diff --git a/Project.toml b/Project.toml
index a7d05380..dbc95034 100644
--- a/Project.toml
+++ b/Project.toml
@@ -30,6 +30,8 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StructTypes = "856f2bd8-1eba-4b0a-8007-ebc267875bd4"
+Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
+SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
 Tar = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
 UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
 
@@ -66,6 +68,8 @@ SparseArrays = "1.6"
 StaticArrays = "=1.9.7"
 Statistics = "1.6"
 StructTypes = "=1.10.0"
+Symbolics = "=5.30.3"
+SymbolicUtils = "=2.0.2"
 Tar = "1.9.3"
 Test = "1.6"
 UUIDs = "1.6"
@@ -91,6 +95,8 @@ Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
 StructTypes = "856f2bd8-1eba-4b0a-8007-ebc267875bd4"
+Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
+SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
 Tar = "a4e569a6-e804-4fa4-b0f3-eef7a1d5b13e"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 UUIDs = "cf7118a7-6976-5b1a-9a39-7adc72f591a4"
diff --git a/docs/src/circuits.md b/docs/src/circuits.md
index 79d7719a..dc6263ac 100644
--- a/docs/src/circuits.md
+++ b/docs/src/circuits.md
@@ -39,6 +39,7 @@ QubitSet
 Braket.Operator
 Braket.QuantumOperator
 FreeParameter
+FreeParameterExpression
 depth
 qubits
 qubit_count
diff --git a/src/Braket.jl b/src/Braket.jl
index ec4b5206..685ce945 100644
--- a/src/Braket.jl
+++ b/src/Braket.jl
@@ -1,7 +1,7 @@
 module Braket
 
 export Circuit, QubitSet, Qubit, Device, AwsDevice, AwsQuantumTask, AwsQuantumTaskBatch
-export metadata, status, Observable, Result, FreeParameter, Job, AwsQuantumJob, LocalQuantumJob, LocalSimulator
+export metadata, status, Observable, Result, FreeParameter, FreeParameterExpression, Job, AwsQuantumJob, LocalQuantumJob, LocalSimulator, subs
 export Tracker, simulator_tasks_cost, qpu_tasks_cost
 export arn, cancel, state, result, results, name, download_result, id, ir, isavailable, search_devices, get_devices
 export provider_name, properties, type
@@ -32,6 +32,8 @@ using DecFP
 using Graphs
 using HTTP
 using StaticArrays
+using Symbolics
+using SymbolicUtils
 using JSON3, StructTypes
 using LinearAlgebra
 using DataStructures
@@ -39,6 +41,9 @@ using NamedTupleTools
 using OrderedCollections
 using Tar
 
+# Operator overloading for FreeParameterExpression
+import Base: +, -, *, /, ^, ==
+
 include("utils.jl")
 """
     IRType
@@ -134,6 +139,107 @@ end
 Base.copy(fp::FreeParameter) = fp
 Base.show(io::IO, fp::FreeParameter) = print(io, string(fp.name))
 
+"""
+    FreeParameterExpression
+    FreeParameterExpression(expr::Union{FreeParameterExpression, Number, Symbolics.Num, String})
+
+Struct representing a [`FreeParameterExpression`](@ref), which can be used in symbolic computations. 
+Instances of [`FreeParameterExpression`](@ref) can represent symbolic expressions involving [`FreeParameter`](@ref), 
+such as mathematical expressions with undetermined values.
+
+This type is often used in combination with [`FreeParameter`](@ref), which represents individual [`FreeParameter`](@ref).
+
+### Examples
+```jldoctest
+julia> α = FreeParameter(:alpha)
+alpha
+
+julia> θ = FreeParameter(:theta)
+theta
+
+julia> gate = FreeParameterExpression("α + 2*θ")
+α + 2θ
+
+julia> gsub = subs(gate, Dict(:α => 2.0, :θ => 2.0))
+6.0
+
+julia> gate + gate
+2α + 4θ
+
+julia> gate * gate
+(α + 2θ)^2
+
+julia> gate₁ = FreeParameterExpression("phi + 2*gamma")
+2gamma + phi
+```
+"""
+struct FreeParameterExpression
+    expression::Symbolics.Num
+    function FreeParameterExpression(expr::Symbolics.Num)
+        new(expr)
+    end
+end
+
+FreeParameterExpression(expr::FreeParameterExpression) = FreeParameterExpression(expr.expression)
+FreeParameterExpression(expr::Number) = FreeParameterExpression(Symbolics.Num(expr))
+FreeParameterExpression(expr) = throw(ArgumentError("Unsupported expression type"))
+
+# Function to validate the input expression string
+function validate_expr(expr::String)
+    allowed_chars = Set("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ0123456789+-*/^()αβγδεζηθικλμνξοπρςστυφχψωϐϑϕϖϘϙϚϛϜϝϞϟϠϡϰϱϴϵ϶ΑΒΓΔΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ ")
+    for char in expr
+        if !(char in allowed_chars)
+            throw(ArgumentError("Unsupported character '$char' in expression. Only ASCII letters (a-z, A-Z), digits (0-9), Greek letters (α-϶, Α-Ω), space( ), and basic mathematical symbols (+ - * / ^ ()) are allowed."))
+        end
+    end
+    return expr
+end
+
+# Function to create FreeParameterExpression from a validated string
+function FreeParameterExpression(expr::String)
+    validated_expr = validate_expr(expr)
+    parsed_expr = parse_expr_to_symbolic(Meta.parse(validated_expr), @__MODULE__)
+    return FreeParameterExpression(parsed_expr)
+end
+
+Base.show(io::IO, fpe::FreeParameterExpression) = print(io, fpe.expression)
+Base.copy(fp::FreeParameterExpression) = fp
+
+function subs(fpe::FreeParameterExpression, parameter_values::Dict{Symbol, <:Number})
+    param_values_num = Dict(Symbolics.variable(string(k); T=Real) => v for (k, v) in parameter_values)
+    subbed_expr = Symbolics.substitute(fpe.expression, param_values_num)
+    if isempty(Symbolics.get_variables(subbed_expr))
+	   subbed_expr = Symbolics.value(subbed_expr)
+        return subbed_expr
+    else
+	subbed_expr = Symbolics.value(subbed_expr)
+	return FreeParameterExpression(subbed_expr)
+    end 
+end
+
+Base.:+(fpe1::FreeParameterExpression, fpe2::Union{FreeParameterExpression, Number, Symbolics.Num}) = 
+    FreeParameterExpression((fpe1 isa FreeParameterExpression ? fpe1.expression : fpe1) + 
+                            (fpe2 isa FreeParameterExpression ? fpe2.expression : fpe2))
+
+Base.:*(fpe1::FreeParameterExpression, fpe2::Union{FreeParameterExpression, Number, Symbolics.Num}) = 
+    FreeParameterExpression((fpe1 isa FreeParameterExpression ? fpe1.expression : fpe1) * 
+                            (fpe2 isa FreeParameterExpression ? fpe2.expression : fpe2))
+
+Base.:-(fpe1::FreeParameterExpression, fpe2::Union{FreeParameterExpression, Number, Symbolics.Num}) = 
+    FreeParameterExpression((fpe1 isa FreeParameterExpression ? fpe1.expression : fpe1) - 
+                            (fpe2 isa FreeParameterExpression ? fpe2.expression : fpe2))
+
+Base.:/(fpe1::FreeParameterExpression, fpe2::Union{FreeParameterExpression, Number, Symbolics.Num}) = 
+    FreeParameterExpression((fpe1 isa FreeParameterExpression ? fpe1.expression : fpe1) /
+                            (fpe2 isa FreeParameterExpression ? fpe2.expression : fpe2))
+
+Base.:^(fpe1::FreeParameterExpression, fpe2::Union{FreeParameterExpression, Number, Symbolics.Num}) = 
+    FreeParameterExpression((fpe1 isa FreeParameterExpression ? fpe1.expression : fpe1) ^
+                            (fpe2 isa FreeParameterExpression ? fpe2.expression : fpe2))
+
+Base.:(==)(fpe1::FreeParameterExpression, fpe2::FreeParameterExpression) = isequal(fpe1.expression, fpe2.expression)
+Base.:!=(fpe1::FreeParameterExpression, fpe2::FreeParameterExpression) = !(isequal(fpe1, fpe2))
+
 include("compiler_directive.jl")
 include("gates.jl")
 include("noises.jl")
diff --git a/src/circuit.jl b/src/circuit.jl
index 2b363d09..a8286950 100644
--- a/src/circuit.jl
+++ b/src/circuit.jl
@@ -20,7 +20,7 @@ mutable struct Circuit
     qubit_observable_mapping::Dict{Int, Observables.Observable}
     qubit_observable_target_mapping::Dict{Int, Tuple}
     qubit_observable_set::Set{Int}
-    parameters::Set{FreeParameter}
+    parameters::Set{Union{FreeParameter, FreeParameterExpression}}
     observables_simultaneously_measureable::Bool
     has_compiler_directives::Bool
     measure_targets::Vector{Int} 
diff --git a/src/gates.jl b/src/gates.jl
index 0da98726..ef80b520 100644
--- a/src/gates.jl
+++ b/src/gates.jl
@@ -48,9 +48,12 @@ for gate_def in (
         $($G) gate.
         """
         struct $G <: AngledGate{$n_angle}
-            angle::NTuple{$n_angle, Union{Real, FreeParameter}}
-            $G(angle::T) where {T<:NTuple{$n_angle, Union{Real, FreeParameter}}} = new(angle)
+            angle::NTuple{$n_angle, Union{Real, FreeParameter, FreeParameterExpression}}
+            $G(angle::T) where {T<:NTuple{$n_angle, Union{Real, FreeParameter, FreeParameterExpression}}} = new(angle)
         end
+        $G(angles::Vararg{Union{Float64, FreeParameter, FreeParameterExpression}}) = $G(tuple(angles...))
+        $G(angles::Vararg{Number}) = $G((Float64(a) for a in angles)...)
+
         chars(::Type{$G}) = $c
         ir_typ(::Type{$G}) = $IR_G
         qubit_count(::Type{$G}) = $qc
@@ -106,9 +109,9 @@ end
 (::Type{G})(x::Tuple{}) where {G<:Gate} = G()
 (::Type{G})(x::Tuple{}) where {G<:AngledGate} = throw(ArgumentError("angled gate must be constructed with at least one angle."))
 (::Type{G})(x::AbstractVector) where {G<:AngledGate} = G(x...)
-(::Type{G})(angle::T) where {G<:AngledGate{1}, T<:Union{Real, FreeParameter}} = G((angle,))
-(::Type{G})(angle1::T1, angle2::T2) where {T1<:Union{Real, FreeParameter}, T2<:Union{Real, FreeParameter}, G<:AngledGate{2}} = G((angle1, angle2,))
-(::Type{G})(angle1::T1, angle2::T2, angle3::T3) where {T1<:Union{Real, FreeParameter}, T2<:Union{Real, FreeParameter}, T3<:Union{Real, FreeParameter}, G<:AngledGate{3}} = G((angle1, angle2, angle3,))
+(::Type{G})(angle::T) where {G<:AngledGate{1}, T<:Union{Real, FreeParameter, FreeParameterExpression}} = G((angle,))
+(::Type{G})(angle1::T1, angle2::T2) where {T1<:Union{Real, FreeParameter, FreeParameterExpression}, T2<:Union{Real, FreeParameter, FreeParameterExpression}, G<:AngledGate{2}} = G((angle1, angle2,))
+(::Type{G})(angle1::T1, angle2::T2, angle3::T3) where {T1<:Union{Real, FreeParameter, FreeParameterExpression}, T2<:Union{Real, FreeParameter, FreeParameterExpression}, T3<:Union{Real, FreeParameter, FreeParameterExpression}, G<:AngledGate{3}} = G((angle1, angle2, angle3,))
 qubit_count(g::G) where {G<:Gate}  = qubit_count(G)
 angles(g::G) where {G<:Gate}       = ()
 angles(g::AngledGate{N}) where {N} = g.angle
diff --git a/test/freeparameterexpression.jl b/test/freeparameterexpression.jl
new file mode 100644
index 00000000..e5c3be81
--- /dev/null
+++ b/test/freeparameterexpression.jl
@@ -0,0 +1,70 @@
+using Braket, Test
+
+@testset "Free parameter expressions" begin
+    α = FreeParameter(:alpha)
+    θ = FreeParameter(:theta)
+    gate = FreeParameterExpression("α + 2*θ")
+    @test copy(gate) === gate
+    gsub = subs(gate, Dict(:α => 2.0, :θ => 2.0))
+    circ = Circuit()
+    circ = H(circ, 0)
+    circ = Rx(circ, 1, gsub)
+    circ = Ry(circ, 0, θ)
+    circ = Probability(circ)
+    new_circ = circ(6.0)
+    non_para_circ = Circuit() |> (ci->H(ci, 0)) |> (ci->Rx(ci, 1, gsub)) |> (ci->Ry(ci, 0, 6.0)) |> Probability
+    @test new_circ == non_para_circ
+    ϕ = FreeParameter(:phi)
+    circ = apply_gate_noise!(circ, BitFlip(ϕ))
+    circ = apply_gate_noise!(circ, PhaseFlip(0.1))
+    new_circ = circ(theta=2.0, alpha=1.0, phi=0.2)
+    non_para_circ = Circuit() |> (ci->H(ci, 0)) |> (ci->Rx(ci, 1, gsub)) |> (ci->Ry(ci, 0, 2.0)) |> Probability |> (ci->apply_gate_noise!(ci, BitFlip(0.2))) |> (ci->apply_gate_noise!(ci, PhaseFlip(0.1)))
+    @test new_circ == non_para_circ
+
+    # creating gates directly 
+    gate = FreeParameterExpression("phi + 2*gamma")
+    gsub₁ = subs(gate, Dict(:phi => 4.0, :gamma => 4.0))
+    @test gsub₁ == 12.0
+    circ = Circuit()
+    circ = H(circ, 0)
+    circ = Rx(circ, 1, gsub₁)
+    circ = Ry(circ, 0, θ)
+    circ = Probability(circ)
+    new_circ = circ(6.0)
+    non_para_circ = Circuit() |> (ci->H(ci, 0)) |> (ci->Rx(ci, 1, gsub₁)) |> (ci->Ry(ci, 0, 6.0)) |> Probability
+    @test new_circ == non_para_circ
+
+    # + operator 
+    fpe1 = FreeParameterExpression("α + θ")
+    fpe2 = FreeParameterExpression("2 * θ")
+    result = fpe1 + fpe2
+    @test result == FreeParameterExpression("2 * θ + α + θ")
+    gsub = subs(result, Dict(:α => 1.0, :θ => 1.0))
+    @test gsub == 4.0 # α + 3θ == 4.0 
+    fpe3 = FreeParameterExpression("2 * θ")
+    # == operator
+    @test fpe3 == fpe2 
+    # != operator
+    @test fpe1 != fpe2 
+    show(fpe3)
+    # - operator
+    result = fpe1 - fpe2
+    @test result == FreeParameterExpression("α - θ")
+    gsub = subs(result, Dict(:α => 1.0, :θ => 1.0))
+    @test gsub == 0.0 # α - θ == 0.0 
+    # * operator
+    result = fpe1 * fpe2
+    @test result == FreeParameterExpression("2(α + θ)*θ")
+    gsub = subs(result, Dict(:α => 1.0, :θ => 1.0))
+    @test gsub == 4.0 # 2(α + θ)*θ == 4.0
+    # / operator
+    result = fpe1 / fpe2
+    @test result == FreeParameterExpression("(α + θ) / (2θ)")
+    gsub = subs(result, Dict(:α => 1.0, :θ => 1.0))
+    @test gsub == 1.0 # (α + θ) / (2θ) == 1.0
+    # ^ operator
+    result = fpe1 ^ fpe2
+    @test result == FreeParameterExpression("(α + θ)^(2θ)")
+    gsub = subs(result, Dict(:α => 1.0, :θ => 1.0))
+    @test gsub == 4.0 # (α + θ)^(2θ) == 4.0
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 91807f74..5e8773aa 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -52,6 +52,7 @@ for group in groups
             include("circuits.jl")
             include("measure.jl")
             include("free_parameter.jl")
+            include("freeparameterexpression.jl")
             include("gates.jl")
             include("observables.jl")
             include("noises.jl")