unitair 0.1.6

PyTorch-based quantum computing

unitair: PyTorch-based quantum circuits

Unitair is a lightweight Python package that brings quantum computing to PyTorch.

Unitair differs from other quantum computing software packages in important ways. Quantum states are PyTorch tensors (the PyTorch version of the NumPy ndarray). There is no special class for quantum states class nor is there an abstract QuantumCircuit class. Unitair doesn't directly rely on any circuit model although it supports circuit-model computation.

Manipulations of quantum states naturally take advantage of PyTorch's strengths. You can

• Apply gates and other operations to a batch of states
• Use gradients to track gate parameters or parameters used to build an initial state
• Set device='cuda' to get GPU-acceleration
• Mix unitair functions with torch.nn networks or any other PyTorch functionality

Cheat whenever possible

Unlike standard quantum circuit simulation, unitair is designed to encourage users to "just get the answer" and does not aim to perform operations in a way that models real quantum circuits or hardware. In this sense, unitair should be regarded as an emulator rather than a simulator.

Functions aim to take shortcuts whenever possible. Rather than applying a Hadamard gate to every qubit starting with |0...0>, the best practice is to use unitair.uniform_superposition which reads off the state directly.

This approach has three notable downsides:

1. unitair does not aim to simulate noise realistically.
2. Users should be aware that manipulations that look simple with unitair may be very complex when constructed with realistic gates.
3. Deployment to hardware or translation to other quantum computing packages is not an intended usage of unitair.

On the other hand, emulation has massive benefits: researchers can test or develop quantum algorithms with lower runtimes than is possible with standard simulation, and states can be manipulated in arbitrary ways, whether physically sensible or not.

Intended users

Unitair was designed with the goal of helping to bridge the fields of quantum computing and machine learning. Anyone with experience in PyTorch (or another machine learning library like TensorFlow) and basic knowledge of quantum computing should find unitair to be very simple. Users that are experts in machine learning or quantum computing but not both should find unitair helpful to start making a connection with the other discipline.

States are tensors

Unitair avoids unnecessary complexity by just using torch.Tensor as the class for quantum states. For example, the state $|00>$ is

import torch  # no need to import unitair yet!

# Intended state: |00>
state = torch.tensor([[1., 0., 0., 0.],
                      [0., 0., 0., 0.]])

This Tensor has size (2, 4). The four columns of this matrix correspond to the computational basis elements $|00>, |01>, |10>,$ and $|11>$ (in that order). Since the quantum state can be written as

1 |00> + 0 |01> + 0 |10> + 0 |11>,

the vector [1., 0., 0., 0.] is sensible. The reason that there are two rows is that coefficients of quantum states are complex numbers. The first and second rows are for real an imaginary parts respectively.

# Intended state: -i |01>
state = torch.tensor([[0., 0., 0., 0.],
                      [0., -1., 0., 0.]])

Batches of states

To exploit the strengths of PyTorch, manipulations should be batched. This means that rather than constructing a tensor with size (2, 4), we might instead construct a tensor with size (3, 2, 4). The unitair interpretation of such a Tensor is that we have 3 quantum states for two qubits. For example:

>>> import unitair
>>> unitair.rand_state(num_qubits=2, batch_dims=(3,))
tensor([[[-0.0222,  0.1360, -0.2531, -0.6884],
         [-0.1672, -0.5563,  0.2098, -0.2482]],
         
        [[ 0.5456, -0.2316,  0.0870,  0.0334],
         [ 0.2550, -0.0349, -0.7393,  0.1649]],
         
        [[ 0.5787,  0.2652,  0.1518, -0.2148],
         [-0.5141, -0.3789,  0.3423, -0.0215]]])

In fact, batch dimensions can be more general thant that:

state_batch = unitair.rand_state(num_qubits=2, batch_dims=(10, 3,))

>>> state_batch.size()
torch.Size([10, 3, 2, 4])

In this case, state_batch[5, 1], is a quantum state for two qubits, as is any other selection of the first two indices of state_batch. This is a batch of 30 states for two qubits organized into the (10, 3) shape.

Manipulating quantum states

Since states are tensors, you are free to do anything to a state that you might do to a torch.Tensor. In particular, you are free to do manipulations that are not unitary or even manipulations that don't correspond to anything physically possible. On the other hand, the unitair package has a number of functions that will let you do operations that are natural in quantum mechanics.

Applying Hadamard gates

We first apply a Hadamard gate to the initial state $|0>$:

from unitair import simulation
from unitair import gates

# Initial state: |0>
state = unitair.unit_vector(index=0, num_qubits=1)
h = gates.hadamard()

state = simulation.apply_operator(
    operator=h,
    state=state,
    qubits=(0,)
)

>>> state
tensor([[0.7071, 0.7071],
        [0.0000, 0.0000]])

Unitair can apply gates to batches of quantum states as well. For example, we can construct a batch consisting of 5 state for one qubit and then apply a Hadamard gate to each of those states in a single call:

state_batch = unitair.rand_state(num_qubits=1, batch_dims=(5,))
h = gates.hadamard()

state_batch = simulation.apply_operator(
    operator=h,
    state=state_batch,
    qubits=(0,)
)

The resulting state_batch has size (5, 2, 2) In fact, state_batch[3] is the same as if we had applied a Hadamard gate directly to the index 3 element of the original state_batch.

Making a Bell state

The Bell state $(|00> + |11>) / \sqrt{2}$ is typically constructed by starting with the state |00>, applying a Hadamard gate to the first qubit, and then applying a CNOT gate from the first to the second qubit. This construction can be done with unitair.

from unitair import simulation
from unitair import gates

# Initial state: |00>
state = unitair.unit_vector(index=0, num_qubits=2)
h = gates.hadamard()
cnot = gates.cnot()

state = simulation.apply_operator(
    operator=h,
    state=state,
    qubits=(0,)
)

state = simulation.apply_operator(
    operator=cnot,
    state=state,
    qubits=(0, 1)
)

>>> state
tensor([[0.7071, 0.0000, 0.0000, 0.7071],
        [0.0000, 0.0000, 0.0000, 0.0000]])

About Unitair

Unitair was written at QC Ware Corp. by Sean Weinberg. Fabio Sanches envisioned and suggested the project in 2020.

If you have questions or feedback, or if you would like to contribute to Unitair, please email [e-mail].