# IEEE QCE21¶

Notes about some of the contributions to the IEEE’s Quantum Week 2021. - December, 2021

## Quantum Approximate Optimization¶

About Pranav Gokhale’s talk at QCE21 [M16]:

initial optimism:

but more recently:

*QAOA for Max-Cut requires hundreds of qubits for quantum speed-up*[52] -> classical \(\textrm{akmaxsat}\) in seconds while QAOA in days (for sparse graphs)*Classical and Quantum Bounded Depth Approximate Algorithm*[57] -> local classical MAX-3-LIN-2 scales better then QAOA*Bounds on approximating Max kXOR with quantum and classical local algorithms*[89] -> QAOA beats classical algorithms, but very far away from “Parisi limit” theoretical benchmark

noise issue:

optimism on

**dense (hyper)graphs**:\(\textrm{akmaxsat}\)’s runtime increases exponentially with graph density

*Optimized fermionic SWAP networks […] for QAOA*[56]

more optimism:

## Quantum Kernel Machines¶

More to digest: with a focus on **quantum kernel machines**
[M21] [M30] [M35]:

*Quantum embeddings for machine learning*, Lloyd & Schuld (2020) [79]about the Hilbert space of the quantum system being a natural space for kernel machines

*Machine learning of high dimensional data on a noisy quantum processor*, FermiLab/Google (2021) [104]use classical data to compute a quantum kernel matrix, then feed this to a classical SVM

beyond classical advantage to be found in an “expressive kernel that is classicaly hard to compute”, rather than in speed up (may be one day with quantum error correction)

*barren plateau*problems i.e. regions with vanishing gradientsGoogle Rainbow chip with 23 qubits

“fixed shot budget” (i.e. optimization is essential)

*Kernel Matrix Completion for Offline Quantum-Enhanced Machine Learning*, IBM (2021) [96]streaming data: a challenge for quantum kernels

matrix completion by a graph-theory-based algorithms using

*Positive Semidefinite Matrix Completion*[126]once the overlap exceeds the rank of the extended matrix, perfect completion is possible: about guessing the rank

*a priori*…

## Realizations¶

### Neutral Atoms¶

About [M38].

neutral atoms trapped in an array of optical tweezers (square or triangular lattice, arbitrary patterns)

atoms encoded in TLS

laser is tuned to drive a coherent transition between the two energy levels

incl. detuning (wrt. Rabi frequency)

Rydberg states, highly excited electronic states - two atoms will interact through large dipole interaction

Rydberg blockade: states get coupled to the entangled Bell state \(\ket{\phi_+}\)

*Many-body physics with individually controlled Rydberg atoms*[R6]

measurement through push-out beams and then fluorescence image of the remaining atoms

analog vs. digital

analog: shine all atoms with the same laser, continuously control the Hamiltonian, of all the qubits at the same time ; and measured at the end

a tunable Ising Hamiltonian

digital: usual circuit, local operations on specific qubits

qubits encoded in 2 hyperfine ground states

atoms don’t interact when not in a Rydberg state: no interaction term in the Hamiltonian

with one resonant pulse (combined with a change of phase of the laser), any arbitrary single-qubit gate can be performed

multi-qubits gates: atoms a brought briefly to the Rydberg state to exploit the Rydberg blockade

controlled Z gate (CZ), see below

no equivalence of the analog approach as a circuit