Assessing quantum coherence in quantum annealers

Abstract

Demonstrating genuine many-body quantum coherence in large-scale quantum processors remains a central challenge for near-term quantum technologies. Recent experiments on D-Wave quantum annealers have investigated quenches of Ising chains and observed defect densities that show Kibble-Zurek scaling, consistent with coherent quantum dynamics. However, identical scaling can arise from classical or thermal processes. Here we propose the use of many-body coherent oscillations (MBCO) as a diagnostic for the identification of system-wide coherence in analog quantum simulators. Solving the time-dependent Schrodinger equation, we show that quenches of a staggered one-dimensional Ising chain across a quantum critical point produce oscillatory signatures in defect observables. We implement this model on the D-Wave Advantage quantum annealer. Using fast-anneal protocols, we find that, although defect densities follow Kibble-Zurek scaling, the expected oscillatory behavior is absent. We demonstrate that static disorder associated with individual qubits is not likely responsible for the absence of MBCO. Modest modifications to annealing schedules can dramatically enhance oscillation visibility. This work gives a general roadmap for the search for quantum coherence in noisy, large-scale quantum platforms.

Figures (6)

• Figure 1: (a) The staggered Ising chain with alternating strong ($J + \Delta$) and weak ($J -\Delta$) bond strengths. For an antiferromagnetic chain, kinks correspond to neighboring spins that are parallel after a quench. (b) Embedding of a staggered 10-qubit Ising chain on the D-Wave Advantage machine. The coloring of the qubits indicate the results of an anneal, with spin-up and spin-down indicated by orange and gray, respectively. (c) D-Wave annealing schedule noauthor_annealing_nodate for the couplings $\mathcal{J}(s)$ and $\Gamma(s)$ in Hamiltonian (\ref{['eq:hamiltonian']}) as a function of the anneal parameter $s = t/\tau$.
• Figure 2: (a) The average difference in kink densities across weak and strong bonds $P$ for annealing times in the reported coherent regime $5$ ns $\le \tau \le 25$ ns for staggered Ising chains of length $L=160$ obtained from D-Wave fast-quench anneals. Each line represents the mean of approximately 75,000 anneals for the indicated bond strengths $J$ and $\Delta$. (b) $P$ for D-Wave (blue) and theory (orange) for $J=0.375$ and $\Delta = 0.125$. Magnified insets show theoretically predicted many-body coherent oscillations are most pronounced for annealing times $\tau \lesssim 15$ ns. These oscillations are absent in the D-Wave data. (c) Fourier transform $S(\Omega)$ of $P(\tau)$ for D-Wave data and theory from (b). Theoretical curve for $S(\Omega)$ exhibits a well-defined peak at $\Omega \approx 5.4~\mathrm{GHz}$. The error window (orange band) has a full width corresponding to 2$\sigma$. (d) Fourier transform $S(\Omega)$ for the theoretical model accounting for disorder in Zeeman field, where $d$ is the strength of the disorder. We find that the prominent feature at $\Omega \approx 5.4~\mathrm{GHz}$ is robust to strong disorder.
• Figure 3: Theoretical results for annealing parameters beyond the range currently accessible on D-Wave. (a) Calculated expectation value of the difference in kink densities $P$ as a function of annealing time $\tau$ for various initial strengths of the parameter $\Gamma(0)$ (see legend in (b)). For these values of $\Gamma(0)$, a doublet peak structure in $S(\Omega)$ is visible. (b) Peaks in the Fourier transform of $S(\Omega)$ of $P$ become more prominent as $\Gamma(0)$ is decreased, in agreement with (a). (c) $S(\Omega)$ for $\Gamma(0)=2.83$ GHz and various disorder strengths $d$. (d) $P(\tau)$ for ultra-short anneal times ($\tau<5$ ns). (Inset) Fourier transform $S(\Omega)$ of $P(\tau)$.
• Figure 4: Sensitivity of $S(\Omega)$ to the range of annealing times included in the Fourier transform. (a) Windows indicate range of annealing times used to calculate the corresponding $S(\Omega)$ curves in (b). The curves in Fig. \ref{['fig:theory_dwave_comp']}c of the main text were obtained using the (red) window. (c) The double peak structure is most clearly visible for the window $0 \leq \tau \leq 20$ ns.
• Figure 5: Results of the iterative shimming procedure applied to the staggered Ising chain for the particular annealing time of $19 ns$. a) Histograms of the averaged magnetization $\tilde{m}$ for the first ten (red) and last ten (green). The distribution narrows and centers around zero as flux-bias offsets and coupler strengths are refined. b) Evolution of the programmed coupler strengths $J_{ij}$ over successive iterations converging toward stable values. c) Convergence of per-qubit flux-bias offset (FBO) values for gradual suppression of residual local-field biases. d) Standard deviation $\sigma_{\tilde{m}}$ of the orbit-averaged magnetization as a function of iteration, indicating rapid stabilization of the ensemble. Together, these panels illustrate how successive flux-bias and coupler adjustments restore symmetry between qubit orbits and minimize frustration, yielding a calibrated embedding faithful to the intended staggered Ising Hamiltonian.