After looking into this question there appears to be many roots for this Jewish tradition. For the most part it is show respect like leaving a flower at a grave. If that does not suite you, here are the reasons I found.

1. When the tradition started, grave monuments were mounds of stones. Visitors added stones to "the mound" to show we are never finished building the monument to the deceased.

2. To tell the visitors that followed that others had also visited the grave.

3. Symbolically, it suggests the continuing presence of love and memory which are as strong and enduring as a rock. And we know that one name for God is "The Rock of Israel." So the rock is a reminder of the presence of the Rock, Whose love truly is stronger than death.

4. It is a sign of respect for the dead. It stems from the symbolism of making sure the burial site is noted by a stone marker. While adding a small stone doesn't really add a permanent marking to the site, it has evolved that this is the way an individual indicates participation in the process of marking a grave. 

5. This tradition may also reflect the biblical practice of marking the grave with a pile of stones. Or, it may be the end result of the custom of writing notes to the deceased and pushing them into crevices in the headstone just as notes are pushed into the Western Wall in Jerusalem. When no crevice could be found, the note was weighted down with a stone. In time, the paper disintegrated or blew away leaving only the stone. Thus, some began to think that the leaving of a stone was the custom... and so it became the custom.

6. There is a belief, with roots in the Talmud, that souls continue to dwell for a while in the graves in which they are placed. In the Eastern European folk imagination, these souls -- even those that were benign in life -- can take on a certain terror in death. The stories of Isaac Bashevis Singer and the plays of the Yiddish theatre, rich in the mythology of Eastern European Jewry, are filled with these types of haunting: souls who returned, for whatever reason, to the world of the living.  The practice of leaving stones atop a grave can be explained as a response to these beliefs. More than a simple marker of one's visit, stones on the grave are the means by which the living help souls remain where they belong -- in the grave where they do no haunting.  Another beautiful answer to the stones on graves question takes its cue from the inscription on many gravestones: the five-letter Hebrew abbreviation taf, nun, tsadi, bet, hey, which stands for "teheye nishmato tsrurah b'tsror haChayyim." This phrase is usually translated as "May his soul be bound up in the bounds of eternal life" -- a phrase wishing for eternal life for the departed.  Yet tsror (the fourth word of the Hebrew phrase) can also be translated as "pebble." Suddenly, the phrase takes on a more nuanced meaning, based on the historical significance of pebbles.

7. In ancient times, shepherds needed a system to keep track of their flocks. On some days, they would go out to pasture with a flock of thirty; on other days a flock of ten; the third day with fifty. As memory was an unreliable way of keeping tabs on the number of the flock that day, the shepherd would carry a sling over his shoulder, and in it keep the number of tsror, pebbles, that corresponded to the number in his flock. That way he could have an accurate daily count.  When we place stones on the grave, and inscribe the motto above on the stone, we are asking God to keep the departed's soul in God's sling. Among all the souls whom God has to watch over, we wish to add the name, the "pebble" of the soul of our departed.

    At times shells were used to mark the grave. One anthropologist in the early 1890s remarked that "nearly every grave has bordering or thrown upon it a few bleached sea-shells of a dozen different kinds." This practice has been traced back to at least the BaKongo belief that the sea shell encloses the soul's immortal presence. There was a prayer to the mbamba sea shell:
As strong as your house you shall keep my life for me. When you leave for the sea, take me along, that I may live forever with you.
Even into the twentieth century some Gullah explained the use of shells on graves as representing the sea:
The sea brought us, the sea shall take us back. So the shells upon our graves stand for water, the means of glory and the land of demise.
source:SCIiway

QR codes are the 2d matrix barcodes created in Japan by a subsidiary of Toyota, Denso-Wave in 1994. They can be found coupons, products, airline ticket, ads, and so on. With a smart phone they can be easily scan. Depending what the barcode it is on, it will bring up promotion, websites, videos and whatever else can be thought of.

Now these barcodes are being placed on tombstones.  They can retrieve photos of the deceased, a message from the person, or maybe a sign in book. Pretty endless since these codes can pull up websites.

Coming from slightly of technical background I do see the problem that over a long period time these barcodes will no longer pull up anything or wrong info. Unless they find a way to keep the information that these codes pull up saved on a server (computer) for now on. Think of  it like a website staying up for 25yr , 50yrs or even 100yrs, eventually the site will go down.

In the mean time, I think these QR codes on tombstones are great ideas!

Here are some sites for further reading:
NPR QR codes on tombstones
Mashable
A tech blog on the subject

People are buried east to west with the head on the western side. This mirrors the layout of Christian churches, and for much the same reason; to view the coming of Christ on Judgment day (Eschaton). In many Christian traditions, ordained clergy are traditionally buried in the opposite orientation, and their coffins carried likewise, so that at the General Resurrection they may rise facing, and ready to minister to, their people.

In Islam, the grave should be aligned perpendicular to the Qibla (i.e. Mecca). 

A tombstone is refered to as a headstone, and the world's biggest one belongs to the heaviest twins in the world. Billy and Benny McCrary weighed 743 and 723lbs. When Billy died in a mini bike stunt, Benny erected the largest tombstone. It weighs 3 tons and 13 feet wide. You can find the tombstone at The Cemetery at Crab Creek Baptist Church outside Hendersonville, North Carolina (35.245342, -82.548065). Berry died in 2001 with heart failure.