CSE 60932 Project

The goal of this project was to create a tool that can convert a quantum circuit to a unitary matrix, and vice versa (decomposing the matrix to a circuit of CNOT and single-qubit gates). It also acts as a quantum circuit simulator, which is a trivial matrix-vector multiplication after the circuit-to-matrix conversion. See the presentation slides for more information.

The project is implemented in Python and depends on NumPy. It consists of the following modules:

• state.py: Defines the State class, which wraps a complex vector to represent the state of a quantum register. It can be converted to or from a sparse dictionary representation, and to a probability distribution that can be used to print a histogram or randomly sampled to simulate a measurement.

• gate.py: Defines the Gate class, which wraps a unitary matrix. It has methods to create an inverted or controlled gate, the composition or tensor product of two gates, or a version of the gate with its inputs permuted. It can also apply itself to a State.

• gates.py: Contains definitions of some common Gates.

• circuit.py: Defines the Circuit class, which is a Gate composed of other Gates. It can be represented as a rudimentary vertical circuit diagram, with vertical qubit wires numbered from right to left. Gates are indicated by two horizontal lines (╪) by default, meant to resemble opposite sides of the box used in conventional circuit diagrams. Control qubits are indicated by a single thick horizontal line (┿), meant to resemble the filled circle and line connecting it to the box. The name of the gate is shown to the right of the circuit. The following represents a circuit for Grover's algorithm:

  ╪╪╪ H ⊗ H ⊗ H
  │╪│ X
  ┿┿╪ CCZ
  │╪│ X
  ╪╪╪ H ⊗ H ⊗ H
  ╪╪╪ X ⊗ X ⊗ X
  ┿┿╪ CCZ
  ╪╪╪ X ⊗ X ⊗ X
  ╪╪╪ H ⊗ H ⊗ H
  

• decomposed_circuit.py: Defines the DecomposedCircuit class, which can decompose an arbitrary unitary matrix to CNOT and single-qubit gates, following sections 4.2, 4.3 and 4.5 of Nielsen and Chuang's "Quantum Computation and Quantum Information".

• main.py: An example program that constructs a circuit (the Grover's algorithm circuit shown above), shows the result of simulating it, and decomposes it.

• test.py: Samples the entire space of single-qubit matrices at regular intervals, and tests that the matrix of the decomposed circuit has an absolute difference of at most 1e-4 in each element.