diff --git a/tests/test_gpu_examples.py b/tests/test_gpu_examples.py
index d98142b7fb..000d8e9152 100644
--- a/tests/test_gpu_examples.py
+++ b/tests/test_gpu_examples.py
@@ -41,7 +41,9 @@
 
 from peft import (
     AdaLoraConfig,
+    LoftQConfig,
     LoraConfig,
+    TaskType,
     get_peft_model,
     prepare_model_for_int8_training,
     prepare_model_for_kbit_training,
@@ -941,6 +943,139 @@ def test_causal_lm_training_multi_gpu(self):
             self.assertIsNotNone(trainer.state.log_history[-1]["train_loss"])
 
 
+@require_torch_gpu
+class LoftQTests(unittest.TestCase):
+    r"""
+    Tests for LoftQ
+    """
+
+    def setUp(self):
+        self.error_factor = 3
+        self.model_id = "hf-internal-testing/tiny-random-BloomForCausalLM"
+        self.tokenizer = AutoTokenizer.from_pretrained(self.model_id)
+        self.inputs = self.tokenizer("All I want is", padding=True, return_tensors="pt").to("cuda")
+
+    def get_errors(self, bits=4, loftq_iter=1):
+        # Helper function that returns the quantization errors (MAE and MSE) when comparing the quantized LoRA model
+        # to the base model, vs the LoftQ quantized model to the base model. We expect the LoftQ quantized model to
+        # have less error than the normal LoRA quantized model. Since we compare logits, the observed error is
+        # already somewhat dampened because of the softmax.
+        model = AutoModelForCausalLM.from_pretrained(self.model_id).cuda().eval()
+        torch.manual_seed(0)
+        logits_base = model(**self.inputs).logits
+        # clean up
+        del model
+        gc.collect()
+        torch.cuda.empty_cache()
+
+        # logits from the normal quantized LoRA model
+        lora_config = LoraConfig(task_type=TaskType.CAUSAL_LM)
+        kwargs = {}
+        if bits == 4:
+            kwargs["load_in_4bit"] = True
+        elif bits == 8:
+            kwargs["load_in_8bit"] = True
+        else:
+            raise ValueError("bits must be 4 or 8")
+
+        quantized_model = get_peft_model(
+            AutoModelForCausalLM.from_pretrained(self.model_id, device_map="auto", **kwargs).eval(),
+            lora_config,
+        )
+        torch.manual_seed(0)
+        logits_quantized = quantized_model(**self.inputs).logits
+        del quantized_model
+        gc.collect()
+        torch.cuda.empty_cache()
+
+        # logits from quantized LoRA model using LoftQ
+        loftq_config = LoftQConfig(loftq_bits=bits, loftq_iter=loftq_iter)
+        lora_config = LoraConfig(task_type=TaskType.CAUSAL_LM, init_lora_weights="loftq", loftq_config=loftq_config)
+        loftq_model = get_peft_model(AutoModelForCausalLM.from_pretrained(self.model_id).cuda().eval(), lora_config)
+        torch.manual_seed(0)
+        logits_loftq = loftq_model(**self.inputs).logits
+        del loftq_model
+        gc.collect()
+        torch.cuda.empty_cache()
+
+        mae_quantized = torch.abs(logits_base - logits_quantized).mean()
+        mse_quantized = torch.pow(logits_base - logits_quantized, 2).mean()
+        mae_loftq = torch.abs(logits_base - logits_loftq).mean()
+        mse_loftq = torch.pow(logits_base - logits_loftq, 2).mean()
+        return mae_quantized, mse_quantized, mae_loftq, mse_loftq
+
+    def test_bloomz_loftq_4bit(self):
+        # In this test, we compare the logits of the base model, the quantized LoRA model, and the quantized model
+        # using LoftQ. When quantizing, we expect a certain level of error. However, we expect the LoftQ quantized
+        # model to have less error than the normal LoRA quantized model. Note that when using normal LoRA, the
+        # quantization error is simply the error from quantization without LoRA, as LoRA is a no-op before training.
+        # We still apply LoRA for the test for consistency.
+
+        mae_quantized, mse_quantized, mae_loftq, mse_loftq = self.get_errors(bits=4)
+        # first, sanity check that all errors are > 0.0
+        self.assertTrue(mae_quantized > 0.0)
+        self.assertTrue(mse_quantized > 0.0)
+        self.assertTrue(mae_loftq > 0.0)
+        self.assertTrue(mse_loftq > 0.0)
+
+        # next, check that LoftQ quantization errors are smaller than LoRA errors by a certain margin
+        factor = 3
+        self.assertTrue(mae_loftq < mae_quantized / factor)
+        self.assertTrue(mse_loftq < mse_quantized / factor)
+
+    def test_bloomz_loftq_4bit_iter_5(self):
+        # Same test as the previous one but with 5 iterations. We should expect the error to be even smaller with more
+        # iterations, but in practice the difference is not that large, at least not for this small base model.
+        mae_quantized, mse_quantized, mae_loftq, mse_loftq = self.get_errors(bits=4, loftq_iter=5)
+        # first, sanity check that all errors are > 0.0
+        self.assertTrue(mae_quantized > 0.0)
+        self.assertTrue(mse_quantized > 0.0)
+        self.assertTrue(mae_loftq > 0.0)
+        self.assertTrue(mse_loftq > 0.0)
+
+        # next, check that LoftQ quantization errors are smaller than LoRA errors by a certain margin
+        self.assertTrue(mae_loftq < mae_quantized / self.error_factor)
+        self.assertTrue(mse_loftq < mse_quantized / self.error_factor)
+
+    def test_bloomz_loftq_8bit(self):
+        # this currently does not work:
+        # https://github.com/huggingface/peft/pull/1150#issuecomment-1838891499
+        if True:  # TODO: remove as soon as the issue is fixed
+            return
+
+        # Same test as test_bloomz_loftq_4bit but with 8 bits.
+        mae_quantized, mse_quantized, mae_loftq, mse_loftq = self.get_errors(bits=8)
+
+        # first, sanity check that all errors are > 0.0
+        self.assertTrue(mae_quantized > 0.0)
+        self.assertTrue(mse_quantized > 0.0)
+        self.assertTrue(mae_loftq > 0.0)
+        self.assertTrue(mse_loftq > 0.0)
+
+        # next, check that LoftQ quantization errors are smaller than LoRA errors by a certain margin
+        self.assertTrue(mae_loftq < mae_quantized / self.error_factor)
+        self.assertTrue(mse_loftq < mse_quantized / self.error_factor)
+
+    def test_bloomz_loftq_8bit_iter_5(self):
+        # this currently does not work:
+        # https://github.com/huggingface/peft/pull/1150#issuecomment-1838891499
+        if True:  # TODO: remove as soon as the issue is fixed
+            return
+
+        # Same test as test_bloomz_loftq_4bit_iter_5 but with 8 bits.
+        mae_quantized, mse_quantized, mae_loftq, mse_loftq = self.get_errors(bits=8, loftq_iter=5)
+
+        # first, sanity check that all errors are > 0.0
+        self.assertTrue(mae_quantized > 0.0)
+        self.assertTrue(mse_quantized > 0.0)
+        self.assertTrue(mae_loftq > 0.0)
+        self.assertTrue(mse_loftq > 0.0)
+
+        # next, check that LoftQ quantization errors are smaller than LoRA errors by a certain margin
+        self.assertTrue(mae_loftq < mae_quantized / self.error_factor)
+        self.assertTrue(mse_loftq < mse_quantized / self.error_factor)
+
+
 @require_bitsandbytes
 @require_torch_gpu
 class MultiprocessTester(unittest.TestCase):