Brief Update on CQN Simulation Stack

Stefan Krastanov
UMass Amherst

May 2023

The Quantum Technology Stack

Materials

Analog Control

Noisy Digital Circuits

Error Correction

Quantum Algorithms

Full-Stack Design and Optimization Toolkit

Types of Dynamics

**Continuous:**
Hamiltonians, Master Equations

Types of Dynamics

Types of Dynamics

**Stochastic:**
Weak Measurements, Feedback

State Representation

Matrix product states and tensor network states

Why so many different representations?

Classically we get to just do stacked Monte Carlo simulations...

... Quantum effects are interesting mostly when Monte Carlo fails!

... or because Monte Carlo fails!

Whe need to marshal diverse simulators together and convert between representations.


                traits = [Qubit(), Qubit(), Qumode()]
                reg = Register(traits)

A register "stores" the states being simulated.


                graph = grid([2,3])
                registers = [...]
                net = RegisterNet(graph, registers)

A "graph" of registers can represent a network.


                initialize!(reg[1], X₁)

A register's slot can be initialized to an arbitrary state, e.g. $|x_1\rangle$ an eigenstate of $\hat{\sigma}_x$.


                initialize!(reg[1], X₁)
                initialize!(reg[2], Z₁)
                apply!((reg[1], reg[2]), CNOT)

Arbitrary quantum gates or channels can be applied.


              project_traceout!(reg[1], σˣ) # Projective measurement

              observable((reg[1],reg[2]), σᶻ⊗σˣ) # Calculate an expectation

Measurements and expectation values...

Full Symbolic Computer Algebra System


              julia> Z₁
              |Z₁⟩


              julia> ( Z₁⊗X₂+Y₁⊗Y₁ ) / √2
              0.707 (|Y₁⟩|Y₁⟩+|Z₁⟩|X₂⟩)

Symbolic to Numeric Conversion


              julia> express( ( Z₁⊗X₂+Y₁⊗Y₁ ) / √2 )
              Ket(dim=4)
                basis: [Spin(1/2) ⊗ Spin(1/2)]
                 0.8535533905932736 + 0.0im
                                0.0 + 0.3535533905932737im
               -0.49999999999999994 + 0.3535533905932737im
                -0.3535533905932737 + 0.0im


              julia> express( Y₁⊗Y₂, CliffordRepr() )
              Rank 2 stabilizer
              + Z_
              + _Z
              ════
              + Y_
              - _Y
              ════

Play with it at areweentangledyet.com