Package for using Matrix Product States (MPS) to simulate quantum circuits.

Installation

After cloning the repository, run

pip install -e .

in the directory with setup.py.

Getting started

The main object is mpsim.MPS which defines a matrix product state of qudits initialized to the all zero state.

An MPS can be acted on by aribtrary one-qudit and two-qudit operations. Operations on >=3 qubits are not supported and must be compiled into a sequence of one- and two-qudit operations.

An MPSOperation consists of a gate and tuple of indices specifying which tensor(s) the gate acts on in the MPS. Gates must be expressed as TensorNetwork.Node objects with the appropriate number of edges. Some common gates are defined in mpsim.gates.

The following program initializes an MPS in the |00> state and prepares a Bell state.

import mpsim

mps = mpsim.MPS(nqudits=2)
mps.h(0)
mps.cnot(0, 1)

print(mps.wavefunction)
# Displays [0.70710677+0.j 0.        +0.j 0.        +0.j 0.70710677+0.j]

Two-qubit gate options

The number of singular values kept for a two-qubit gate can be set by the keyword argument maxsvals.

The following program prepares the same Bell state but only keeps one singular value after the CNOT.

import mpsim

mps = mpsim.MPS(nqudits=2)
mps.h(0)
mps.cnot(0, 1, maxsvals=1)

print(mps.wavefunction)
# Displays [0.70710674+0.j 0.        +0.j 0.        +0.j 0.        +0.j]

Note that the wavefunction after truncation is not normalized. An MPS can be renormalized at any time by calling the MPS.renormalize() method.

Cirq integration

Circuits defined in Cirq can be simulated with MPS as follows.

import cirq
from mpsim.mpsim_cirq.simulator import MPSimulator

# Define the circuit
qreg = cirq.LineQubit.range(2)
circ = cirq.Circuit(
    cirq.ops.H.on(qreg[0]),
    cirq.ops.CNOT(*qreg)
)

# Do the simulation using the MPS Simulator
sim = MPSimulator()
mps = sim.simulate(circ)
print(mps.wavefunction)
# Displays [0.70710677+0.j 0.        +0.j 0.        +0.j 0.70710677+0.j]

One can truncate singular values for two-qubit operations by passing in options to the MPSimulator.

sim = MPSimulator(options={"maxsvals": 1})
mps = sim.simulate(circ)
print(mps.wavefunction)
# Displays [0.70710674+0.j 0.        +0.j 0.        +0.j 0.        +0.j]

See help(MPSimulator) for a full list of options.