Abstract: There is provided a method and apparatus for at least one of optimizing, monitoring and controlling a real physical system. Data representative of the physical system are obtained and used to generate one or more Hamiltonians. These Hamiltonians, in turn, are used in a quantum signal processing circuit of a quantum computer to simulate imaginary time evolution of a thermal pure quantum (TPQ) state of a collection of qubits that represent a Gibbs state of the system. Optionally, a Bayesian machine may be trained based on the evolution of the TPQ state to predict behavior of the physical system over time. Classical shadow tomography is then used to provide a classical representation of a TPQ state to a classical computer, to thereby facilitate classical optimization or control of the real physical system.

Abstract: The is provided a computer-implemented method for generating a quantum circuit from a Unitary Coupled Cluster (UCC) Ansatz, wherein the Ansatz represents an excitation of a reference state by a parameterised operator including excitation operators, and wherein the Ansatz includes multi-qubit Pauli operators that are determined from each excitation operator. The method comprises: partitioning the Pauli operators into mutually commuting sets and sequencing the Pauli operators by set; generating Pauli gadgets from the Pauli operators by Trotterization, wherein the Pauli gadgets have a same sequencing by set as the Pauli operators; diagonalising each set of Pauli gadgets to convert the Pauli gadgets into phase gadgets; and transforming the phase gadgets into one- and two-qubit native gates to generate the quantum circuit. Moreover, there is also provided a system that is configured to implement the method.

Abstract: Secure, semi-classical authentication schemes are presented. An authentication token is generated by applying a pre-determined measurement to a plurality of random quantum states to obtain a sequence of classical measurement outcomes. The token is validated by receiving the classical measurement outcomes and verifying whether the sequence corresponds to a statistically plausible result for the pre-determined measurement of the plurality of quantum states.

Abstract: A security test logic system can include a non-transitory memory configured to store measurements from a measurement apparatus, the measurement outputs comprising indications of presence or absence of coincidences where particles are detected at more than one detector at substantially the same time, the detectors being at the end of different channels from a particle source and having substantially the same length. The system can include a processor configured to compute a test statistic from the stored measurements. The test statistic may express a Bell inequality, and the system can compare the test statistic with a threshold. The processor can be configured to generate and output a certificate certifying that the measurements are from a quantum system if the value of the computed test statistic passes the threshold.

Abstract: A security test logic system can include a non-transitory memory configured to store measurements from a measurement apparatus, the measurement outputs comprising indications of presence or absence of coincidences where particles are detected at more than one detector at substantially the same time, the detectors being at the end of different channels from a particle source and having substantially the same length. The system can include a processor configured to compute a test statistic from the stored measurements. The test statistic may express a Bell inequality, and the system can compare the test statistic with a threshold. The processor can be configured to generate and output a certificate certifying that the measurements are from a quantum system if the value of the computed test statistic passes the threshold.

Abstract: Concepts, systems and methods are described for generating a quantum circuit from a Unitary Coupled Cluster (UCC) ansatz which represents the excitation of a reference state by a parameterised operator including excitation operators. The UCC ansatz includes multi-qubit Pauli operators, referred to as Pauli strings, determined from each excitation operator. The method comprises partitioning the Pauli strings into mutually commuting sets and sequencing the Pauli strings by set. Pauli gadgets are then generated from the Pauli strings by Trotterization, the Pauli gadgets having the same sequencing by set as the Pauli strings. Each set of Pauli gadgets is diagonalised to convert the Pauli gadgets into phase gadgets which are then transformed into one- and two-qubit native gates to generate the quantum circuit.

Abstract: Concepts, systems and methods are described for generating a quantum circuit from a Unitary Coupled Cluster (UCC) ansatz which represents the excitation of a reference state by a parameterised operator including excitation operators. The UCC ansatz includes multi-qubit Pauli operators, referred to as Pauli strings, determined from each excitation operator. The method comprises partitioning the Pauli strings into mutually commuting sets and sequencing the Pauli strings by set. Pauli gadgets are then generated from the Pauli strings by Trotterization, the Pauli gadgets having the same sequencing by set as the Pauli strings. Each set of Pauli gadgets is diagonalised to convert the Pauli gadgets into phase gadgets which are then transformed into one- and two-qubit native gates to generate the quantum circuit.

Abstract: A security test logic system can include a non-transitory memory configured to store measurements from a measurement apparatus, the measurement outputs comprising indications of presence or absence of coincidences where particles are detected at more than one detector at substantially the same time, the detectors being at the end of different channels from a particle source and having substantially the same length. The system can include a processor configured to compute a test statistic from the stored measurements. The test statistic may express a Bell inequality, and the system can compare the test statistic with a threshold. The processor can be configured to generate and output a certificate certifying that the measurements are from a quantum system if the value of the computed test statistic passes the threshold.