diff --git a/src/poetry/puzzle/provider.py b/src/poetry/puzzle/provider.py
index 7b75211cd84..1d2121f916f 100644
--- a/src/poetry/puzzle/provider.py
+++ b/src/poetry/puzzle/provider.py
@@ -138,7 +138,7 @@ def __init__(
         self._is_debugging: bool = self._io.is_debug() or self._io.is_very_verbose()
         self._in_progress = False
         self._overrides: dict[DependencyPackage, dict[str, Dependency]] = {}
-        self._deferred_cache: dict[Dependency, Package] = {}
+        self._deferred_cache: dict[int, Package] = {}
         self._load_deferred = True
         self._source_root: Path | None = None
         self._installed = installed
@@ -288,7 +288,7 @@ def search_for_vcs(self, dependency: VCSDependency) -> list[Package]:
         dependency._source_resolved_reference = package.source_resolved_reference
         dependency._source_subdirectory = package.source_subdirectory
 
-        self._deferred_cache[dependency] = package
+        self._deferred_cache[hash(dependency)] = package
 
         return [package]
 
@@ -315,8 +315,8 @@ def get_package_from_vcs(
         )
 
     def search_for_file(self, dependency: FileDependency) -> list[Package]:
-        if dependency in self._deferred_cache:
-            _package = self._deferred_cache[dependency]
+        if hash(dependency) in self._deferred_cache:
+            _package = self._deferred_cache[hash(dependency)]
 
             package = _package.clone()
         else:
@@ -325,7 +325,7 @@ def search_for_file(self, dependency: FileDependency) -> list[Package]:
             dependency._constraint = package.version
             dependency._pretty_constraint = package.version.text
 
-            self._deferred_cache[dependency] = package
+            self._deferred_cache[hash(dependency)] = package
 
         self.validate_package_for_dependency(dependency=dependency, package=package)
 
@@ -352,8 +352,8 @@ def get_package_from_file(cls, file_path: Path) -> Package:
         return package
 
     def search_for_directory(self, dependency: DirectoryDependency) -> list[Package]:
-        if dependency in self._deferred_cache:
-            _package = self._deferred_cache[dependency]
+        if hash(dependency) in self._deferred_cache:
+            _package = self._deferred_cache[hash(dependency)]
 
             package = _package.clone()
         else:
@@ -362,7 +362,7 @@ def search_for_directory(self, dependency: DirectoryDependency) -> list[Package]
             dependency._constraint = package.version
             dependency._pretty_constraint = package.version.text
 
-            self._deferred_cache[dependency] = package
+            self._deferred_cache[hash(dependency)] = package
 
         self.validate_package_for_dependency(dependency=dependency, package=package)
 
@@ -378,8 +378,8 @@ def get_package_from_directory(cls, directory: Path) -> Package:
         return PackageInfo.from_directory(path=directory).to_package(root_dir=directory)
 
     def search_for_url(self, dependency: URLDependency) -> list[Package]:
-        if dependency in self._deferred_cache:
-            return [self._deferred_cache[dependency]]
+        if hash(dependency) in self._deferred_cache:
+            return [self._deferred_cache[hash(dependency)]]
 
         package = self.get_package_from_url(dependency.url)
 
@@ -396,7 +396,7 @@ def search_for_url(self, dependency: URLDependency) -> list[Package]:
         dependency._constraint = package.version
         dependency._pretty_constraint = package.version.text
 
-        self._deferred_cache[dependency] = package
+        self._deferred_cache[hash(dependency)] = package
 
         return [package]