
A64.00012: Optimizing fermionic encodings for both Hamiltonian and hardware Riley Chien, Joel Klassen In this work we present a method for generating a fermionic encoding tailored to a set of target fermionic operators and to a target hardware connectivity. Our method uses brute force search, over the space of all encodings which map from Majorana monomials to Pauli operators, to find an encoding which optimizes a target cost function. In contrast to earlier works in this direction, our method searches over an extremely broad class of encodings which subsumes all known second quantized encodings that constitute algebra homomorphisms. In order to search over this class, we give a clear mathematical explanation of how precisely it is characterized, and how to translate this characterization into constructive search criteria. A benefit of searching over this class is that our method is able to supply fairly general optimality guarantees on solutions. A second benefit is that our method is, in principal, capable of finding more efficient representations of fermionic systems when the set of fermionic operators under consideration are faithfully represented by a smaller quotient algebra. Given the high algorithmic cost of performing the search, we adapt our method to handle translationally invariant systems that can be described by a small unit cell that is less costly. We demonstrate our method on various pairings of target fermionic operators and hardware connectivities. We additionally show how our method can be extended to find error detecting fermionic encodings in this class. |
Monday, March 6, 2023 10:48AM - 11:00AM |
A64.00013: Dynamical simulation of periodically driven systems on near term quantum computers Timo Eckstein, Piotr J Czarnik, Refik Mansuroglu, Jianxin Zhu, Michael J Hartmann, Lukasz Cincio, Zoe Holmes, Andrew T Sornborger Quantum simulation may be one of the first practical applications to see a quantum advantage. While algorithms for simulating time-independent systems on near-term hardware is a very active area, techniques for simulating time-dependent systems are less developed. Standard iterative Trotterization-based approaches to simulating time-dependent quantum simulation require fine grained time steps resulting in untenably deep circuits. In contrast, we show that if we restrict ourselves to periodically drive “Floquet” systems then near-term quantum simulations can be feasible. Our proposed simulation algorithm, which does not require any form of costly additional optimization procedure, translates the time dependent problem into a time-independent one. This opens the possibility of simulating driven systems using more efficient methods for simulating independent systems. In numerical investigations we study transversally driven versions of the Ising, XX-YY, Heisenberg and Axial Next-Nearest-Neighbour Ising models. We find our proposed approach can outperform the standard Trotter approach by several orders of magnitude. |
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