Session H42: Advances in Digital Quantum Simulation

Small-scale quantum computers: current state of the art and applications

This talk discusses the various applications of small scale quantum computers consisting of a few hundred qubits and capable of performing a few thousand quantum logic operations reliably without error corrections. Such small scale quantum computers could perform useful quantum simulations of many-body quantum systems, including processes of many body localization and scrambling. I will show that such small scale quantum computers could also be useful for quantum machine learning, revealing patterns in quantum states and in classical data that could not be revealed by even the most powerful classical supercomputer.   

Divide and Conquer Approach to Quantum Hamiltonian Simulation

The difficulty of simulating quantum mechanical systems is a primary motivation for the development of quantum computers. Quantum simulation has important applications to problems in physics and chemistry. We show a novel divide and conquer approach for simulating Hamiltonian dynamics. We can obtain fast simulation algorithms using Hamiltonian structure. Considering a sum of Hamiltonians we split them into groups, simulate each group separately, and combine the partial results. Simulation is customized to take advantage of the properties of each group, and hence yield refined bounds to the overall simulation cost. We illustrate our results using the electronic structure problem of quantum chemistry.   

Experimentally simulating the dynamics of quantum light and matter at ultrastrong coupling using circuit QED (1) - implementation and matter dynamics -

The field dipole coupling of quantum light and matter, described by the quantum Rabi model, leads to exotic phenomena when the coupling strength $g$ becomes comparable or larger than the atom and photon frequencies $\omega_{q, r}$. In this ultra-strong coupling regime, excitations are not conserved, leading to collapse-revival dynamics in atom and photon parity and Schr{\"o}dinger-cat-like atom-photon entanglement. We realize a quantum simulation of the Rabi model using a transmon qubit coupled to a resonator. In this first part, we describe our analog-digital approach to implement up to 90 symmetric Trotter steps, combining single-qubit gates with the Jaynes-Cummings interaction naturally present in our circuit QED system. Controlling the phase of microwave pulses defines a rotating frame and enables simulation of arbitrary parameter regimes of the Rabi model. We demonstrate measurements of qubit parity dynamics showing revivals at $g/\omega_r>0.8$ for $\omega_q=0$ and characteristic dynamics for nondegenerate $\omega_q$ from $g/4$ to $g$.   

Experimentally simulating the dynamics of quantum light and matter at ultrastrong coupling using circuit QED (2) - light dynamics and light-matter entanglement -

Light-matter interaction can lead to large photon build-up and hybrid atom-photon entanglement in the ultrastrong coupling (USC) regime, where the coupling strength becomes comparable to the eigenenergies of the system. Accessing the cavity degree of freedom, however, is an outstanding challenge in natural USC systems. In this talk, we directly probe light field dynamics in the USC regime using a digital simulation of the quantum Rabi model in a planar circuit QED chip with a transmon moderately coupled to a resonator. We produce high-accuracy USC light-matter dynamics, using second-order Trotterisation and up to 90 Trotter steps. We probe the average photon number, photon parity and perform Wigner tomography of the simulated field. Finally, we combine tomography of the resonator with qubit measurements to evidence the Schr{\"o}dinger-cat-like atom-photon entanglement which is a key signature of light-matter dynamics in the USC regime.   

Digital-analog quantum simulation of generalized Dicke models with superconducting circuits

We propose a digital-analog quantum simulation of generalized Dicke models with superconducting circuits, including Fermi-Bose condensates, biased and pulsed Dicke models, for all regimes of light-matter coupling. We encode these classes of problems in a set of superconducting qubits coupled with a bosonic mode implemented by a transmission line resonator. Via digital-analog techniques, an efficient quantum simulation can be performed in state-of-the-art circuit quantum electrodynamics platforms, by suitable decomposition into analog qubit-bosonic blocks and collective single-qubit pulses through digital steps. Moreover, just a single global analog block would be needed during the whole protocol in most of the cases, superimposed with fast periodic pulses to rotate and detune the qubits. Therefore, a large number of digital steps may be attained with this approach, providing a reduced digital error. Additionally, the number of gates per digital step does not grow with the number of qubits, rendering the simulation efficient. This strategy paves the way for the scalable digital-analog quantum simulation of many-body dynamics involving bosonic modes and spin degrees of freedom with superconducting circuits.   

Quantum Algorithm for Simulating Scalar Quantum Electrodynamics Field Theory

In this study, we present a quantum algorithm to calculate the scattering amplitudes in scalar quantum electrodynamics (QED) field theory. Since the spectrum of the variables of this quantum field theory is continuous, this algorithm facilitates the continuous variables (CV) in quantum computing. As a result, the proposed quantum algorithm provides an exponential speed up over the classical methods that is used to calculate the scattering amplitudes in scalar QED field theory.   

Understanding errors in digital quantum simulation of fermionic systems

The simulation of complex fermionic systems is one of the most anticipated applications of quantum computing. Various properties of such systems can be described by time-dependent correlation functions of two fermionic operators. Fermions can be mapped onto qubits, e.g., via the Jordan-Wigner transformation. We discuss how (anti-)time sorted correlation functions can be measured in the qubit system. Deploying Keldish formalism, we investigate the effects of relaxation, and dephasing of the qubits, as well as gate errors in an quantum algorithm using the Trotter expansion. We analyze how this translates to a simulated fermionic system, allowing for qualitative understanding of errors of a quantum simulation.   

Boson sampling of many-body quantum random walkers on a lattice

The Boson sampling problem introduced by Aaronson and Arkhipov, showed quantum supremacy in terms of sampling complexity for the output distribution of photons scattering from a linear optical network. We study here an analogous problem in case of multiple boson continuous-time quantum random walkers on a lattice, e.g., Bosonic atoms in an optical lattice. Results are presented for the special case of a 1 D lattice with nearest neighbor and uniform hopping amplitude. We demonstrate that the sampling problem is classically tractable until the time of evolution passes the logarithmic scale in the number of particles. We also conjecture that this problem is classically hard beyond the logarithmic scale. Periodic and hard wall boundary conditions lead to the same result when number of lattice sites are substantially larger than the number of particles. When extended to arbitrary hopping amplitudes and on-site interactions, this corresponds to sampling complexity for a general Bose-Hubbard model.   

Verification of a translationally invariant Ising Spin Quantum Simulator

We present a verification scheme for a quantum simulator to sample the partition function of the Ising model at imaginary temperatures. Based on a two dimensional lattice of interacting spins in a fixed local magnetic field that can simulate natural quantum many body systems, this sampling problem is believed to be hard to simulate classically. It is therefore a candidate for demonstrating the supremacy of quantum simulation over classical computing. However, to demonstrate quantum supremacy one needs to verify that the sampler is indeed producing a sample that is close to the correct one in total variation distance. We propose a verification scheme that achieves this by requiring the verifier to be capable of imperfect single qubit preparation. Our scheme has a quadratic improvement over the original protocol (by Gao/Wang/Duan) in the number of elementary operations. Moreover, the extra computation required from the simulator for the test is simpler than the original computation. Finally, our scheme is proven to be secure in a composable setting, that is, in a setting where the device may run other protocols in serial or parallel composition.   

A device-oriented optimizer for solving ground state problems on an approximate quantum computer, Part I: Theory

Quantum-classical variational eigensolvers provide a method to solve for ground state of Hamiltonian problems. Their performance has been recently investigated for interacting fermionic problems, which are believed to be suitable bench tests for medium-sized quantum computers. The overhead cost in terms of computational time, size and quality of the actual available quantum hardware is therefore crucial. In this talk we first present methods to reduce the number of qubits required to encode fermionic problems. We then discuss how the efficiency of the quantum part of the optimization problem can be increased by a device-oriented design of the state preparation. We present a numerical study of the method for generic fermionic problems of increasing size, including molecular structure ones.   

A device-oriented optimizer for solving ground state problems on an approximate quantum computer, Part II: Experiments for interacting spin and molecular systems

Hybrid quantum-classical algorithms can be used to find variational solutions to generic quantum problems. Here, we present an experimental implementation of a device-oriented optimizer that uses superconducting quantum hardware. The experiment relies on feedback between the quantum device and classical optimization software which is robust to measurement noise. Our device-oriented approach uses naturally available interactions for the preparation of trial states. We demonstrate the application of this technique for solving interacting spin and molecular structure problems.   

Adiabatic ground-state preparation in the Dicke model

The Dicke model is an important model in quantum optics. It describes the interaction of $N$ two-level atoms with a single-mode radiation field through the dipole coupling. In the thermodynamic limit, when the number of two-level atoms goes to infinity, the model exhibits a transition to a superradiant phase at a critical coupling strength. We study the geometrical properties of the Dicke model's ground-state manifold. On the one hand, for a small number of two-level atoms we exploit the Riemannian quantum metric structure of the ground-state manifold to construct optimal protocols for the task of adiabatic ground-state preparation in a fixed amount of time, on the other hand, for the limit of a large number of atoms we use a time-dependent mean-field theory to describe the dynamics of the system and hence use a classical analogue of the metric to define geodesics for the adiabatic ground-state preparation.   

Quantum Vertex Model for Reversible Classical Computing

We present a planar vertex model that encodes the result of a universal reversible classical computation in its ground state. The approach involves Boolean variables (spins) placed on links of a two-dimensional lattice, with vertices representing logic gates. Large short-ranged interactions between at most two spins implement the operation of each gate. The lattice is anisotropic with one direction corresponding to “computational” time, and with transverse boundaries storing the computation’s input and output. The model displays no finite temperature phase transitions, including no glass transitions, independent of circuit. The computational complexity is encoded in the scaling of the relaxation rate into the ground state with the system size. We use thermal annealing and a novel and more efficient heuristic ”annealing with learning” to study various computational problems. To explore faster relaxation routes, we construct an explicit mapping of the vertex model into the Chimera architecture of the D-Wave machine, initiating a novel approach to reversible classical computation based on quantum annealing.