METHOD OF PERFORMING A QUANTUM COMPUTATION, APPARATUS FOR PERFORMING A QUANTUM COMPUTATION

A method of performing a quantum computation is provided. The method includes providing a quantum system (300) comprising constituents (302). The method includes encoding a computational problem (110) into a problem Hamiltonian (150) of the quantum system. The problem Hamiltonian is a single-body Hamiltonian being a sum of summand problem Hamiltonians (152). The method includes determining a constraint Hamiltonian (250) of the quantum system. The constraint Hamiltonian is a sum of summand constraint Hamiltonians (252). A ground state of a total Hamiltonian encodes a solution to the computational problem. The total Hamiltonian includes a sum of the problem Hamiltonian and the constraint Hamiltonian. The method includes determining a first subset S1 of the summand constraint Hamiltonians of the constraint Hamiltonian and a second subset S2 of the summand constraint Hamiltonians of the constraint Hamiltonian. The method includes performing N rounds of operations, wherein N ≥ 2. Each round includes preparing an initial quantum state. Each round includes evolving the quantum system according to a sequence of unitary operators. The sequence includes problem-encoding unitary operators, constraint-enforcing unitary operators and unitary driver operators. Each problem-encoding unitary operator is a unitary time evolution operator of a summand problem Hamiltonian of the problem Hamiltonian or is a unitary time evolution operator of a sum of summand problem Hamiltonians of the problem Hamiltonian. Each constraint-enforcing unitary operator is a unitary time evolution operator of a summand constraint Hamiltonian taken from the first subset of the summand constraint Hamiltonians of the constraint Hamiltonian, or is a unitary time evolution operator of a sum of summand constraint Hamiltonians taken from said first subset. Each unitary driver operator is a unitary operator that commutes with every summand constraint Hamiltonian from the second subset of the summand constraint Hamiltonians of the constraint Hamiltonian. Each round includes performing a measurement of one or more constituents of the quantum system. The method includes outputting a result (590) of the quantum computation.