Session B69: Next Challenges in Quantum Simulation

Making Predictions in a Quantum World

I will review an experimentally feasible procedure for converting a quantum state into a succinct classical description of the state, its classical shadow. Classical shadows can be applied to predict efficiently many properties of interest, including expectation values of local observables and few-body correlation functions. Efficient classical machine learning algorithms using classical shadows can address quantum many-body problems such as classifying quantum phases of matter. I will also explain how experiments that exploit quantum memory can learn properties of a quantum system far more efficiently than conventional experiments.   

On the complexity of implementing Trotter steps

Quantum dynamics can be simulated on a quantum computer by exponentiating elementary terms from the Hamiltonian in a sequential manner. However, such an implementation of Trotter steps has gate complexity depending on the total Hamiltonian term number, comparing unfavorably to algorithms using more advanced techniques. We develop methods to perform faster Trotter steps with complexity sublinear in the number of terms. We achieve this for a class of Hamiltonians whose interaction strength decays with distance according to power law. Our methods include one based on a recursive block encoding and one based on an average-cost simulation, overcoming the normalization-factor barrier of these advanced quantum simulation techniques. We also realize faster Trotter steps when certain blocks of Hamiltonian coefficients have low rank. Combining with a tighter error analysis, we show that it suffices to use $left(eta^{1/3}n^{1/3}+frac{n^{2/3}}{eta^{2/3}} ight)n^{1+o(1)}$ gates to simulate uniform electron gas with $n$ spin orbitals and $eta$ electrons in second quantization in real space, asymptotically improving over the best previous work. We obtain an analogous result when the external potential of nuclei is introduced under the Born-Oppenheimer approximation. We prove a circuit lower bound when the Hamiltonian coefficients take a continuum range of values, showing that generic $n$-qubit $2$-local Hamiltonians with commuting terms require at least $Omega(n^2)$ gates to evolve with accuracy $epsilon=Omega(1/poly(n))$ for time $t=Omega(epsilon)$. Our proof is based on a gate-efficient reduction from the approximate synthesis of diagonal unitaries within the Hamming weight-$2$ subspace, which may be of independent interest. Our result thus suggests the use of Hamiltonian structural properties as both necessary and sufficient to implement Trotter steps with lower gate complexity.   

Algebraic techniques for quantum chemistry on a quantum computer

Quantum chemistry problem is one of the attractive targets for demonstrating quantum advantage of quantum computing technology. Quantum computing algorithms for solving this problem require algebraic operations with the electronic Hamiltonian. Dealing with this Hamiltonian in the second quantized form can be facilitated by partitioning it into a sum of fragments diagonalizable using rotations from either small Lie groups or the Clifford group. These fragments are convenient for performing various algebraic manipulations required in circuit compiling and quantum measurement. In this talk, I will illustrate how the Hamiltonian partitioning can be used to improve performance of the Variational Quantum Eigensolver and Quantum Phase Estimation algorithms.    

    

Quantum Simulations of the Standard Model

Future quantum simulations are expected to be able to provide robust predictions of the properties and dynamics of quantum many-body systems of importance to Standard Model physics research, to complement and support the theoretical, computational and experimental research activities in high-energy and nuclear physics. They will advance our understanding of, for example, dense, non-equilibrium, strongly interacting quarks, gluons, leptons found in the earliest moments of the universe, in dense systems of neutrinos produced in extreme astrophysical environments, in the fragmentation of particles and nuclei in high-energy collisions produced in the laboratory, and in the properties of nuclei, particularly in light of the role of quantum correlations, entanglement and emergent symmetries. I will give an overview of the state-of-the-art of quantum simulations of lattice gauge theories and neutrino systems, their unique aspects along with their connections with simulations in other research areas, estimates of quantum resource, and outline of the exciting road ahead.   

Simulating one-dimensional quantum chromodynamics on a quantum computer:Real-time evolutions of tetraquarks

Quantum chromodynamics - the theory of quarks and gluons - has been known for decades, but it is yet to be fully understood. A recent example is the prediction and experimental discovery of tetraquarks, that opened a new research field. Crucially, numerous unsolved questions of the standard model can exclusively be addressed by nonperturbative calculations. Quantum computers can solve problems for which well established QCD methods are inapplicable, such as real-time evolution. We take a key step in exploring this possibility by performing a realtime evolution of tetraquark physics in one-dimensional SU(3) gauge theory on a superconducting quantum computer. Our experiment represents a first quantum computation involving quarks with three colour degrees of freedom, i.e. with the gauge group of QCD.