Protocols to exploit non-linear quantum mechanical effects to parallelize any process (such as computational, mechanical or biological), inhibit the dilution of non-linear quantum mechanical effects and enhance the shot noise limit of quantum measurement devices are described. The key concept behind these protocols is the use of a device that can communicate across different arms of a quantum superposition even in the presence of decoherence using non-linear quantum mechanical interactions (such as the expectation values of classical sources of electromagnetism and gravitation). By communicating across different arms of a quantum superposition, the protocol can collect the results of parallelizable tasks performed in each arm of the superposition, arrive at well defined final states across the superposition and use the strength of the observed non-linearity to measure the properties of the superposition itself.

Protocols to exploit non-linear quantum mechanical effects to parallelize any process (such as computational, mechanical or biological), inhibit the dilution of non-linear quantum mechanical effects and enhance the shot noise limit of quantum measurement devices are described. The key concept behind these protocols is the use of a device that can communicate across different arms of a quantum superposition even in the presence of decoherence using non-linear quantum mechanical interactions (such as the expectation values of classical sources of electromagnetism and gravitation). By communicating across different arms of a quantum superposition, the protocol can collect the results of parallelizable tasks performed in each arm of the superposition, arrive at well defined final states across the superposition and use the strength of the observed non-linearity to measure the properties of the superposition itself.

Systems, computer-implemented methods and/or computer program products are provided to facilitate operation of a quantum circuit on a set of qubits via providing and implementing decompositions of one or more unitary matrices. According to an embodiment, a system can implement a unitary matrix by providing and implementing a decomposition of the unitary matrix, to thereby facilitate operation of and/or operate a quantum circuit on a set of qubits. The 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 unitary matrix management component that decomposes a defined 4×4 unitary matrix into a defined circuit comprising a sequence of universal gates. The sequence of universal gates can be a same sequence for each defined 4×4 unitary matrix of a set of candidate 4×4 unitary matrices including the defined 4×4 unitary matrix.

Aspects of the present disclosure relate generally to systems and methods for use in the implementation and/or operation of quantum information processing (QIP) systems, and more particularly, to the computation of joint probability distributions with quantum computers. Improvements in the computation of joint probability distributions are described by designing quantum machine learning algorithms to model copulas. Moreover, any copula is shown to be naturally mapped to a multipartite maximally entangled state. A variational ansatz referred to herein as a “qopula” creates arbitrary correlations between variables while maintaining the copula structure starting from a set of Bell pairs for two variables, or Greenberger-Horne-Zeilinger (GHZ) states for multiple variables. Generative learning algorithms may be demonstrated on quantum computers, and more particularly, in trapped-ion quantum computers. The approach described herein is shown to have advantages over classical models.

Aspects of the present disclosure relate generally to systems and methods for use in the implementation and/or operation of quantum information processing (QIP) systems, and more particularly, to the computation of joint probability distributions with quantum computers. Improvements in the computation of joint probability distributions are described by designing quantum machine learning algorithms to model copulas. Moreover, any copula is shown to be naturally mapped to a multipartite maximally entangled state. A variational ansatz referred to herein as a “qopula” creates arbitrary correlations between variables while maintaining the copula structure starting from a set of Bell pairs for two variables, or Greenberger-Horne-Zeilinger (GHZ) states for multiple variables. Generative learning algorithms may be demonstrated on quantum computers, and more particularly, in trapped-ion quantum computers. The approach described herein is shown to have advantages over classical models.

The driver Hamiltonian is modified in such a way that the quantum approximate optimization algorithm (QAOA) running on a circuit-model quantum computing facility (e.g., actual quantum computing device or simulator), may better solve combinatorial optimization problems than with the baseline/default choice of driver Hamiltonian. For example, the driver Hamiltonian may be chosen so that the overall Hamiltonian is non-stoquastic.

The disclosure describes the implementation of automated techniques for optimizing quantum circuits of the size and type expected in quantum computations that outperform classical computers. The disclosure shows how to handle continuous gate parameters and report a collection of fast algorithms capable of optimizing large-scale-scale quantum circuits. For the suite of benchmarks considered, the techniques described obtain substantial reductions in gate counts. In particular, the techniques in this disclosure provide better optimization in significantly less time than previous approaches, while making minimal structural changes so as to preserve the basic layout of the underlying quantum algorithms. The results provided by these techniques help bridge the gap between computations that can be run on existing quantum computing hardware and more advanced computations that are more challenging to implement in quantum computing hardware but are the ones that are expected to outperform what can be achieved with classical computers.

The computer implemented method of solving a Hamiltonian can include performing, in a tensor network contracting a plurality of tensors in the network, a Lanczos method acting on the uncontracted tensors, the Lanczos method including evaluating a recursive relation of an equation including using the equation at least two times, forming a block tridiagonal matrix having a block size greater than one, based on the recursive relation, and diagonalizing the block tridiagonal matrix to obtain new tensors and energy levels of the tensor network, wherein at least one of the uncontracted tensors of the network has an index for the group of excitations; and solving for the rest of the tensor network, yielding an energy level solution of the Hamiltonian, outputting the energy level solution.

The computer implemented method of solving a Hamiltonian can include performing, in a tensor network contracting a plurality of tensors in the network, a Lanczos method acting on the uncontracted tensors, the Lanczos method including evaluating a recursive relation of an equation including using the equation at least two times, forming a block tridiagonal matrix having a block size greater than one, based on the recursive relation, and diagonalizing the block tridiagonal matrix to obtain new tensors and energy levels of the tensor network, wherein at least one of the uncontracted tensors of the network has an index for the group of excitations; and solving for the rest of the tensor network, yielding an energy level solution of the Hamiltonian, outputting the energy level solution.

A method includes causing activation, at a first time, of a first set of squeezed light sources from a plurality of squeezed light sources of a Gaussian boson sampling (GBS) circuit. At a second time after the first time, a first photon statistic is detected at a first output port from a plurality of output ports of the GBS circuit. At a third time after the first time, a second set of squeezed light sources from the plurality of squeezed light sources of the GBS circuit is activated, the second set of squeezed light sources being different from the first set of squeezed light sources. At a fourth time after the third time, a second photon statistic is detected at a second output port from the plurality of output ports of the GBS circuit. At least one transformation matrix is estimated that represents a linear optical interferometer of the GBS circuit based on the first photon statistic and the second photon statistic.