A double-slit proposal for quantum annealing

Abstract

We formulate and analyze a double-slit proposal for quantum annealing, which involves observing the probability of finding a two-level system (TLS) undergoing evolution from a transverse to a longitudinal field in the ground state at the final time $t_f$. We demonstrate that for annealing schedules involving two consecutive diabatic transitions, an interference effect is generated akin to a double-slit experiment. The observation of oscillations in the ground state probability as a function of $t_f$ (before the adiabatic limit sets in) then constitutes a sensitive test of coherence between energy eigenstates. This is further illustrated by analyzing the effect of coupling the TLS to a thermal bath: increasing either the bath temperature or the coupling strength results in a damping of these oscillations. The theoretical tools we introduce significantly simplify the analysis of the generalized Landau-Zener problem. Furthermore, our analysis connects quantum annealing algorithms exhibiting speedups via the mechanism of coherent diabatic transitions to near-term experiments with quantum annealing hardware.

19 pages, 3 figures

References in corpus (37)

• Quantum Annealing in the Transverse Ising Model
• Adiabatic Quantum Computing
• The Magnus expansion and some of its applications
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Quantum annealing with more than one hundred qubits
• Landau-Zener-Stuckelberg interferometry
• Quantum Annealing and Analog Quantum Computation
• Shortcuts to adiabaticity by counter-diabatic driving
• Mach-Zehnder Interferometry in a Strongly Driven Superconducting Qubit
• Observation of topological phenomena in a programmable lattice of 1,800 qubits
• Quantum Adiabatic Markovian Master Equations
• Landau-Zener interferometry with superconducting qubits
• A coherent beam splitter for electronic spin states
• Quantum Speedup by Quantum Annealing
• Analytically solvable driven time-dependent two-level quantum systems
• Decoherence in adiabatic quantum computation
• Observation of classical-quantum crossover of 1/f flux noise and its paramagnetic temperature dependence
• Reverse annealing for the fully connected $p$-spin model
• Modernizing Quantum Annealing using Local Searches
• Staying positive: going beyond Lindblad with perturbative master equations
• A Coherent Quantum Annealer with Rydberg Atoms
• Training A Quantum Optimizer
• Coarse-Graining Can Beat the Rotating Wave Approximation in Quantum Markovian Master Equations
• Exactly solvable two-level quantum systems and Landau-Zener interferometry
• Improved Error-Scaling for Adiabatic Quantum State Transfer
• Shortcuts to adiabaticity from linear response theory
• Scaling analysis and instantons for thermally-assisted tunneling and Quantum Monte Carlo simulations
• Quantum annealing for the number partitioning problem using a tunable spin glass of ions
• Reexamination of the evidence for entanglement in the D-Wave processor
• Adiabatic optimization versus diffusion Monte Carlo
• Time-Reversal Symmetry and Universal Conductance Fluctuations in a Driven Two-Level System
• Exploring More-Coherent Quantum Annealing
• Necessary Adiabatic Run Times in Quantum Optimization
• Spectral Gap Analysis for Efficient Tunneling in Quantum Adiabatic Optimization
• Sensitivity of quantum speedup by quantum annealing to a noisy oracle
• Landau-Zener-Stueckelberg interferometry with driving fields in the quantum regime
• Resonance in a driven two-level system: analytical results without the rotating wave approximation

Cited by in corpus (14)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond
• Dynamics of reverse annealing for the fully-connected $p$-spin model
• Why and when is pausing beneficial in quantum annealing?
• Variationally Scheduled Quantum Simulation
• Adaptive variational simulation for open quantum systems
• Generalized Adiabatic Impulse Approximation
• Customized quantum annealing schedules
• Locally Suppressed Transverse-Field Protocol for Diabatic Quantum Annealing
• Pulsed quantum annealing
• Demonstration of long-range correlations via susceptibility measurements in a one-dimensional superconducting Josephson spin chain
• Mapping State Transition Susceptibility in Quantum Annealing
• Decoherence of a tunable capacitively shunted flux qubit
• Quantitative analysis of the effectiveness of mid-anneal measurement in quantum annealing