Method of performing a quantum computation, apparatus for performing a quantum computation

An apparatus for performing a quantum computation, comprising:

• a quantum system comprising constituents;
• a classical computing system configured to:
• encode a computational problem into a problem Hamiltonian of the quantum system, wherein the problem Hamiltonian is a single-body Hamiltonian being a sum of summand problem Hamiltonians;
• determine a constraint Hamiltonian of the quantum system, the constraint Hamiltonian being a sum of summand constraint Hamiltonians, wherein a ground state of a total Hamiltonian encodes a solution to the computational problem, wherein the total Hamiltonian includes a sum of the problem Hamiltonian and the constraint Hamiltonian;
• and
• determine 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;
• a quantum processing system comprising a unitary evolution device and a measurement device, the quantum processing system being configured to perform N rounds of operations, wherein N≥2, wherein each round comprises:
• evolving, by the unitary evolution device, the quantum system according to a sequence of unitary operators, the sequence including problem-encoding unitary operators, constraint-enforcing unitary operators and unitary driver operators,
• wherein 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,
• wherein 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, and
• wherein 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;
• and
• performing, by the measurement device, a measurement of one or more constituents of the quantum system,
• the classical computing system being further configured to output a result of the quantum computation.