diff --git a/Project.toml b/Project.toml
index e55a43f..1e463f6 100644
--- a/Project.toml
+++ b/Project.toml
@@ -4,20 +4,22 @@ authors = ["Ritter.Marc <Ritter.Marc@physik.uni-muenchen.de>, Hiroshi Shinaoka <
 version = "0.7.0"
 
 [deps]
+BitIntegers = "c3b6d118-76ef-56ca-8cc7-ebb389d030a1"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 QuanticsGrids = "634c7f73-3e90-4749-a1bd-001b8efc642d"
 TensorCrossInterpolation = "b261b2ec-6378-4871-b32e-9173bb050604"
 
 [compat]
+BitIntegers = "0.3.5"
 QuanticsGrids = "0.3"
-TensorCrossInterpolation = "0.9"
+TensorCrossInterpolation = "0.9.16"
 julia = "1.6"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+Glob = "c27321d9-0574-5035-807b-f59d2c89b15c"
 JET = "c3a54625-cd67-489e-a8e7-0a5a0ff4e31b"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
-Glob = "c27321d9-0574-5035-807b-f59d2c89b15c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
diff --git a/src/QuanticsTCI.jl b/src/QuanticsTCI.jl
index 0edc347..7fa09a2 100644
--- a/src/QuanticsTCI.jl
+++ b/src/QuanticsTCI.jl
@@ -10,6 +10,11 @@ import Base: sum
 export quanticscrossinterpolate, evaluate, sum, integral
 export cachedata, quanticsfouriermpo
 
+import BitIntegers
+import BitIntegers: UInt256, UInt512, UInt1024
+
+BitIntegers.@define_integers 2048 MyInt2048 MyUInt2048
+
 include("tciinterface.jl")
 include("fouriertransform.jl")
 
diff --git a/src/tciinterface.jl b/src/tciinterface.jl
index f029b0b..edb7dec 100644
--- a/src/tciinterface.jl
+++ b/src/tciinterface.jl
@@ -87,7 +87,22 @@ function quanticscrossinterpolate(
            ? q -> f(only(QG.quantics_to_origcoord(grid, q)))
            : q -> f(QG.quantics_to_origcoord(grid, q)...))
 
-    qf = TCI.CachedFunction{ValueType}(qf_, qlocaldimensions)
+    maxlinearindex = prod(BigInt.(qlocaldimensions))
+    if maxlinearindex < typemax(UInt256)
+        keytype = UInt256
+    elseif maxlinearindex < typemax(UInt512)
+        keytype = UInt512
+    elseif maxlinearindex < typemax(UInt1024)
+        keytype = UInt1024
+    elseif maxlinearindex < typemax(MyUInt2048)
+        keytype = MyUInt2048
+    else
+        keytype = BigInt
+    end
+    if keytype === BigInt
+        @warn "Using BigInt as key type. This will lead to significant memory usage and performance degradation."
+    end
+    qf = TCI.CachedFunction{ValueType, keytype}(qf_, qlocaldimensions)
 
     qinitialpivots = (initialpivots === nothing
                       ? [ones(Int, length(qlocaldimensions))]