Feature Description
Support Density based matrix simulation for gate based quantum computation.
Motivation
Density matrices represent mixed quantum states that arise when systems interact with their environment, enabling realistic modeling of noise and decoherence. This goes beyond the normal statevector simulation we already support.
This capability is essential for developing quantum error correction techniques and testing algorithms in conditions that match actual quantum hardware.
Technical Details (if known)
Implementation would extend the backend simulation engine to support density operators (2^n × 2^n matrices) alongside state vectors. The core challenge is memory efficiency, as density matrices scale as O(4^n) compared to O(2^n) for statevectors.
Recommended approaches can be sparse matrix representation, leveraging matrix symmetry properties, and GPU acceleration. Key operations to implement: unitary evolution via ρ → UρU†, quantum channels via Kraus operators, and partial trace operations. For larger qubit counts, consider trajectory-based methods.
Consider a simple Hadamard gate (H) applied to a single qubit in the |0⟩ state:
Statevector approach:
Initial state: |ψ⟩ = |0⟩ = [1, 0]ᵀ
Apply H: H|ψ⟩ = 1/√2 [1, 1]ᵀ
Density matrix approach:
Initial state: ρ = |0⟩⟨0| = [[1, 0], [0, 0]]
Apply H: HρH† = H[[1, 0], [0, 0]]H† = 1/2 [[1, 1], [1, 1]]
In the implementation, Qitara already has the unitary matrix for H defined. The only difference is that instead of applying H directly to a vector, we apply H to the left and H† to the right of a matrix. This pattern applies to all unitary gates, allowing reuse of the same gate definitions with a different application method.
Acceptance Criteria
How do we know this is complete? Include expected output, test cases, or behavior.
Related Issues / References
Additional Notes
A pretty easy way to do this is just create a copy of cpu.rs (that currently simulates gates using statevector operations on a CPU), and change the parts that need changing, and go up from there.
Feature Description
Support Density based matrix simulation for gate based quantum computation.
Motivation
Density matrices represent mixed quantum states that arise when systems interact with their environment, enabling realistic modeling of noise and decoherence. This goes beyond the normal statevector simulation we already support.
This capability is essential for developing quantum error correction techniques and testing algorithms in conditions that match actual quantum hardware.
Technical Details (if known)
Implementation would extend the backend simulation engine to support density operators (2^n × 2^n matrices) alongside state vectors. The core challenge is memory efficiency, as density matrices scale as O(4^n) compared to O(2^n) for statevectors.
Recommended approaches can be sparse matrix representation, leveraging matrix symmetry properties, and GPU acceleration. Key operations to implement: unitary evolution via ρ → UρU†, quantum channels via Kraus operators, and partial trace operations. For larger qubit counts, consider trajectory-based methods.
Consider a simple Hadamard gate (H) applied to a single qubit in the |0⟩ state:
Statevector approach:
Initial state: |ψ⟩ = |0⟩ = [1, 0]ᵀ
Apply H: H|ψ⟩ = 1/√2 [1, 1]ᵀ
Density matrix approach:
Initial state: ρ = |0⟩⟨0| = [[1, 0], [0, 0]]
Apply H: HρH† = H[[1, 0], [0, 0]]H† = 1/2 [[1, 1], [1, 1]]
In the implementation, Qitara already has the unitary matrix for H defined. The only difference is that instead of applying H directly to a vector, we apply H to the left and H† to the right of a matrix. This pattern applies to all unitary gates, allowing reuse of the same gate definitions with a different application method.
Acceptance Criteria
How do we know this is complete? Include expected output, test cases, or behavior.
Related Issues / References
Additional Notes
A pretty easy way to do this is just create a copy of cpu.rs (that currently simulates gates using statevector operations on a CPU), and change the parts that need changing, and go up from there.