Abstract: A method of performing a quantum computation includes providing a quantum system comprising constituents; encoding a computational problem into a problem Hamiltonian of the quantum system; determining a constraint Hamiltonian of the quantum system; the constraint Hamiltonian a sum of summand constraint Hamiltonians; 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; 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; performing N rounds of operations, wherein N?2, each round includes preparing an initial quantum state and evolving the quantum system according to a sequence of unitary operators where the sequence includes problem-encoding unitary operators, constraint-enforcing unitary operators and unitary driver operators; and outputting a r

Abstract: This application concerns methods and apparatus for performing a quantum algorithm of logical qubits. The quantum algorithm is performed on a quantum system of physical qubits. The method includes providing a quantum system comprising a plurality of physical qubits in a spatial arrangement. The number of physical qubits is larger than the number of logical qubits. The logical qubits are encoded into physical qubits. A physical qubit represents either the parity of two or more logical qubits or a single logical qubit. Constraint-fulfilling sets of physical qubits fulfil constraints and each constraint-fulfilling set comprises a number of physical qubits such that every logical qubit is represented by zero or an even number of physical qubits in that set. The method includes enabling quantum interactions between logical qubits by performing quantum interactions on physical qubits. Further, at least a portion of the physical qubits is measured to obtain a readout.