diff --git a/benchmarks/quantized_matmul_kernel/autotune.py b/benchmarks/quantized_matmul_kernel/autotune.py
new file mode 100644
index 000000000000..f2d1858df64c
--- /dev/null
+++ b/benchmarks/quantized_matmul_kernel/autotune.py
@@ -0,0 +1,132 @@
+# To run, do python myscripts/autotune_quantized_matmul_pallas_kernel2.py 2>&1 | tee out.txt
+# Then in the out.txt, extract lines with "Add to table:" and replace the string with 4 spaces, then copy to the block table in the pallas kernel.
+import time
+from typing import List
+
+import jax
+import jax.numpy as jnp
+from jax import lax
+from jax import random
+import numpy as np
+import functools
+from jax.experimental import pallas as pl
+from jax.experimental.pallas import tpu as pltpu
+from torch_xla.experimental.pallas_kernels.quantized_matmul_kernel import (
+    quantized_matmul_int8,
+    get_tuned_block_sizes,
+    TUNED_BLOCK_SIZES,
+)
+
+def _quantize_tensor(x, n_bits: int = 8, dim: int = -1):
+  max_val = jnp.amax(jnp.abs(x), axis=dim, keepdims=True)
+  int_min = -2**(n_bits - 1)
+  int_max = 2**(n_bits - 1) - 1
+  scale = max_val / int_max
+  x_int = jnp.clip(jnp.rint(x / scale), int_min, int_max).astype(jnp.int8)
+  return x_int, scale.astype(x.dtype)
+
+def find_factors_multiple_of_128(n: int) -> List[int]:
+    """
+    Finds all factors of an integer n that are also multiples of 128.
+
+    Args:
+        n: The integer for which to find factors.
+
+    Returns:
+        A list of integers that are factors of n and are multiples of 128.
+        Returns an empty list if n is 0 or if no such factors exist.
+        Handles negative input by taking the absolute value.
+    """
+    # Handle edge case for 0
+    if n == 0:
+        return []
+
+    # Work with the absolute value for factor finding
+    n_abs = abs(n)
+
+    # We are looking for factors f such that n_abs % f == 0 AND f % 128 == 0.
+    # This means f must be a multiple of 128.
+    # So, we only need to check multiples of 128 up to n_abs.
+
+    factors = []
+    multiplier = 1
+    potential_factor = 128 * multiplier
+
+    # Iterate through multiples of 128 (128, 256, 384, ...)
+    # as long as they are less than or equal to n_abs
+    while potential_factor <= n_abs:
+        # Check if this multiple of 128 is a factor of n_abs
+        if n_abs % potential_factor == 0:
+            factors.append(potential_factor)
+
+        # Move to the next multiple of 128
+        multiplier += 1
+        potential_factor = 128 * multiplier # Calculate the next potential factor
+
+    return factors
+
+# Benchmarking script starts.
+
+# one off
+# batch_sizes = [16, 32]
+# out_in_features = [(128, 256), (256, 128)]
+# batch_block_sizes = [128, 256]
+
+# for real
+batch_sizes = [16, 32, 64, 128, 256, 512, 1024, 2048]
+out_in_features = [(6144, 4096), (4096, 4096), (28672, 4096), (4096, 14336), (1280, 8192), (8192, 1024), (7168, 8192), (8192, 3584)]
+batch_block_sizes = [128, 256, 512, 1024, 2048]
+
+for bs in batch_sizes:
+  for n_output_features, n_input_features in out_in_features:
+    out_block_sizes = find_factors_multiple_of_128(n_output_features)
+    in_block_sizes = find_factors_multiple_of_128(n_input_features)
+    print(f'Benchmarking w8a8 matmul with bs={bs}, n_output_features={n_output_features}, n_input_features={n_input_features}, for block sizes: {out_block_sizes=}, {in_block_sizes=}')
+
+    dtype = jnp.bfloat16
+    prng_key = jax.random.key(1234)
+    k0, k1 = jax.random.split(prng_key, 2)
+    x = jax.random.normal(k0, (bs, n_input_features), dtype=dtype)
+    w = jax.random.normal(k1, (n_output_features, n_input_features), dtype=dtype)
+    w_w8a8_jax, scalar_jax = _quantize_tensor(w, n_bits=8, dim=-1)
+    scalar_jax = scalar_jax.squeeze()
+    assert scalar_jax.shape == (n_output_features,)
+
+    vmem_limit_80_mb = 80 * 1024 * 1024
+    best_time = None
+    best_batch_block_size = None
+    best_out_block_size = None
+    best_in_block_size = None
+    skip_trial = False
+    for batch_block_size in batch_block_sizes:
+      if bs < batch_block_size and best_time is not None:
+        continue
+      for out_block_size in out_block_sizes:
+        for in_block_size in in_block_sizes:
+          skip_trial = False
+          print(f'Benchmarking w8a8 matmul bs={bs}, n_output_features={n_output_features}, n_input_features={n_input_features} with batch_block_size={batch_block_size}, out_block_size={out_block_size}, in_block_size={in_block_size}', flush=True)
+          for _ in range(10):  # warming up
+            try:
+              quantized_matmul_int8(x, w_w8a8_jax, scalar_jax, quantize_activation=True, batch_block_size=batch_block_size, out_block_size=out_block_size, in_block_size=in_block_size, vmem_limit_bytes=vmem_limit_80_mb).block_until_ready()
+            except Exception as e:
+              print(f'Failed to run quantized_matmul with batch_block_size={batch_block_size}, out_block_size={out_block_size}, in_block_size={in_block_size} due to {e}', flush=True)
+              skip_trial = True
+              break
+          if skip_trial:
+            continue
+          num_iterations = 30
+          start_time = time.perf_counter_ns()
+          for _ in range(num_iterations):
+            quantized_matmul_int8(x, w_w8a8_jax, scalar_jax, quantize_activation=True, batch_block_size=batch_block_size, out_block_size=out_block_size, in_block_size=in_block_size, vmem_limit_bytes=vmem_limit_80_mb).block_until_ready()
+          end_time = time.perf_counter_ns()
+          elapsed_time = (end_time - start_time) / num_iterations
+          print(f'Benchmarked w8a8 matmul with batch_block_size={batch_block_size}, out_block_size={out_block_size}, in_block_size={in_block_size}, time={elapsed_time}')
+          if best_time is None or elapsed_time < best_time:
+            best_time = elapsed_time
+            best_batch_block_size = batch_block_size
+            best_out_block_size = out_block_size
+            best_in_block_size = in_block_size
+    print(f'Best batch_block_size={best_batch_block_size}, out_block_size={best_out_block_size}, in_block_size={best_in_block_size}, time={best_time}')
+    print(f'Add to table: (6, {bs}, {n_output_features}, {n_input_features}, \'{jnp.dtype(dtype).name}\', {True}): ({best_batch_block_size}, {best_out_block_size}, {best_in_block_size}),')
+
+# key should be: bs, n_output_features, n_input_features, dtype, quantize_activation
diff --git a/benchmarks/quantized_matmul_kernel/benchmark.py b/benchmarks/quantized_matmul_kernel/benchmark.py
new file mode 100644
index 000000000000..e83ea146f0fe
--- /dev/null
+++ b/benchmarks/quantized_matmul_kernel/benchmark.py
@@ -0,0 +1,74 @@
+import time
+from typing import List
+
+import jax
+import jax.numpy as jnp
+from jax import lax
+from jax import random
+import numpy as np
+import functools
+from jax.experimental import pallas as pl
+from jax.experimental.pallas import tpu as pltpu
+from torch_xla.experimental.pallas_kernels.quantized_matmul_kernel import (
+    quantized_matmul_int8,
+)
+
+cases = {
+  "TP=1":{
+    "bs_nums": {16: 127, 128: 901, 256: 1, 512: 512, 1024: 5, 2048: 846},
+    "out_in_features": [(6144, 4096), (4096, 4096), (28672, 4096), (4096, 14336)],
+  },
+  "TP=8": {
+    "bs_nums": {16: 1016, 64: 64, 128: 1440, 512: 8, 1024: 32, 2048: 7032},
+    "out_in_features": [(1280, 8192), (8192, 1024), (7168, 8192), (8192, 3584)],
+  },
+}
+
+# one off, for testing
+# cases = {
+#   "TP=1":{
+#     "bs_nums": {16: 1, 128: 2},
+#     "out_in_features": [(128, 128)],
+#   },
+#   "TP=8": {
+#     "bs_nums": {16: 1, 128: 2},
+#     "out_in_features": [(256, 256)],
+#   },
+# }
+
+def _quantize_tensor(x, n_bits: int = 8, dim: int = -1):
+  max_val = jnp.amax(jnp.abs(x), axis=dim, keepdims=True)
+  int_min = -2**(n_bits - 1)
+  int_max = 2**(n_bits - 1) - 1
+  scale = max_val / int_max
+  x_int = jnp.clip(jnp.rint(x / scale), int_min, int_max).astype(jnp.int8)
+  return x_int, scale.astype(x.dtype)
+
+def run_benchmark(bs_nums, out_in_features: List[tuple]):
+  elapsed_time_ms = 0
+  print(f"Running benchmark with bs_nums: {bs_nums} and out_in_features: {out_in_features}")
+  for bs, num_occur in bs_nums.items():
+    for n_output_features, n_input_features in out_in_features:
+      dtype = jnp.bfloat16
+      prng_key = random.key(1234)
+      k0, k1 = jax.random.split(prng_key, 2)
+      x = jax.random.normal(k0, (bs, n_input_features), dtype=dtype)
+      w = jax.random.normal(k1, (n_output_features, n_input_features), dtype=dtype)
+      w_w8a8_jax, scalar_jax = _quantize_tensor(w, n_bits=8, dim=-1)
+      scalar_jax = scalar_jax.squeeze()
+      assert scalar_jax.shape == (n_output_features,)
+      num_warmup = 5
+      for _ in range(num_warmup):
+        quantized_matmul_int8(x, w_w8a8_jax, scalar_jax, quantize_activation=True).block_until_ready()
+      start_time = time.perf_counter_ns()
+      for _ in range(num_occur):
+        quantized_matmul_int8(x, w_w8a8_jax, scalar_jax, quantize_activation=True).block_until_ready()
+      end_time = time.perf_counter_ns()
+      elapsed_time_ms += (end_time - start_time)/(1e6)
+  return elapsed_time_ms
+
+for case, value in cases.items():
+  bs_nums = value["bs_nums"]
+  out_in_features = value["out_in_features"]
+  elapsed_time_ms = run_benchmark(bs_nums, out_in_features)
+  print(f"Benchmarking {case} took {elapsed_time_ms:.2f} ms")
diff --git a/benchmarks/quantized_matmul_kernel/microbenchmark.py b/benchmarks/quantized_matmul_kernel/microbenchmark.py
new file mode 100644
index 000000000000..21efa645f5d8
--- /dev/null
+++ b/benchmarks/quantized_matmul_kernel/microbenchmark.py
@@ -0,0 +1,2 @@
+# I plan to create one but I think the kernel should reside in g3 and so the microbenchmark should be in g3 using xprof.
+# So I'll not create a microbenchmark for now.
diff --git a/torch_xla/experimental/pallas_kernels/quantized_matmul_kernel.py b/torch_xla/experimental/pallas_kernels/quantized_matmul_kernel.py
index e2d4903ae260..6693b8ddb6b3 100644
--- a/torch_xla/experimental/pallas_kernels/quantized_matmul_kernel.py
+++ b/torch_xla/experimental/pallas_kernels/quantized_matmul_kernel.py
@@ -212,70 +212,70 @@ def quantized_matmul_int8(
 #    - out_block_size
 #    - in_block_size
 TUNED_BLOCK_SIZES = {
-    (6, 16, 6144, 4096, 'bfloat16', True): (128, 768, 4096),
-    (6, 16, 4096, 4096, 'bfloat16', True): (128, 2048, 2048),
-    (6, 16, 28672, 4096, 'bfloat16', True): (128, 1792, 2048),
-    (6, 16, 4096, 14336, 'bfloat16', True): (128, 512, 7168),
-    (6, 16, 1280, 8192, 'bfloat16', True): (128, 256, 8192),
-    (6, 16, 8192, 1024, 'bfloat16', True): (128, 8192, 256),
-    (6, 16, 7168, 8192, 'bfloat16', True): (128, 512, 8192),
+    (6, 16, 6144, 4096, 'bfloat16', True): (128, 6144, 1024),
+    (6, 16, 4096, 4096, 'bfloat16', True): (128, 4096, 1024),
+    (6, 16, 28672, 4096, 'bfloat16', True): (128, 3584, 2048),
+    (6, 16, 4096, 14336, 'bfloat16', True): (128, 4096, 1792),
+    (6, 16, 1280, 8192, 'bfloat16', True): (128, 1280, 2048),
+    (6, 16, 8192, 1024, 'bfloat16', True): (128, 1024, 1024),
+    (6, 16, 7168, 8192, 'bfloat16', True): (128, 7168, 1024),
     (6, 16, 8192, 3584, 'bfloat16', True): (128, 2048, 3584),
     (6, 32, 6144, 4096, 'bfloat16', True): (128, 1536, 4096),
-    (6, 32, 4096, 4096, 'bfloat16', True): (128, 4096, 2048),
-    (6, 32, 28672, 4096, 'bfloat16', True): (128, 2048, 2048),
-    (6, 32, 4096, 14336, 'bfloat16', True): (128, 256, 14336),
-    (6, 32, 1280, 8192, 'bfloat16', True): (128, 256, 8192),
-    (6, 32, 8192, 1024, 'bfloat16', True): (128, 1024, 1024),
-    (6, 32, 7168, 8192, 'bfloat16', True): (128, 3584, 2048),
-    (6, 32, 8192, 3584, 'bfloat16', True): (128, 1024, 3584),
-    (6, 64, 6144, 4096, 'bfloat16', True): (128, 512, 4096),
-    (6, 64, 4096, 4096, 'bfloat16', True): (128, 2048, 2048),
-    (6, 64, 28672, 4096, 'bfloat16', True): (128, 1792, 2048),
+    (6, 32, 4096, 4096, 'bfloat16', True): (128, 4096, 1024),
+    (6, 32, 28672, 4096, 'bfloat16', True): (128, 4096, 2048),
+    (6, 32, 4096, 14336, 'bfloat16', True): (128, 4096, 1792),
+    (6, 32, 1280, 8192, 'bfloat16', True): (128, 1280, 2048),
+    (6, 32, 8192, 1024, 'bfloat16', True): (128, 8192, 256),
+    (6, 32, 7168, 8192, 'bfloat16', True): (128, 1792, 4096),
+    (6, 32, 8192, 3584, 'bfloat16', True): (128, 8192, 896),
+    (6, 64, 6144, 4096, 'bfloat16', True): (128, 1536, 2048),
+    (6, 64, 4096, 4096, 'bfloat16', True): (128, 2048, 1024),
+    (6, 64, 28672, 4096, 'bfloat16', True): (128, 3584, 2048),
     (6, 64, 4096, 14336, 'bfloat16', True): (128, 4096, 1024),
-    (6, 64, 1280, 8192, 'bfloat16', True): (128, 1280, 4096),
-    (6, 64, 8192, 1024, 'bfloat16', True): (128, 4096, 1024),
-    (6, 64, 7168, 8192, 'bfloat16', True): (128, 512, 8192),
+    (6, 64, 1280, 8192, 'bfloat16', True): (128, 1280, 2048),
+    (6, 64, 8192, 1024, 'bfloat16', True): (128, 8192, 1024),
+    (6, 64, 7168, 8192, 'bfloat16', True): (128, 3584, 2048),
     (6, 64, 8192, 3584, 'bfloat16', True): (128, 2048, 1792),
-    (6, 128, 6144, 4096, 'bfloat16', True): (128, 1536, 4096),
-    (6, 128, 4096, 4096, 'bfloat16', True): (128, 1024, 4096),
-    (6, 128, 28672, 4096, 'bfloat16', True): (128, 1024, 4096),
-    (6, 128, 4096, 14336, 'bfloat16', True): (128, 2048, 2048),
-    (6, 128, 1280, 8192, 'bfloat16', True): (128, 640, 4096),
+    (6, 128, 6144, 4096, 'bfloat16', True): (128, 6144, 1024),
+    (6, 128, 4096, 4096, 'bfloat16', True): (128, 4096, 2048),
+    (6, 128, 28672, 4096, 'bfloat16', True): (128, 28672, 512),
+    (6, 128, 4096, 14336, 'bfloat16', True): (128, 2048, 3584),
+    (6, 128, 1280, 8192, 'bfloat16', True): (128, 1280, 1024),
     (6, 128, 8192, 1024, 'bfloat16', True): (128, 2048, 1024),
-    (6, 128, 7168, 8192, 'bfloat16', True): (128, 896, 8192),
-    (6, 128, 8192, 3584, 'bfloat16', True): (128, 1024, 3584),
-    (6, 256, 6144, 4096, 'bfloat16', True): (256, 1536, 4096),
-    (6, 256, 4096, 4096, 'bfloat16', True): (256, 512, 4096),
-    (6, 256, 28672, 4096, 'bfloat16', True): (256, 896, 4096),
-    (6, 256, 4096, 14336, 'bfloat16', True): (256, 4096, 2048),
-    (6, 256, 1280, 8192, 'bfloat16', True): (256, 1280, 4096),
-    (6, 256, 8192, 1024, 'bfloat16', True): (256, 2048, 1024),
-    (6, 256, 7168, 8192, 'bfloat16', True): (256, 512, 8192),
-    (6, 256, 8192, 3584, 'bfloat16', True): (256, 1024, 3584),
+    (6, 128, 7168, 8192, 'bfloat16', True): (128, 1792, 4096),
+    (6, 128, 8192, 3584, 'bfloat16', True): (128, 8192, 896),
+    (6, 256, 6144, 4096, 'bfloat16', True): (256, 3072, 4096),
+    (6, 256, 4096, 4096, 'bfloat16', True): (256, 2048, 4096),
+    (6, 256, 28672, 4096, 'bfloat16', True): (256, 3584, 4096),
+    (6, 256, 4096, 14336, 'bfloat16', True): (256, 4096, 1792),
+    (6, 256, 1280, 8192, 'bfloat16', True): (256, 1280, 2048),
+    (6, 256, 8192, 1024, 'bfloat16', True): (256, 4096, 1024),
+    (6, 256, 7168, 8192, 'bfloat16', True): (256, 1792, 4096),
+    (6, 256, 8192, 3584, 'bfloat16', True): (256, 8192, 512),
     (6, 512, 6144, 4096, 'bfloat16', True): (512, 2048, 4096),
-    (6, 512, 4096, 4096, 'bfloat16', True): (512, 1024, 4096),
-    (6, 512, 28672, 4096, 'bfloat16', True): (512, 1792, 4096),
-    (6, 512, 4096, 14336, 'bfloat16', True): (512, 4096, 1792),
+    (6, 512, 4096, 4096, 'bfloat16', True): (512, 4096, 512),
+    (6, 512, 28672, 4096, 'bfloat16', True): (512, 4096, 4096),
+    (6, 512, 4096, 14336, 'bfloat16', True): (512, 4096, 2048),
     (6, 512, 1280, 8192, 'bfloat16', True): (512, 1280, 2048),
     (6, 512, 8192, 1024, 'bfloat16', True): (512, 4096, 1024),
-    (6, 512, 7168, 8192, 'bfloat16', True): (512, 1792, 4096),
-    (6, 512, 8192, 3584, 'bfloat16', True): (512, 2048, 3584),
-    (6, 1024, 6144, 4096, 'bfloat16', True): (1024, 1024, 4096),
-    (6, 1024, 4096, 4096, 'bfloat16', True): (1024, 2048, 4096),
-    (6, 1024, 28672, 4096, 'bfloat16', True): (1024, 3584, 4096),
-    (6, 1024, 4096, 14336, 'bfloat16', True): (1024, 2048, 2048),
-    (6, 1024, 1280, 8192, 'bfloat16', True): (1024, 1280, 2048),
-    (6, 1024, 8192, 1024, 'bfloat16', True): (256, 8192, 1024),
-    (6, 1024, 7168, 8192, 'bfloat16', True): (1024, 1792, 8192),
-    (6, 1024, 8192, 3584, 'bfloat16', True): (1024, 2048, 3584),
+    (6, 512, 7168, 8192, 'bfloat16', True): (512, 7168, 512),
+    (6, 512, 8192, 3584, 'bfloat16', True): (512, 8192, 512),
+    (6, 1024, 6144, 4096, 'bfloat16', True): (512, 6144, 4096),
+    (6, 1024, 4096, 4096, 'bfloat16', True): (256, 4096, 4096),
+    (6, 1024, 28672, 4096, 'bfloat16', True): (1024, 4096, 4096),
+    (6, 1024, 4096, 14336, 'bfloat16', True): (1024, 4096, 1792),
+    (6, 1024, 1280, 8192, 'bfloat16', True): (512, 1280, 4096),
+    (6, 1024, 8192, 1024, 'bfloat16', True): (512, 8192, 1024),
+    (6, 1024, 7168, 8192, 'bfloat16', True): (512, 7168, 1024),
+    (6, 1024, 8192, 3584, 'bfloat16', True): (256, 8192, 3584),
     (6, 2048, 6144, 4096, 'bfloat16', True): (256, 6144, 4096),
-    (6, 2048, 4096, 4096, 'bfloat16', True): (1024, 2048, 4096),
+    (6, 2048, 4096, 4096, 'bfloat16', True): (512, 4096, 4096),
     (6, 2048, 28672, 4096, 'bfloat16', True): (1024, 4096, 4096),
-    (6, 2048, 4096, 14336, 'bfloat16', True): (1024, 4096, 1024),
-    (6, 2048, 1280, 8192, 'bfloat16', True): (512, 1280, 8192),
+    (6, 2048, 4096, 14336, 'bfloat16', True): (1024, 4096, 2048),
+    (6, 2048, 1280, 8192, 'bfloat16', True): (2048, 1280, 1024),
     (6, 2048, 8192, 1024, 'bfloat16', True): (256, 8192, 1024),
-    (6, 2048, 7168, 8192, 'bfloat16', True): (1024, 1792, 8192),
-    (6, 2048, 8192, 3584, 'bfloat16', True): (2048, 2048, 3584),
+    (6, 2048, 7168, 8192, 'bfloat16', True): (256, 7168, 8192),
+    (6, 2048, 8192, 3584, 'bfloat16', True): (512, 8192, 3584),
 }