Code-division multiple-access multiuser demodulator by using quantum fluctuations

We examine the average-case performance of a code-division multiple-access (CDMA) multiuser demodulator in which quantum fluctuations are utilized to demodulate the original message within the context of Bayesian inference. The quantum fluctuations are built into the system as a transverse field in the infinite-range Ising spin glass model. We evaluate the performance measurements by using statistical mechanics. We confirm that the CDMA multiuser modulator using quantum fluctuations achieve roughly the same performance as the conventional CDMA multiuser modulator through thermal fluctuations on average. We also find that the relationship between the quality of the original information retrieval and the amplitude of the transverse field is somehow a “universal feature” in typical probabilistic information processing, viz., in image restoration, error-correcting codes, and CDMA multiuser demodulation.

Figure 1

CDMA multiuser demodulation with quantum fluctuations.

Figure 2

(a) Dependence of overlap $M$ on level of thermal fluctuations $T$ for $\alpha =2.0$ and $T_0=1.0$. (b) Dependence of overlap $M$ on level of quantum fluctuations $\Gamma$ for $\alpha =2.0$ and $T_0=1.0$.

Figure 3

(a) Value of overlap on $\Gamma$-$T$ plane for $T_0=1.0$ and $\alpha =2.0$. Solid line indicates location of peak in overlap. (b) Dependence of $M_{\mathrm{top}}$ on $\Gamma$ corresponding to solid line in panel (a).

Figure 4

Overlap $M$ vs chip ratio $\alpha$. (a) Results for $T_0=1.0$ and $T=T_0$. (b) Results for $T_0=0.08$ and $T=T_0$. Bistable solutions coexist for $\Gamma =0$ in region ${\alpha }_1<\alpha <{\alpha }_2$.

Figure 5

(a) Spinodal line at $T_0=T=0.08$. (b) Spinodal line at $T_0=0.08$ and $T=0.05$. Solid line represents $\Gamma \left({\alpha }_1\right)$ and dotted line represents $\Gamma \left({\alpha }_2\right)$.

Figure 6

Difference between overlaps with and without transverse field for $T_0=1.0$ and $T=0.5$. Closed circles labeled A, B, C, and D denote points at which $\Delta M=0$ holds.

Figure 7

Improvable regions in $T$-$\Gamma$ (left) and $\Gamma$-$\alpha$ (right) planes for $T_0=1.0$. Dashed lines indicate border at which $\Delta M=0$ holds for $\alpha =2.0$ (a) and $T=0.5$ (b).

Figure 8

Upper two panels indicate value of overlap as a function of controlled parameters, temperature, and strength of transverse field for image restoration (left) and Sourlas code (right). Overlap is maximum on solid lines. Lower two panels indicate improvable and worsened regions for image restoration (left) and Sourlas code (right). $\Delta M=0$ holds on dashed lines. We set the parameters to ${\tau }_0=\tau =1.0,h=0.9$, and ${\beta }_0=0.9$ for the image restoration model and $J=J_0=1.0$, and $p=3$ for the Sourlas code following previous studies [7, 8].