Quantum fluctuation theorem for error diagnostics in quantum annealers

Abstract

Near term quantum hardware promises unprecedented computational advantage. Crucial in its development is the characterization and minimization of computational errors. We propose the use of the quantum fluctuation theorem to benchmark the accuracy of quantum annealers. This versatile tool provides simple means to determine whether the quantum dynamics are unital, unitary, and adiabatic, or whether the system is prone to thermal noise. Our proposal is experimentally tested on two generations of the D-Wave machine, which illustrates the sensitivity of the fluctuation theorem to the smallest aberrations from ideal annealing. In addition, for the optimally operating D-Wave machine, our experiment provides the first experimental verification of the integral fluctuation in an interacting, many-body quantum system.

Generalized energy measurements and quantum work compatible with fluctuation theorems

“…Finally, the requirement of error-free measurements appearing in the conditions for the validity of fluctuation theorems might put a severe restriction on the experimental realization and the practical usefulness of the fluctuation relations for quantum mechanical systems. However, the necessity of our conditions for the validity of fluctuation theorems suggests a potential application of fluctuation theorems to a diagnostic verification of the accuracy of quantum measurements in a similar spirit to [34]. Moreover, other measurement strategies that can yield erroneous results may still be of practical use as long as the errors are superimposed on the sought-for work distribution in an a priori known way that makes a correction possible after the measurement.…”

Experimental characterization of the energetics of quantum logic gates

“…Remarkably, the fast-paced miniaturization process enabled by research in quantum information processing opens realistic possibilities to engineer and implement miniature-scale quantum machines akin to standard (macroscopic) engines that process and transform energy 7,8 . The challenge in this respect is to make use of the emerging field of quantum thermodynamics, which aims at establishing a framework for the thermodynamics of quantum processes and systems, to design energy-efficient quantum machines [9][10][11][12] possibly able to outperform their classical counterparts 3 , or benchmark the performance of quantum devices from a thermodynamic perspective, as recently done for the interesting case of quantum annealears 13,14 .…”

Disorder-assisted graph coloring on quantum annealers

“…The quality of a quantum computation/annealing can be measured in various ways [47]. For instance, one may try to count defects [26], estimate fluctuations [27], calculate the fidelity between the final state, |ψ(τ) , and the true ground state of the problem Hamiltonian [48], |φ , or simply determine the difference between their corresponding energies, δ E = ψ(τ)|Ĥ |ψ(τ) − φ |Ĥ |φ [24].…”