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Automatic Parallelisation of Quantum Circuits Using the Measurement Based Quantum Computing. Einar Pius. 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
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Automatic Parallelisation of Quantum Circuits Using the Measurement Based Quantum Computing Einar Pius
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 Automatic 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 Automatic 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 Automatic 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 Automatic 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 Automatic 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 Automatic 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 Automatic 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) Automatic Parallelisation of Quantum Circuits
The implementation Automatic Parallelisation of Quantum Circuits
The implementation Automatic Parallelisation of Quantum Circuits
Experiments with the program • The Toffoli staircase circuit • Depth will decrease by a constant amount Automatic Parallelisation of Quantum Circuits
Experiments with the program • The Toffoli + CNOT staircase circuit • The depth of the parallelised circuit will be constant 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 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 Automatic Parallelisation of Quantum Circuits