International Business Machines Corporation

Paul Kristan Temme

Jay Michael Gambetta

Antonio Mezzacapo

Abhinav Kandala

Ewout Van Den Berg

Sergey Bravyi

Antonio Corcoles-Gonzalez

Ramis Movassagh

Salvatore Bernardo Olivadese

Lev Samuel Bishop

Maika Takita

Zlatko Kristev Minev

Youngseok Kim

Dmitri Maslov

Stefan Woerner

Christophe Piveteau

Jennifer Ranae Glick

Tanvi Pradeep Gujarati

David Sutter

Andrew Eddins

Vojtech Havlicek

Techniques for mitigating readout error for quantum expectation are presented. Calibration component applies first random Pauli gates to qubits at first output of first circuit prior to first readout measurements of the qubits. Estimation component applies second random Pauli gates to qubits at second output of second circuit prior to second readout measurements of the qubits, and generates an error-mitigated readout determination based on first random Pauli gates applied to qubits at first circuit output and second random Pauli gates applied to qubits at second circuit output. Calibration component determines calibration data based on first readout measurements. Estimation component determines estimation data based on second readout measurements. Estimation component determines normalization scalar value based on the calibration data, determines estimation scalar value based on the estimation data, and determines the error-mitigated readout determination associated with a circuit of interest based on the normalization scalar value and estimation scalar value.

Readout-error mitigation for quantum expectation

A system comprises a memory that stores and a processor that executes computer executable components stored in the memory, wherein the computer executable components comprise an execution component that directs execution, employing a quantum processor, of an error mitigation set of quantum circuits that were noise-adjusted by employing noise scaling, and an evaluation component that evaluates, at an evaluation, results of the execution of the error mitigation set of quantum circuits, wherein the evaluation comprises a first generation of a first average expectation value corresponding to a noise-attenuated result of the execution, and wherein the evaluation further comprises a second generation of a second average expectation value corresponding to a noise-amplified result of the same execution.

Probabalistic amplification and attenuation of quantum errors using a single dataset

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.

Single-shot error mitigation for Clifford circuits

Systems, computer-implemented methods or computer program products to facilitate mitigating quantum errors associated with one or more quantum gates. A noise modeling component can generate a sparse error model of noise associated with one or more quantum gates; employ the sparse error model; and draw samples from an inverse noise model. An insertion component can insert the samples to mitigate errors associated with the one or more quantum gates. The insertion component can reduce the noise by running circuit instances augmented with samples from the inverse noise model. The noise modeling component includes a noise shaping component that can shape the noise affecting one or more quantum gates by twirling to form a Pauli channel.

Pauli-Lindbladian based noise modeling and mitigation

The illustrative embodiments provide a method, system, and computer program product for quantum feature kernel alignment using a hybrid classical-quantum computing system. An embodiment of a method for hybrid classical-quantum decision maker training includes receiving a training data set. In an embodiment, the method includes selecting, by a first processor, a sampling of objects from the training set, each object represented by at least one vector. In an embodiment, the method includes applying, by a quantum processor, a set of quantum feature maps to the selected objects, the set of quantum maps corresponding to a set of quantum kernels. In an embodiment, the method includes evaluating, by a quantum processor, a set of parameters for a quantum feature map circuit corresponding to at least one of the set of quantum feature maps.

Quantum feature kernel alignment

Systems and techniques that facilitate Hamiltonian simulation based on simultaneous-diagonalization are provided. In various embodiments, a partition component can partition one or more Pauli operators of a Hamiltonian into one or more subsets of commuting Pauli operators. In various embodiments, a diagonalization component can generate one or more simultaneous-diagonalization circuits corresponding to the one or more subsets. In various aspects, a one of the one or more simultaneous-diagonalization circuits can diagonalize the commuting Pauli operators in a corresponding one of the one or more subsets. In various embodiments, an exponentiation component can generate one or more exponentiation circuits corresponding to the one or more subsets. In various aspects, a one of the one or more exponentiation circuits can exponentiate the simultaneously diagonalized commuting Pauli operators in a corresponding one of the one or more subsets. In various embodiments, a simulation component can concatenate the one or more simultaneous-diagonalization circuits, the one or more exponentiation circuits, and one or more adjoints of the one or more simultaneous-diagonalization circuits of the one or more subsets to simulate a time evolution of the Hamiltonian.

Hamiltonian simulation based on simultaneous-diagonalization

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.

Fault-tolerant T-gates via quasiprobability decomposition

Techniques and a system to facilitate quantum computation are provided. In one example, a system includes a processor that executes computer executable components stored in a memory; a quantum feature map circuit component that estimates a kernel associated with a feature map; and a support vector machine component that performs a classification using the estimated kernel.

Quantum feature kernel estimation using an alternating two layer quantum circuit

Techniques using short depth circuits as quantum classifiers are described. In one embodiment, a system is provided that comprises: quantum hardware, a memory that stores computer-executable components and a processor that executes computer-executable components stored in the memory. In one implementation, the computer-executable components comprise a calibration component that calibrates quantum hardware to generate a short depth quantum circuit. The computer-executable components further comprise a cost function component that determines a cost function for the short depth quantum circuit based on an initial value for a parameter of a machine-learning classifier. The computer-executable components further comprise a training component that modifies the initial value for the parameter during training to a second value for the parameter based on the cost function for the short depth quantum circuit.

Short depth circuits as quantum classifiers

Techniques for performing cost function deformation in quantum approximate optimization are provided. The techniques include mapping a cost function associated with a combinatorial optimization problem to an optimization problem over allowed quantum states. A quantum Hamiltonian is constructed for the cost function, and a set of trial states are generated by a physical time evolution of the quantum hardware interspersed with control pulses. Aspects include measuring a quantum cost function for the trial states, determining a trial state resulting in optimal values, and deforming a Hamiltonian to find an optimal state and using the optimal state as a next starting state for a next optimization on a deformed Hamiltonian until an optimizer is determined with respect to a desired Hamiltonian.

Cost function deformation in quantum approximate optimization

Generating trial states for a variational quantum Eigenvalue solver (VQE) using a quantum computer is described. An example method includes selecting a number of samples S to capture from qubits for a particular trial state. The method further includes mapping a Hamiltonian to the qubits according the trial state. The method further includes setting up an entangler in the quantum computer, the entangler defining an entangling interaction between a subset of the qubits of the quantum computer. The method further includes reading out qubit states after post-rotations associated with Pauli terms in the target Hamiltonian, the reading out being performed for S samples. The method further includes computing an energy state using the S qubit states. The method further includes, in response to the estimated energy state not converging with an expected energy state, computing a new trial state for the VQE and iterating to compute the estimated energy using the new trial state.

Hardware-efficient variational quantum eigenvalue solver for quantum computing machines

Systems, computer-implemented methods, and computer program products to facilitate external port measurement of qubit port responses 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 an analysis component that can analyze responses of a multi-mode readout device coupled to a qubit. The computer executable components can further comprise an assignment component that can assign a readout state of the qubit based on the responses. In some embodiments, the multi-mode readout device can be electrically coupled to at least one of the qubit or an environment of the qubit based on a defined electrical coupling value.

Multi-mode qubit readout and qubit state assignment

One or more time correlations of noise within a quantum computing circuit of a quantum processor are determined. The quantum computing circuit includes one or more qubits. A coherence time for each qubit is determined, and one or more stretch factors are determined based upon the time correlations of the noise and the coherence times. A first loop is initialized that performs for each of the stretch factors: initializing the qubits to a ground state, executing the quantum computing circuit with a the stretch factor, performing one or more single-qubit post-rotations associated with one or more expectation values, measuring a state of each qubit to determine the one or more expectation values of interest, and resetting each qubit to the ground state. A mitigated estimate is determined for the expectation values based upon an extrapolation of the expectation values determined for each stretch factor.

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Ossining, NY, United States of America

Paul Kristan Temme