CQT Colloquium on strongly interacting photons in superconducting qubit arrays

 Yesterday at CQT Jonathan Simon from Stanford University gave a wonderful colloquium talk on "Many-body Ramsey Spectroscopy in the Bose Hubbard Model," covering experimental studies of strongly interacting quantum fluids of photons in arrays of superconducting qubits, spanning work from 2019 on the preparation of photonic Mott insulating states to ongoing studies of entangled many-body states of light.

A good colloquium talk should understandable to a broad audience (ideally, including undergraduates) while still going into enough depth to keep specialists in the topic interested. If you cannot frame your research in terms of some simplified model, chances are you do not yet fully understand it.

Simon did this using the neat example of emergence in 2D point clouds: observing non-trivial emergent properties requires three key ingredients: many particles, interactions between the particles, and dissipation (in this case, friction) to allow the system to relax to some ordered state. When all three are included, the cloud self-organizes into a triangular lattice with properties qualitatively different from those of the individual constituent particles, supporting low energy vibrational modes (phonons).

Typically, a colloquium talk will cover research spanning several years. It is important to have some clear common motivation. In this case, the question of how to make quantum states of light exhibit similar emergent properties? Three ingredients are required: give photons an effective mass, achieve strong photon-photon interactions, and introduce a suitable form of dissipation that allows the system to relax to some interesting equilibrium state while preserving non-trivial many-particle effects.

After this framing, the talk went deep into how these ingredients can be realized using arrays of superconducting qubits, and how the relevant dimensionless quantities (interaction strength vs hopping strength vs photon lifetime) compare to other platforms, such as cold atoms (handy, given the mix of expertise in the audience).

The talk finished with a vision for the future - to connect this "photonic quantum simulator" to a small-scale quantum processor to test NISQ-friendly algorithms, such as shadow tomography of many-body quantum states.

A recording will probably be uploaded to the CQT Youtube page later. In the meantime, related talks given at JQI and Munich are already available online!

Recently in glossy journals

Engineering topological states in atom-based semiconductor quantum dots

Very nice work implementing the SSH / Hubbard model using quantum dots, forming a platform for studying the interplay between band topology and quantum interactions. The accompanying press release from the spin-off company (Silicon Quantum Computing) is unfortunately pure hype, however. This is not a molecular simulation - it is an implementation of a model. A neat example of analogue quantum simulation, but this is not a general-purpose reprogrammable integrated quantum circuit. 

Quantum advantage in learning from experiments

 

An exponential quantum advantage for quantum machine learning! The fine print is that the advantage is for learning from quantum data.

An on-chip photonic deep neural network for image classification

 

A photonic neural network that uses optoelectronics to implement nonlinear activation functions. "Direct, clock-less processing of optical data eliminates analogue-to-digital conversion and the requirement for a large memory module, allowing faster and more energy efficient neural networks for the next generations of deep learning systems."

arXiv highlights

Posting has been less frequent as I've been busy finishing revisions on some submitted manuscripts. Quite a few noteworthy preprints were posted this week:

 

Topogivity: A Machine-Learned Chemical Rule for Discovering Topological Materials

The authors propose a machine-learning approach for discovering new classes of topological materials. Looks interesting, but hard to say more because frustratingly all the details are delegated to supplementary materials which are not included...

Estimating the Euclidean Quantum Propagator with Deep Generative Modelling of Feynman paths

In the path integral formulation of quantum mechanics the probability amplitude of a particle transiting from state A to state B is given by summing over all possible trajectories between A and B, weighted by the action of each trajectory. While this is a theoretically elegant picture, the summation is extremely difficult to evaluate in practice due to the enormous number of possible trajectories. Here the authors show how machine learning techniques can be used to efficiently sample from those trajectories that contribute significantly to the transition amplitude.

 

Quantifying information scrambling via Classical Shadow Tomography on Programmable Quantum Simulators

By mapping evolution operators to density matrices in a higher-dimensional Hilbert space one can use shadow tomography to efficiently characterise quantum channels. Related works: arXiv:2110.02965 and arXiv:2110.03629.

Observation of wave-packet branching through an engineered conical intersection

When a Hamiltonian with two near-degenerate energy levels varies slowly in time, non-adiabatic Landau-Zener transitions between the energy eigenstates occur. A wavepacket initially in one eigenstate will end up in a superposition of the two eigenstates. A similar phenomenon plays a crucial role in certain chemical reaction dynamics and can be understood qualitatively in terms of the potential energy surfaces during the reaction. Quantum simulation of these complicated reaction dynamics is one potential near-term application of quantum processors, demonstrated here at a small scale using circuit QED.

Experimental observation of thermalisation with noncommuting charges

Macroscopic thermal states are described by conserved quantities such as the total energy or particle number. Curiously, the conserved quantities characterising certain thermal quantum states known as non-Abelian thermal states do not commute with each other and thus cannot simultaneously have well-defined values. This work reports the observation of a non-Abelian thermal state using a trapped ion quantum simulator.

 

To See a World in a Grain of Sand -- The Scientific Life of Shoucheng Zhang

Qi and Zhang's Reviews of Modern Physics article on topological insulators and superconductors was one of my first introductions to topological phases and I was shocked to hear of his passing in 2018. I enjoyed learning more about his life by reading this article.

 

Thermofield double states

Quantum simulation of materials at finite temperatures requires the generation of thermal quantum states.

Thermal quantum states are given by density matrices in which the eigenstate occupation probability follows the Boltzmann distribution.

Such density matrices cannot be generated from pure unitary quantum evolution. They either require the quantum system to interact with some environment, or to trace over some components of an entangled quantum state.

The latter approach is the most promising for the generation of thermal states of arbitrary quantum Hamiltonians. One approach based on thermofield double states, enables the generation of an N qubit thermal state using a 2N qubit pure state, i.e. two copies of the system of interest.

How to prepare thermofield double states?

One approach recently implemented in ion trap and superconducting qubit experiments employs the quantum approximate optimization algorithm (QAOA). The idea is that the infinite temperature (fully mixed) state is easy to prepare and the ground state of a simple (mixing) Hamiltonian that entangles pairs of qubits, one from the system of interest, and the other from the subsystem to be traced out. One can also identify a Hamiltonian that whose ground state describes the system of interest at zero temperature.

In the limit of a large number of steps, QAOA effectively performs an adiabatic transformation from the infinite temperature double state (easy to prepare) to the zero temperature one (hard to prepare). This suggests it should also be able to well-approximate intermediate temperature states using comparatively shallow circuits by solving a variational optimization problem; the cost function used is some measure of fidelity of the obtained density matrix with respect to a thermal state at the desired temperature.

Other approaches are based on deterministic algorithms, but require deeper circuits not really suitable for near-term quantum processors, for example relying on the phase estimation algorithm to obtain the desired thermal state.

Last year researchers from China proposed an alternate scheme which uses a continuous variable quantum state (qmode) to assist with the preparation of the thermofield double state. In this case, the challenges appear to be preparation of the required qmode resource state, decomposing the target Hamiltonian into a series of unitaries controlled by the qmode, and finite precision in measuring the quadrature of the qmode.

Since future materials science applications of quantum processors will primarily be concerned with simulating finite temperature properties, developing more efficient and robust schemes for the preparation of thermal states will be a topic of growing interest in the coming years.

Quantum simulation with cold atoms and superconducting qubits

 Two interesting preprints on quantum simulation appeared on arXiv today:

1. Thermalization dynamics of a gauge theory on a quantum simulator, by the USTC team and collaborators. This experiment uses a 71-site optical lattice for cold atoms to simulate the quench dynamics of a one-dimensional U(1) gauge theory. I am not very familiar with U(1) gauge theory and found this paper an informative introduction to the topic, by translating it to the more familiar setting of the Bose-Hubbard model. Basically, the study considers a 1D lattice comprising two detuned sublattices. In the limit where the inter-site hopping is much weaker than the detuning, and the local atom-atom interaction is resonant with the detuning, one can obtain an effective Hamiltonian with a hopping interaction term. Single particle hopping between the two sublattices is forbidden and only pairwise hopping can occur. In the limit of strong interactions, the dynamics becomes constrained to a subset of the full Hilbert space: the deeper sublattice can only be occupied by either 0 or 2 particles, while the shallower sublattice can be occupied by only 0 or 1 particles. This realizes an analogy with U(1) gauge theory by labelling the shallower sublattice as the "matter" field, and the deeper sublattice as the "gauge" field. The experiments then study thermalization in this model when an initial state with uniform "matter" density is quenched. Thus, the dynamics of the Bose-Hubbard model in complex lattices can be mapped onto more exotic gauge fields. It will be interesting to consider this direction further, and whether similar ideas can be realized in photonic lattices with weak and/or mean-field interactions.

2. Observation of Time-Crystalline Eigenstate Order on a Quantum Processor, by the Google AI team and collaborators. This work studies time-crystalline order, which was previously observed using other platforms. Quantum processors are natural for studying periodically-driven phases such as these, owning to description of their dynamics in terms of sequences of Floquet operators. The main innovation in this work appears to be the introduction of continuously-tunable two-qubit CPhase gates, which enables the implementation of strong tunable disorder in an effective Ising interaction between neighbouring qubits. The other two terms comprising the periodic driving are simple single qubit rotations. Using the flexible tunability of their quantum processor, the authors are able to study the stability of the time crystalline order with respect to changes in the system parameters, scaling with the system size (considering a linear chain of up to 20 qubits), and the properties of the entire spectrum of the system.

Scarry quantum systems

There are various classes of non-equilibrium dynamics supported by isolated many-body quantum systems. In systems obeying the eigenstate thermalization hypothesis, initially-ordered states evolve into states that appear to be in thermal equilibrium with a fictitious bath. On the other hand, many-body localised systems retain memory of the initial state indefinitely via a set of emergent local conserved quantities. Recently peculiar quantum phases hosting co-existing thermal and athermal states with similar energy densities have been discovered. The athermal (or non-ergodic) eigenstates embedded within a chaotic spectrum are dubbed "quantum many-body scars".

Interest in this topic appears to have been sparked by a 2017 experiment using a 1D chain of 51 trapped Rydberg atoms, where long-lived interaction-induced oscillations of the atomic states were observed. A subsequent theory paper analyzed this behaviour using a relatively simple effective model, where strong interactions constrain the dynamics of certain initial states to a small subset of the full Hilbert space. Remarkably, the set of anomalous non-ergodic eigenstates is not necessarily limited to a small fraction of the full spectrum; models with confining interaction potentials or geometrical frustration can exhibit a fragmentation of the spectrum into an exponentially large number of disconnected sectors of various sizes!

One motivation for studying many-body quantum scars is that their long-lived coherent dynamics may be useful as a means of storing and manipulating quantum information. However, we still need to better understand what precise model features give rise to this non-ergodicity, and how to control and maximise the lifetime of the coherent many-body dynamics, such as by optimising longer-range interactions. Experiments using arrays of 200 Rydberg atoms published last month have demonstrated the importance of the underlying lattice geometry (persistent coherent dynamics were only observed in bipartite lattices) as well as the ability to stabilise the many-body scars using periodic driving. In the future I think it will be important to come up with more flexible ways to identify and measure the quantum many-body scarring and Hilbert space fragmentation, in particular to quantify its robustness to various perturbations.