Bulletin of the American Physical Society
2021 Fall Meeting of the APS Division of Nuclear Physics
Volume 66, Number 8
Monday–Thursday, October 11–14, 2021; Virtual; Eastern Daylight Time
Session EN: Minisymposium: Developments in Quantum Simulations for Nuclear Physics II: algorithms |
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Chair: Martin Savage, UW-Seattle Room: Studio 1 |
Tuesday, October 12, 2021 11:45AM - 11:57AM |
EN.00001: Hamiltonian simulation in the low-energy subspace Burak Sahinoglu, Rolando D Somma We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low-energy of a Hamiltonian $H$. This is a central problem in physics with vast applications in many-body systems and beyond, where the interesting physics takes place in the low-energy sector. We analyze error bounds induced by product formulas that approximate the evolution operator and show that these bounds depend on an effective low-energy norm of $H$. We find improvements over the best previous complexities of product formulas that apply to the general case, and these improvements are more significant for long evolution times that scale with the system size and/or small approximation errors. To obtain these improvements, we prove exponentially-decaying upper bounds on the leakage to high-energy subspaces due to the product formula. Our results provide a path to a systematic study of Hamiltonian simulation at low energies, which will be required to push quantum simulation closer to reality, and will find applications in fields such as condensed-matter, nuclear physics, high-energy and quantum chemistry. |
Tuesday, October 12, 2021 11:57AM - 12:09PM |
EN.00002: Two point functions on a quantum computer. Alessandro Baroni, Alessandro Roggero, Joseph A Carlson, Rajan Gupta, Gabriel Perdue, Andy Li In this talk we will present results on current quantum hardware for the calculation of the real time response function of a simplified nuclear Hamiltonian interacting |
Tuesday, October 12, 2021 12:09PM - 12:21PM |
EN.00003: Quantum gate optimization strategies using alternate Hilbert space decomposition Valentina Amitrano, Francesco Pederiva, francesco turro, Piero Luchi Quantum computing has become a field in which increasing research efforts have been invested in recent decades. Current machines have an increasing number of qubits and simulations are be- coming more and more efficient. Despite this fact, any non-trivial algorithm requires a coherence time and a fidelity that are not within reach of near-term hardware. The problem of effectively and efficiently decomposing a unitary transformation is of fundamental importance in order to carry out digital quantum simulations, i.e consisting of a finite sequence of quantum gates according to the Solovay-Kitaev theorem. The decoherence and the low fidelity of transformations involving several qubits are currently the most important limitation on quantum computation. The opti- mization of a circuit is an NP-hard problem that requires more and more research efforts. |
Tuesday, October 12, 2021 12:21PM - 12:33PM |
EN.00004: Strategies for Quantum-Accelerated Interpolator Construction in Classical Simulations of Lattice Field Theories Artur R Avkhadiev, Phiala E Shanahan, Ross D Young Optimized interpolating operators have the potential to accelerate the computation of hadron and nuclear matrix elements in lattice QCD. With decreased overlap onto low-lying excited states, optimized interpolated states require less euclidean time evolution to suppress unwanted contributions. This makes for a more efficient preparation of initial and final states in matrix elements, reducing computational costs. |
Tuesday, October 12, 2021 12:33PM - 12:45PM |
EN.00005: Symplectic Algebra for Quantum Computing Lattice Field Theory Richard C Brower Lattice Field Theory quatum computing starts with a Hamiltonian discretized on |
Tuesday, October 12, 2021 12:45PM - 12:57PM |
EN.00006: Fast-forwarding quantum evolution Shouzhen Gu, Rolando D Somma, Burak Sahinoglu We investigate the problem of fast-forwarding quantum evolution, whereby the dynamics of certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time. We provide a definition of fast-forwarding that considers the model of quantum computation, the Hamiltonians that induce the evolution, and the properties of the initial states. Our definition accounts for any asymptotic complexity improvement of the general case and we use it to demonstrate fast-forwarding in several quantum systems. We show that some local spin systems whose Hamiltonians can be taken into block diagonal form using an efficient quantum circuit, such as those that are permutation-invariant, can be exponentially fast-forwarded. We also show that certain classes of positive semidefinite local spin systems, also known as frustration-free, can be polynomially fast-forwarded, provided the initial state is supported on a subspace of sufficiently low energies. Last, we show that all quadratic fermionic systems and number-conserving quadratic bosonic systems can be exponentially fast-forwarded. Our results extend the classes of physical Hamiltonians that were previously known to be fast-forwarded, and include models from nuclear physics such as the Lipkin-Meshkov-Glick Hamiltonian. |
Tuesday, October 12, 2021 12:57PM - 1:09PM |
EN.00007: Imaginary Time Propagation on a Physical Quantum Chip francesco turro In standard computation one possibility for computing ground state properties of a given system is to operate a Wick rotation on the real time evolution operator. The resulting propagator is not unitary, and implements a dissipation mechanism. Evolution in imaginary time is a well-known technique for finding the ground state of quantum many-body systems, and the heart of a number of numerical methods, including Quantum Monte Carlo techniques, that have been used with great success in quantum chemistry, condensed matter and nuclear physics. Although the great use, the computation time increases exponentially due to the exponential growth of the model space with the increasing number of particles. There is therefore a desire to develop quantum versions of prominent quantum many-body methods, and in particular quantum algorithms that can be efficiently applied to emerging prototypes of quantum computing platforms. |
Tuesday, October 12, 2021 1:09PM - 1:21PM |
EN.00008: Variational Fast Forwarding for NISQ Simulations ZOE HOLMES Quantum simulation has the potential to transform fields from quantum chemistry and material science to nuclear physics. However, while quantum hardware is rapidly reaching the stage where it can outperform classical supercomputers, we remain in the noisy intermediate-scale quantum (NISQ) era in which devices are prone to errors and susceptible to decoherence. The resulting short coherence times of near term quantum computers restrict the length of times that may be successfully simulated thus limiting the usefulness of quantum simulations.Here we present a hybrid quantum-classical algorithm, called Variational Fast Forwarding (VFF), to address the challenge of how to perform genuinely useful simulations with NISQ devices. The number of gates required for a VFF simulation does not scale with the length of time to be simulated and thus enables simulations of long times using a fixed number of gates. To achieve this, VFF approximately diagonalises a Trotter approximation of the short-time evolution using a hybrid quantum-classical variational method, and in turn this diagonalisation allows for arbitrary time simulations with the same circuit structure.We test the capability of VFF through extensive numerical simulations of the Hubbard, Ising, and Heisenberg models, and we implement VFF on IBM's and Riggeti's quantum computers to demonstrate simulation beyond the coherence time. In contrast to prior work on variational quantum simulations, we further provide a rigorous analysis of VFF's simulation errors. We find that the simulation error of VFF scales at worst linearly in the fast-forwarded simulation time. This enables us to derive a natural termination condition for the algorithm which is framed in terms of the required average fidelity of the simulation. We further present two refinements of the VFF algorithm. |
Tuesday, October 12, 2021 1:21PM - 1:33PM |
EN.00009: Locality and Conservation Laws: How, in the presence of symmetry, locality restricts realizable unitaries Iman Marvian According to an elementary result in quantum computing, any unitary transformation on a composite system can be generated using 2-local unitaries, i.e., those that act only on two subsystems. Besides its fundamental importance in quantum computing, this result can also be regarded as a statement about the dynamics of systems with local Hamiltonians: although locality puts various constraints on the short-term dynamics, it does not restrict the possible unitary evolutions that a composite system with a general local Hamiltonian can experience after a sufficiently long time. We ask if such universality remains valid in the presence of conservation laws and global symmetries. In particular, can k-local symmetric unitaries on a composite system generate all symmetric unitaries on that system? Surprisingly, it turns out that the answer is negative in the case of continuous symmetries, such as U(1) and SU(2): generic symmetric unitaries cannot be implemented, even approximately, using local symmetric unitaries. In the context of quantum thermodynamics, this means that generic energy-conserving unitary transformations on a composite system cannot be implemented by applying local energy-conserving unitary transformations on the components. We also show how this no-go theorem can be circumvented via catalysis: any globally energy-conserving unitary can be implemented using a sequence of 2-local energy-conserving unitaries, provided that one can use a single ancillary qubit (catalyst). |
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