4-photon quantum states using topological edge modes

Topologically protected quantum entanglement emitters

This study was published in Nature Photonics last week. The experiments implement a topological ring resonator lattice using silicon photonics. A bright pump beam injected into opposite edges of the lattice can then generates two- and four-photon quantum states via four-wave mixing. The relative phase of the two pump beams can be used to control the degree of entanglement of the generated photons. This is to the best of my knowledge the first work to demonstrate generation of four-photon quantum states using a topological lattice.

 

What I found most surprising about this study is the author list, which includes PsiQuantum CEO Jeremy L. O’Brien under a University of Western Australia affiliation. Getting into Western Australia during the pandemic and their border closure (not even visitors from other Australian states allowed in) must have been quite a challenge!

 

Singapore Quantum Jobs

Qove Laboratory seeks postdoctoal fellows and PhD students: designing and building quantum technologies for quantum networks based on superconducting circuits, rare-earth ions, and integrated photonics. This is a newly-funded NRF Fellowship project with funding for 5 years.

Senior Research Fellow / Research Fellow positions at the School of Electrical & Electronic Engineering, Nanyang Technological University on development finite difference time domain methods for coupled electromagnetic and quantum systems. I guess this is related to the new Quantum Science & Engineering Centre announced at the end of last year.

Research Director in Quantum Computing and Quantum Communication at JPMorgan Chase’s Future Lab for Applied Research and Engineering. They are after someone with at least 12 years' relevant experience to investigate applications to finance, AI, optimization, and quantum key distribution.

PRX Quantum seeks an Associate Editor. The part-time Associate Editor is welcomed to maintain their current position–be it in academia, industry, or others, while contributing to PRX Quantum. They should also hold high standards for peer review, and be committed to building an exceptional reputation for the journal. Researchers from anywhere in the world can apply. This is a great opportunity!

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.

 

ICOAM 2022 - call for abstracts

6th International Conference on Optical Angular Momentum
12–17 June 2022
Tampere University, Finland

ICOAM covers topics broadly related to the fields of structured light and singular optics. The conference was supposed to be held last year, but was postponed due to covid. The organisers are optimistic it can be held in person this year. The submission deadline for contributed abstracts is 1st March.

I did not yet have a chance to attend any conference from this series, but I've met many of the committee members at other events (SOILM13, Singular Optics, BIRS) and I'm sure they will put together a very thought-provoking and inspiring series of talks!

arXiv picks

 

Topological Molecules and Topological Localization of a Rydberg Electron on a Classical Orbit

Here the authors show conditions under which electrons in highly excited orbitals of Rydberg atoms (or interacting atoms) can be used to emulate topological tight binding models. The key idea is that a periodically-modulated driving field (or interaction strength) induces "hopping" on an effective tight binding lattice formed by the electron orbitals (or orbitals of the atomic related position)

 

Quantized Fractional Thouless Pumping of Solitons

Following up on previous work (summarised here and here), Jurgensen and collaborators now observe fractional topological pumping of solitons in a periodically-driven waveguide lattice. Here fractional pumping means that multiple cycles of the periodic modulation are required to obtain a shifted copy of the original beam profile. It is quite remarkable that such an analogy with fractional quantum Hall systems can be observed using a classical nonlinear optical system.

Persistent Homology of ℤ2 Gauge Theories

Here the authors use persistent homology to study topological order in Z2 gauge theories, whose ground states consist of loops of occupied links. The idea here is that the positions of the occupied links in the ground state define a point cloud, whose shape can be reliably analyzed using persistent homology to detect phase transitions. Potential applications to models of topological quantum error-correcting codes are discussed as a direction for future work.

Roadmap on Topological Photonics

A comprehensive survey on current and future directions of topological photonics by many big names in the field.

 

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.

Mapping optimization problems onto boson sampling circuits

Certain properties and applications of shallow bosonic circuits

This arXiv preprint comes from ORCA Computing, an Oxford University spin-off company pursuing fibre optic-based quantum computing. In brief, the fibre optic platform uses trains of time-delayed single photon pulses and number-resolved photon detection.

The authors consider how variational quantum eigensolvers, an immensely popular class of algorithms for near-term qubit-based systems such as superconducting quantum processors, may be mapped to shallow linear interferometers employed for boson sampling experiments. Their idea is:

1. Boson sampling circuits sample from a distribution integer strings (n1,n2,...nM), where ni corresponds to n photons detected in mode i.

2. Taking the parity of the output maps this to a distribution of bitstrings (b1,...,bM), which can be interpreted as a measurement of a qubit-based system in the computational basis.

3. Under certain constraints this parity mapping allows one to sample from a complete basis of the qubit Hilbert space and thereby measure cost functions of binary optimization problems such as QUBO.

4. Output observables obey the parameter shift rule, making gradient-based minimization of the cost function to solve the optimization problem practical.

I think studies such as this on mappings between qubit-based and bosonic NISQ devices are important. While a few general-purpose optimization algorithms for qubit systems have been developed, proposed applications of NISQ bosonic circuits remain largely limited to "hardware native" schemes, i.e. simulation of properties of bosonic Hamiltonians such as molecular vibration spectra. This work provides a general scheme by which one might solve more general optimization problems using boson sampling devices, making them much more valuable for end-users.

However, two caveats I can see:

1. The QAOA algorithm is perhaps the most promising variational quantum algorithm, because it is a structured (problem-inspired) circuit with relatively few free parameters that need to be optimized, with some rigorous performance guarantees. While linear interferometers are described by a manageable number of free parameters, there is no guarantee that this kind of hardware-efficient circuit can always express the optimal solution to the optimization problem at hand.

2. The elephant in the room: Are the proposed circuits hard to simulate on a classical computer? While exact boson sampling is provably hard, hardness of the approximate sampling problem rests on the number of optical modes M being much larger than N^2, where N is the total number of input photons. In this limit there is a very low probability of detecting more than one photon in any output mode and the number resolved detection and parity map are not required. In their proof of concept simulations, however, the authors consider only the case M ~ N...