Abstract: Systems and techniques that facilitate efficient synthesis of optimal multi-qubit Clifford circuits are provided. In various embodiments, a system can receive as input a number n representing a quantity of qubits. In various instances, the system can generate, via a cost-invariant reduction function, as output a library of different n-qubit canonical representatives that respectively correspond to different cost-invariant equivalence classes of n-qubit Clifford group elements. In various embodiments, a system can receive as input a first Clifford group element. In various aspects, the system can search a database of canonical representatives, wherein different canonical representatives in the database respectively correspond to different cost-invariant equivalence classes of Clifford group elements.

Abstract: Systems and techniques that facilitate improved single-shot error mitigation for Clifford circuits are provided. For a Clifford circuit, various embodiments described herein can facilitate two-sided or one-sided Pauli checks. In various aspects, left-side Pauli operators of two-sided Pauli checks can be selected randomly without replacement, and right-side Pauli operators of two-sided Pauli checks can be identified via commutation identities respectively relating the Clifford circuit to the left-side Pauli operators. In various instances, Pauli operators of one-sided Pauli checks can be selected via commutation identities respectively relating the Clifford circuit to Z-type Paulis selected randomly without replacement. For either two-sided or one-sided Pauli checks, various embodiments described herein can involve implementation of interleaved SWAP gates, which can allow such two-sided or one-sided Pauli checks to be performed on linear nearest neighbor coupling topologies.

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 partitioned template matching and/or symbolic peephole optimization are provided. In various embodiments, a system can comprise a template component, which can perform template matching on a Clifford circuit associated with a set of qubits. In various aspects, the system can comprise a partition component, which can partition, prior to the template matching, the Clifford circuit into a computation stage, a Pauli stage, and a SWAP stage. In various instances, the template matching can be performed on the computation stage. In various embodiments, the system can comprise a symbolic component, which can select a subset of qubits from the set of qubits, rewrite at least one entangling gate in the computation stage such that a target of the at least one entangling gate is in the subset of qubits, and replace the at least one rewired entangling gate with a symbolic Pauli gate.

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 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: 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 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: 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: 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, 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: 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 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 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 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: Techniques for quantum entanglement forging for quantum simulations are presented. A decomposer component can decompose a weakly entangled variational state into respective local components of the weakly entangled variational state, wherein the respective local components describe respective tensor product states. A quantum computing simulator component can perform respective quantum simulations of the respective local components of the weakly entangled variational state, and can determine respective portions of variational energy contributed by the respective tensor product states associated with the respective local components based on the respective quantum simulations of the respective local components of the weakly entangled variational state. An energy determination component can determine a variational energy associated with the weakly entangled variational state based on the respective portions of the variational energy contributed by the respective tensor product states.

Abstract: Systems and techniques that facilitate partitioned template matching and/or symbolic peephole optimization are provided. In various embodiments, a system can comprise a template component, which can perform template matching on a Clifford circuit associated with a set of qubits. In various aspects, the system can comprise a partition component, which can partition, prior to the template matching, the Clifford circuit into a computation stage, a Pauli stage, and a SWAP stage. In various instances, the template matching can be performed on the computation stage. In various embodiments, the system can comprise a symbolic component, which can select a subset of qubits from the set of qubits, rewrite at least one entangling gate in the computation stage such that a target of the at least one entangling gate is in the subset of qubits, and replace the at least one rewired entangling gate with a symbolic Pauli gate.

Abstract: Techniques that combine quantum error correction and quantum error mitigation are used to simulate a fault-tolerant T-gate with low sampling overhead using the quasiprobability decomposition method. In some embodiments, the T-gate can be simulated using two logical bits and a magic state preparation that mitigates the need for magic state distillation and consequently has a low sampling overhead. Alternatively, the T-gate can be simulated based on code deformation performed on the surface code. Noise is removed from the T-gate using quasiprobability decomposition based on a learned logical error rate.