Abstract: In a general aspect, hybrid quantum/classical algorithms are executed in a computing system. A first set of values representing a measurement of a reduced density matrix (RDM) is obtained. The first set of values is based on sampling quantum states generated by a quantum processor. A classical processor generates a second, different set of values to represent the measurement of the RDM. The second set of values is constructed based on the first set of values by a process that imposes one or more n-representability conditions on the second set of values to represent the measurement of the RDM.

Abstract: In a general aspect, hybrid quantum/classical algorithms are executed in a computing system. A first set of values representing a measurement of a reduced density matrix (RDM) is obtained. The first set of values is based on sampling quantum states generated by a quantum processor. A classical processor generates a second, different set of values to represent the measurement of the RDM. The second set of values is constructed based on the first set of values by a process that imposes one or more n-representability conditions on the second set of values to represent the measurement of the RDM.

Abstract: In some embodiments, a computing system may comprise a memory for storing a ledger; a computer processor for verification of the ledger, wherein the computer processor comprises at least one of a classical computer processor configured to run a virtual quantum machine and a quantum computer comprising a plurality of qubits; wherein the ledger is configured to store arbitrary classical information and quantum information which is verifiable using the computer processor. Furthermore, in some embodiments the computing system is configured to perform operations comprising: adding to the ledger using the computer processor to solve a mathematically difficult problem which is Quantum-Merlin-Arthur-complete (QMA-complete). In embodiments, a blockchain includes a quantum state. In some aspects, a unitary operator corresponding to a quantum rotation is found when new transaction data are to be secured in the blockchain.

Abstract: In a general aspect, a computing system is configured to execute a quantum approximate optimization algorithm. In some aspects, a control system identifies a pair of qubit devices in a quantum processor. The quantum processor includes a connection that provides coupling between the pair of qubit devices. ZZ coupling between the pair of qubit devices is activated to execute a cost function defined in the quantum approximate optimization algorithm. The cost function is associated with a maximum cut problem, and the ZZ coupling is activated by allowing the pair of qubits to evolve under a natural Hamiltonian for a time period ?. One or more of the pair of qubit devices is measured to obtain an output from an execution of the quantum approximate optimization algorithm.

Abstract: In some aspects, a quantum simulation method includes generating a set of models representing a quantum system. The set of models includes subsystem models representing respective fragments of the quantum system. The quantum system is simulated by operating the set of models on a computer system that includes a classical processor unit and multiple unentangled quantum processor units (QPUs), and the unentangled QPUs operate the respective subsystem models. In some examples, density matrix embedding theory (DMET) is used to compute an approximate ground state energy for the quantum system.

Abstract: In a general aspect, a computing system is configured to execute a quantum approximate optimization algorithm. In some aspects, a control system identifies a pair of qubit devices in a quantum processor. The quantum processor includes a connection that provides coupling between the pair of qubit devices. ZZ coupling between the pair of qubit devices is activated to execute a cost function defined in the quantum approximate optimization algorithm. The cost function is associated with a maximum cut problem, and the ZZ coupling is activated by allowing the pair of qubits to evolve under a natural Hamiltonian for a time period ?. One or more of the pair of qubit devices is measured to obtain an output from an execution of the quantum approximate optimization algorithm.

Abstract: In a general aspect, values of input parameters for a quantum approximate optimization algorithm (QAOA) are selected by a Bayesian optimizer. The QAOA can be configured to solve a combinatorial optimization problem (COP), such as Maximum Cut. A hybrid classical-quantum computing system can be used to execute the QAOA and select the input parameters.

Abstract: In a general aspect, a computing system is configured to execute a quantum approximate optimization algorithm. In some aspects, a control system identifies a pair of qubit devices in a quantum processor. The quantum processor includes a connection that provides coupling between the pair of qubit devices. ZZ coupling between the pair of qubit devices is activated to execute a cost function defined in the quantum approximate optimization algorithm. The cost function is associated with a maximum cut problem, and the ZZ coupling is activated by allowing the pair of qubits to evolve under a natural Hamiltonian for a time period ?. One or more of the pair of qubit devices is measured to obtain an output from an execution of the quantum approximate optimization algorithm.