Einar Pius
Automatic Parallelisation of Quantum Circuits
Using the Measurement Based Quantum
Computing
2Automatic Parallelisation of Quantum Circuits
Motivation
• Quantum computation uses quantum mechanical properties
to represent data and perform operations on it
• Quantum bits (qubits) can be kept stable only for short time
– Due to quantum decoherence
• Algorithms must have as few steps as possible to be able to run on current experimental quantum computers
A two qubit quantum processor created at Yale University in 2009
3Automatic Parallelisation of Quantum Circuits
Goal of this project
• Creating a program that automatically decrease the number
of sequential steps required to perform a quantum
computation
• This was done by applying algebraic transformations to
quantum algorithms
– This may reduce the depth of the quantum computation due to
parallelisation
A two qubit quantum processor created at Yale University in 2009
4Automatic Parallelisation of Quantum Circuits
What we did not do
• Quantum computers do not exist yet
• This was a theoretical project
• No quantum computation was done in this project
A two qubit quantum processor created at Yale University in 2009
5Automatic Parallelisation of Quantum Circuits
Quantum Circuit
• Quantum Circuit is a model of quantum computation
• Qubits are represented by horizontal wires
• Operations on the qubits are represented as gates
6Automatic Parallelisation of Quantum Circuits
Quantum Circuit
• Quantum Circuit is a model of quantum computation
• Qubits are represented by horizontal wires
• Operations on the qubits are represented as gates
• The gates are applied sequentially from left to right
• Gates on the distinct qubits can be applied in parallel
7Automatic Parallelisation of Quantum Circuits
Project Goal
• Transform a quantum circuit to an equivalent quantum circuit
whose depth is less than or equal to the original depth
8Automatic Parallelisation of Quantum Circuits
The parallelisation process
• Translation to the Measurement Based Quantum Computing
(MBQC) model
• Optimisations on MBQC representation
– Standardisation– Signal sifting– Pauli resetting
• Translation back to quantum circuit
• Optimisations on the final circuit
• Result:
– In general the depth of the circuit increases by a log(n) factor– For some circuits the computational depth decreases
9Automatic Parallelisation of Quantum Circuits
A new algorithm
• Translation to MBQC model
• Optimisations on MBQC representation
– Standardisation– Signal sifting– Pauli resetting
• Translation back to quantum circuit
• Optimisations on the final circuit
• We created a new iterative algorithm that translates the
quantum circuits to MBQC model and optimises them
– Runtime O(n³)
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Automatic Parallelisation of Quantum Circuits
Experiments with the program
• The Toffoli staircase circuit
– Depth will decrease by a constant amount
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Automatic Parallelisation of Quantum Circuits
Experiments with the program
• The Toffoli + CNOT staircase circuit
– The depth of the parallelised circuit will be
constant
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Automatic Parallelisation of Quantum Circuits
Experiments with the program
• A new set of gates
– Every circuit consisting of only the following gates:– The CNOT gate– The ∧Z gate– The ω gate– The phase gate Z(α)– The J(-π/2) gate
– These circuits can be parallelise to a logarithmic depth
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Automatic Parallelisation of Quantum Circuits
Results
• A program for automatic parallelisation of quantum circuits
was created
• A new O(n³) algorithm for translating the quantum circuits to
an optimised MBQC computation was designed
• Three new classes of quantum circuits that could benefit
from the implemented parallelisation method were found
– The Toffoli circuit– The Toffoli + CNOT circuit– A set of gates consisting of CNOT, ∧Z, ω, Z(α), J(-π/2) gates
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