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 gradients
Google 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