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...

Postdocs in topological waves

Lille, France: Postdoc in topological phoXonic (photonic / phononic) crystals

The objective of this post-doc position is to propose and develop numerically a dual phononic and photonic (phoXonic) topologic insulator for optomechanical applications on a single Si-based platform. This approach is expected to allow (i) to generate MHz and GHz mechanical waves optically, and (ii) to transport the acoustic and optical information through a single topological waveguide.

Application Deadline: 7 February

Stockholm, Sweeden: Postdoc in theoretical physics and topological phenomena 

The position involves research in the theory of topological phases in collaboration with Emil J. Bergholtz and other researchers in Stockholm as well as with our collaborators elsewhere.  A suitable background is a PhD in theoretical physics specializing in theoretical condensed matter physics, high energy physics or mathematical physics.

Application Deadline: 28 February

Focking lasers, how do they work?

Fock lasers based on deep-strong coupling of light and matter

This summary is a little late because the preprint was posted when I was travelling last year.

This paper proposes a new kind of quantum light source using hybrid light-matter systems in the deep strong coupling regime. This is the regime in which the photonic mode with frequency ω (say, a microwave cavity) and a two-level system with transition frequency ω0 (such as a superconducting qubit) are coupled with a strength g >> ω, ω0. This hybrid system can act as a cavity with an effective nonlinearity of extremely high order, which gives rise to an N-photon blockade: the first N states can be populated, but the (N+1)th state cannot. When this hybrid system is coupled to an external pump it relaxes to a steady state in which the photon number distribution is strongly peaked at a Fock state with N = g^2 photons.

How does it work? The key is the spectrum of the hybrid system in the deep strong coupling regime. The low energy spectrum looks just like an ordinary quantum harmonic oscillator, with a uniform spacing ω between adjacent energy levels. But the eigenstates look very different, thanks to the photon-qubit coupling.

The ground state is twofold degenerate: the photonic mode is in a (Gaussian) coherent state displaced from the origin by +g (or -g), while the qubit's spin points in the -x (or +x) direction. Since g is large, these two states have a negligible overlap with each other; they are essentially independent.

 

 Two degenerate ladders of excited states are obtained by adding photons to each ground state. Each photon added increases the energy by ω (hence, the linear spectrum). The photonic wavefunction broadens and becomes more strongly oscillatory, just like excited states of the quantum harmonic oscillator. But each wavefunction's centre of mass is displaced by +g (or -g).

When the photon number reaches the critical value of N = g^2, the photonic parts of the two wavefunctions start to overlap and can therefore interfere. This means that the two ladders can no longer be treated independently; they become coupled. Interference between the -x and +x spin states of the qubit generates a nonzero z component of the spin. This gives an additional energy shift ω0 𝜎z (due to the qubit part of the Hamiltonian) that destroys the uniform level spacing. Because the large n harmonic oscillator wavefunctions oscillate rapidly, this energy shift is highly sensitive to n, making the spectrum nonlinear for n > g^2. Thus, only N quanta with energy ω can be resonantly coupled to the system before it tunes itself out of resonance. This is the mechanism behind the N-photon blockade.

These plots are based on g = 5. State-of-the-art experiments can reached g=2. Hopefully further improvements in superconducting quantum circuits will allow us to push g to even higher values.