Simulating Quantum Many-Body Systems on Noisy Intermediate-Scale Quantum Computers

During the last fifteen years, ultracold atoms in optical lattices have emerged as very versatile and powerful Quantum Simulators to study the many-body physics of interacting particles in periodic potentials. Not only can they faithfully reproduce many prototypical effects from condensed matter physics, they also enable radically new systems with fascinating physics and hold promise for wider quantum information applications. After a brief review of fundamental properties and key experiments that already reach far beyond what can be computed classically, this talk will present an outlook into current and coming developments for realizing more complex lattice geometries.

We present a quantum processor comprised of a chain of 171Yb+ ions with individual Raman beam addressing and individual readout [1]. This fully connected system can be configured to run any sequence of single- and two-qubit gates, making it in effect an arbitrarily programmable digital quantum computer. We use this versatile setup to realize various quantum algorithms, such as a quantum random walk which corresponds to the digital simulation of the Dirac equation. We also add a classical optimization layer to our quantum computing stack to create a quantum-classical hybrid machine that can realize variational optimization methods, like the quantum approximate optimization algorithm (QAOA). With this we produce so-called thermofield doubles [2], which allow the efficient creation of finite temperature quantum states, and correspond to "traversable wormholes" in the study of gravity [3]. Finally, work towards scaling up the architecture will also be discussed. [1] S. Debnath et al., Nature 563:63 (2016) [2] D. Zhu et al., arXiv:1906.02699 (2019) [3] P. Gao et al., JHEP 2017, 151 (2017)

Tensor networks focus computational and entanglement resources in interesting regions of Hilbert space. Applied to NISQ machines they allow simulation of quantum systems that are much larger than the computational machine. This is achieved by parallelising the quantum simulation. We demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We have written CIRQ and Qiskit code that translate infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution arbitrary one-dimensional systems. Illustrative simulated output of these codes for achievable sizes of circuit will be shown. Authors: Fergus Barratt, James Dborin, Matthias Bal, Vid Stojevic, Frank Pollmann, Andrew G Green

The Variational Quantum Eigensolver (VQE) is an algorithm that may enable the near-term application of small-scale quantum computers to solve quantum chemistry and optimization problems. The variational nature of such a quantum-classical hybrid algorithm allows one to construct the trial wave function of quantum simulation by gate-based control in available hardware [1]. Meanwhile, techniques in Nuclear Magnetic Resonance (NMR) have been revisited recently to propose the substitution of pulsed entangling gates in quantum algorithms with continuous time evolution by inherent interaction of the system Hamiltonian [2]. As a demonstration, we report a quantum chemistry simulation using the VQE on a 2-qubit superconducting device [3] in which we use fixed frequency qubits and build the algorithm using the native 2-qubit interaction resulting from a static capacitive coupling. The quantum circuit of the VQE is constructed by varying the timings of echo pulses to manipulate the native ZZ coupling. This method allows us to implement a VQE algorithm without needing repeated multi-qubit-gate tune-up and enables simple implementation of error mitigation [4,5]. Furthermore, we show systematic and time-efficient schemes to rescale the effective Hamiltonian from free evolution of the system Hamiltonian and spin echo pulse sequences [6]. We discuss how this NMR-inspired method fits naturally to the implementation of variational algorithms with large multi-qubit system. [1] A. Kandala, et al., Nature, 549 242-246 (2017). [2] A. Parra-Rodriguez, et al., arXiv:1812.03637 [quant-ph]. [3] J. Rahamim, et al., Appl. Phys. Lett. 110, 222602 (2017). [4] K. Temme, et al., Phys. Rev. Lett. 119, 180509 (2017). [5] Y. Li, et al., Phys. Rev. X 7, 021050 (2017). [6] G. Bhole, et al., arXiv:1911.04806v2 [quant-ph].

The recent experimental demonstration of quantum supremacy heralds the era of noisy intermediate-scale quantum (NISQ) technologies. In this experiment, we use a processor with 53 programmable superconducting qubits, Sycamore, creating quantum states in a space of dimension $2^{53}$. Sycamore is built with a new 2D architecture where each qubit is coupled to up to four neighbors in a square array, with tunable coupling to each neighbor. This allows us to perform operations simultaneously across the device while maintaining high fidelity. A key challenge in operating a NISQ processor is automated calibration to optimize operations such as quantum gates and readout. In this presentation, we share an overview of the hardware involved, such as electronics, cryogenics, and superconducting circuits, and explain how we calibrate and benchmark the Sycamore processor.

First, I will consider quantum algorithms which are composed of so-called matchgates. Whereas such an algorithm can always be compressed into an exponentially smaller quantum computation, the usage of an additional resource, the so-called magic states, elevates the computational power to universal quantum computation, while maintaining the same gate set. I will present the characterization of these magic states and discuss the consequences of these results in the context of quantum computation. Then, some methods to verify and validate quantum computations will be discussed.

One of the most exciting predictions of topological physics is that the quasiparticle excitations of a topological phase, anyons, exhibit braiding statistics. In contrast to bosons and fermions, exchanging a pair of anyons can pick up an arbitrary phase or even implement a rotation in the degenerate ground state subspace. Despite intense interest in topological phases, no experiment has yet conclusively demonstrated braiding. In this talk, I will discuss near term approaches to demonstrating braiding using topological superconductors hosting Majorana zero modes, as well as using an array of superconducting qubits prepared in the surface code ground state but without active error correction.

Recently, protocols based on statistical correlations of randomized measurements were developed for probing synthetic quantum many-body systems, to access Rényi entropies, many-body fidelities and out-of-time-ordered correlators. After a general introduction to randomized measurements, I focus in this talk mostly on protocols to measure topological invariants, being quantized, highly nonlocal correlators of the many-body wavefunction. In the context of symmetry protected topological (SPT) phases of one-dimensional spin systems, I discuss explicitly how to measure invariants arising from inversion, time-reversal and unitary onsite symmetries. This enables to systematically probe the complete classification of bosonic SPT phases in one dimension experimentally. I illustrate the technique and its application in the context of the extended bosonic SSH model, as realized with Rydberg tweezer arrays.

tbc

We explore the physics of confinement in the transverse field Ising model with a longitudinal field in relation to quantum simulation capabilities of state-of-the-art quantum computers. Confinement has been shown to drastically alter the non-equilibrium dynamics starting from selected initial states. We report quantitative confinement signatures on an IBM quantum computer observed via two distinct velocities for information propagation from domain walls and their mesonic bound states. Our results are a crucial step for exploring non-perturbative quantum interaction phenomena which are beyond the capabilities of classical computers.

Photons have been closely related to the development of quantum information processing. Many of the first demonstrations of quantum information protocols have been done using photons. While photons are handy to manipulate and control, there are also clear limitations. For example, photons do not interact each other strongly. I will discuss what we can do using photons for quantum simulations.