Abstract: Systems, computer-implemented methods, and computer program products to facilitate synthesis of a quantum circuit are provided. According to an embodiment, a system can comprise a memory that stores computer executable components and a processor that executes the computer executable components stored in the memory. The computer executable components can comprise a circuit generation component that generates, iteratively, quantum circuits from 1 to N two-qubit gates, wherein at least one or more iterations (1, 2, . . . , N) adds a single two-qubit gate to circuits from a previous iteration based on using added single 2-qubit gates that represent operations distinct from previous operations relative to previous iterations. The computer executable components can further comprise a circuit identification component that identifies, from the quantum circuits, a desired circuit that matches a quantum circuit representation.

Abstract: A method of generating a randomized benchmarking protocol includes providing a randomly generated plurality of Hadamard gates; applying the Hadamard gates to a plurality of qubits; and generating randomly a plurality of Hadamard-free Clifford circuits. Each of the plurality of Hadamard-free Clifford circuits is generated by at least randomly generating a uniformly distributed phase (P) gate, and randomly generating a uniformly distributed linear Boolean invertible matrix of conditional NOT (CNOT) gate, and combining the P and CNOT gates to form each of the plurality of Hadamard-free Clifford circuits. The method also includes combining each of the plurality of Hadamard-free Clifford circuits with corresponding each of the plurality of Hadamard gates to form a sequence of alternating Hadamard-free Clifford-Hadamard pairs circuit to form the randomized benchmarking protocol; and measuring noise in a quantum mechanical processor using the randomized benchmarking protocol.

Abstract: A method of generating a randomized benchmarking protocol includes providing a randomly generated plurality of Hadamard gates; applying the Hadamard gates to a plurality of qubits; and generating randomly a plurality of Hadamard-free Clifford circuits. Each of the plurality of Hadamard-free Clifford circuits is generated by at least randomly generating a uniformly distributed phase (P) gate, and randomly generating a uniformly distributed linear Boolean invertible matrix of conditional NOT (CNOT) gate, and combining the P and CNOT gates to form each of the plurality of Hadamard-free Clifford circuits. The method also includes combining each of the plurality of Hadamard-free Clifford circuits with corresponding each of the plurality of Hadamard gates to form a sequence of alternating Hadamard-free Clifford-Hadamard pairs circuit to form the randomized benchmarking protocol; and measuring noise in a quantum mechanical processor using the randomized benchmarking protocol.

Abstract: A method of generating a random uniformly distributed Clifford unitary circuit (C) includes: generating a random Hadamard (H) gate; drawing a plurality of qubits from a probability distribution of qubits; applying the random H gate to the plurality of qubits drawn from the probability distribution; and generating randomly a first Hadamard-free Clifford circuit (F1) and a second Hadamard-free Clifford circuit (F2). The first and second Hadamard-free Clifford circuits is generated by at least randomly generating a uniformly distributed phase (P) gate, and randomly generating a uniformly distributed linear Boolean invertible conditional NOT (CNOT) gate, and combining the P and CNOT gates to form the first and second Hadamard-free Clifford circuits. The method further includes combining the generated first Hadamard-free circuit (F1) and the second Hadamard-free Clifford circuit (F2) with the generated random Hadamard (H) gate to form the random uniformly distributed Clifford unitary circuit (C).

Abstract: A method of mitigating quantum readout errors by stochastic matrix inversion includes performing a plurality of quantum measurements on a plurality of qubits having predetermined plurality of states to obtain a plurality of measurement outputs; selecting a model for a matrix linking the predetermined plurality of states to the plurality of measurement outputs, the model having a plurality of model parameters, wherein a number of the plurality of model parameters grows less than exponentially with a number of the plurality of qubits; training the model parameters to minimize a loss function that compares predictions of the model with the matrix; computing an inverse of the model based on the trained model parameters; and providing the computed inverse of the model to a noise prone quantum readout of the plurality of qubits to obtain a substantially noise free quantum readout.

Abstract: Systems, computer-implemented methods, and computer program products to facilitate estimation of an expected energy value of a Hamiltonian based on data of the Hamiltonian, the quantum state produced by a quantum device and/or entangled measurements are provided. According to an embodiment, a system can comprise a memory that stores computer executable components and a processor that executes the computer executable components stored in the memory. The computer executable components can comprise a selection component that selects a quantum state measurement basis having a probability defined based on a ratio of a Pauli operator in a Hamiltonian of a quantum system. The computer executable components can further comprise a measurement component that captures a quantum state measurement of a qubit in the quantum system based on the quantum state measurement basis.

Abstract: Systems and techniques that facilitate precision-preserving qubit reduction based on spatial symmetries in fermionic systems are provided. In one or more embodiments, a symmetry component can generate a diagonalized second quantization representation of a spatial point group symmetry operation. The spatial point group symmetry operation can be associated with a molecule (e.g., a geometrical rotation, reflection, and/or inversion of a physical molecule that results in a new molecular orientation that is substantially the same as the original molecular orientation). In one or more embodiments, a transformation component can convert the diagonalized second quantization representation into a single Pauli string. In one or more embodiments, a tapering component can taper off qubits in a computational quantum algorithm that models properties of the molecule, based on the single Pauli string.

Abstract: A technique relates to reducing qubits required on a quantum computer. A Fermionic system is characterized in terms of a Hamiltonian. The Fermionic system includes Fermions and Fermionic modes with a total number of 2M Fermionic modes. The Hamiltonian has a parity symmetry encoded by spin up and spin down parity operators. Fermionic modes are sorted such that the first half of 2M modes corresponds to spin up and the second half of 2M modes corresponds to spin down. The Hamiltonian and the parity operators are transformed utilizing a Fermion to qubit mapping that transforms parity operators to a first single qubit Pauli operator on a qubit M and a second single qubit Pauli operator on a qubit 2M. The qubit M having been operated on by the first single qubit Pauli operator and the qubit 2M having been operated on by the second single qubit Pauli operator are removed.

Abstract: A technique relates to reducing qubits required on a quantum computer. A Fermionic system is characterized in terms of a Hamiltonian. The Fermionic system includes Fermions and Fermionic modes with a total number of 2M Fermionic modes. The Hamiltonian has a parity symmetry encoded by spin up and spin down parity operators. Fermionic modes are sorted such that the first half of 2M modes corresponds to spin up and the second half of 2M modes corresponds to spin down. The Hamiltonian and the parity operators are transformed utilizing a Fermion to qubit mapping that transforms parity operators to a first single qubit Pauli operator on a qubit M and a second single qubit Pauli operator on a qubit 2M. The qubit M having been operated on by the first single qubit Pauli operator and the qubit 2M having been operated on by the second single qubit Pauli operator are removed.

Abstract: A technique relates to reducing qubits required on a quantum computer. A Fermionic system is characterized in terms of a Hamiltonian. The Fermionic system includes Fermions and Fermionic modes with a total number of 2M Fermionic modes. The Hamiltonian has a parity symmetry encoded by spin up and spin down parity operators. Fermionic modes are sorted such that the first half of 2M modes corresponds to spin up and the second half of 2M modes corresponds to spin down. The Hamiltonian and the parity operators are transformed utilizing a Fermion to qubit mapping that transforms parity operators to a first single qubit Pauli operator on a qubit M and a second single qubit Pauli operator on a qubit 2M. The qubit M having been operated on by the first single qubit Pauli operator and the qubit 2M having been operated on by the second single qubit Pauli operator are removed.

Abstract: A technique relates to reducing qubits required on a quantum computer. A Fermionic system is characterized in terms of a Hamiltonian. The Fermionic system includes Fermions and Fermionic modes with a total number of 2M Fermionic modes. The Hamiltonian has a parity symmetry encoded by spin up and spin down parity operators. Fermionic modes are sorted such that the first half of 2M modes corresponds to spin up and the second half of 2M modes corresponds to spin down. The Hamiltonian and the parity operators are transformed utilizing a Fermion to qubit mapping that transforms parity operators to a first single qubit Pauli operator on a qubit M and a second single qubit Pauli operator on a qubit 2M. The qubit M having been operated on by the first single qubit Pauli operator and the qubit 2M having been operated on by the second single qubit Pauli operator are removed.