Abstract: The method can perform a quantum computation including, in sequence, initializing a plurality of qubits of a quantum processor, applying a sequence of quantum logic gates onto the qubits in accordance with a parameterized quantum circuit which is based on a problem Hamiltonian H?problem and at least one additional Hamiltonian H?k which does not commute with H?problem, and measuring the expectation value of H?problem in the final state of the qubits.

Abstract: The generally quantum system can have : a first quantum subsystem having a first set of eigenstates; a second quantum subsystem having a second set of eigenstates; a coupler connected to both the first quantum system and to the second quantum system, the coupler having a third set of eigenstates; at least one interaction drive configured to control interaction between the first set of eigenstates and the second set of eigenstates via transitions within the third set of eigenstates; an auxiliary quantum subsystem connected to the coupler; and an attenuation drive selectively operable at a drive amplitude to generate a set of stabilized states in the auxiliary quantum system, said set of stabilized states being entangled with the third set of eigenstates in a manner that the probability of said transition within the third set of eigenstates is set by a probability of transition in the set of stabilized states.

Abstract: A quantum circuit called a “qumon” is provided to cancel unwanted ZZ interaction in a superconducting qubit architecture. The qumon qubit has a high coherence, and a positive anharmonicity that may be tuned to cancel the negative anharmonicity in a coupled qubit, such as a transmon qubit. The qumon has three parallel branches, in which are a shunt capacitor; a Josephson junction having weighted energy level and capacitance; and several Josephson junctions in series. The weight is chosen to provide the desired anharmonicity, and the transverse flux noise and transverse charge noise each decrease in proportion to the number of the Josephson junctions in series. Because unwanted ZZ interactions are canceled, qumon qubits and transmon qubits may be capacitively coupled in an alternating pattern to provide a surface code in which these interactions are canceled in an extensible way.

Abstract: The computer implemented method of solving a Hamiltonian can include performing, in a tensor network contracting a plurality of tensors in the network, a Lanczos method acting on the uncontracted tensors, the Lanczos method including evaluating a recursive relation of an equation including using the equation at least two times, forming a block tridiagonal matrix having a block size greater than one, based on the recursive relation, and diagonalizing the block tridiagonal matrix to obtain new tensors and energy levels of the tensor network, wherein at least one of the uncontracted tensors of the network has an index for the group of excitations; and solving for the rest of the tensor network, yielding an energy level solution of the Hamiltonian, outputting the energy level solution.

Abstract: A quantum circuit called a “qumon” is provided to cancel unwanted ZZ interaction in a superconducting qubit architecture. The qumon qubit has a high coherence, and a positive anharmonicity that may be tuned to cancel the negative anharmonicity in a coupled qubit, such as a transmon qubit. The qumon has three parallel branches, in which are a shunt capacitor; a Josephson junction having weighted energy level and capacitance; and several Josephson junctions in series. The weight is chosen to provide the desired anharmonicity, and the transverse flux noise and transverse charge noise each decrease in proportion to the number of the Josephson junctions in series. Because unwanted ZZ interactions are canceled, qumon qubits and transmon qubits may be capacitively coupled in an alternating pattern to provide a surface code in which these interactions are canceled in an extensible way.