Intel® Quantum Simulator Backend

Intel® Quantum Simulator (IQS) is a full-state simulator working at the qubit level, abstracting the physics of the specific implementaion. It is available as a standalone open-source project, but it also comes fully integrated as one of the backends of the Intel® Quantum SDK [KWP+22]. IQS is designed to take full advantage of High Performance Computing (HPC) infrastructure and allows both multi-thread (shared memory, using OpenMP) and multi-process parallelization (distributed memory, using MPI) [GHBS20].

The API has already being described in the context of full-state simulators (see Configuring the FullStateSimulator). Here we focus on the possibility of adding a customizable noise model in the simulation. The programmer does not need to be familiar with IQS, and no IQS code or APIs need to be used.

Customizable noise modeling

The user can customize the action of every quantum operation within the template provided below by defining appropriate functions. The action of each operation is divided in three parts:

  • Pre-operation: Apply one or more of the following phenomenological noise channels:

    • Dephasing channel

    • Depolarizing channel

    • Amplitude damping

    • Bitflip channel

    Each effect is characterized by an intensity parameter.

  • Operation itself: The choice here is whether to apply the ideal operation or a user-provided process matrix (also known as the \(\chi\) matrix). In the latter case, the user can include all noise effects directly in the process matrix, and thus avoid pre- or post-operation actions. However, we find it convenient to provide the pre- and post-operation templates to facilitate writing standard noise models quickly.

  • Post-operation: Similar to the pre-operation case, the user can apply one or more of the following phenomenological noise models:

    • Dephasing channel

    • Depolarizing channel

    • Amplitude damping

    • Bitflip channel

    Each effect is characterized by an intensity parameter.

Custom operation definition

The definition of a custom operation is provided by means of objects of type iqsdk::IqsCustomOp, which can be initialized as follows:

IqsCustomOp op = {pre_dephasing, pre_depolarizing, pre_amplitude_damping, pre_bitflip,
                 process_matrix, label,
                 post_dephasing, post_depolarizing, post_amplitude_damping, post_bitflip};

where:

  • pre_dephasing, pre_depolarizing, pre_amplitude_damping, pre_bitflip are scalar values representing the intensity of pre-operations.

  • process_matrix is a std::vector<std::complex<double>> in row-major format. When the operation is ideal, one can simply use an empty vector as process_matrix.

  • label is a string used as unique tag for the process matrix. If multiple operations use the same process matrix (for example, the CZ gate on different pairs of simulated physical qubits), assigning the same label reduces the memory and computation by using a single process matrix.

  • post_dephasing, post_depolarizing, post_amplitude_damping, post_bitflip are scalar values representing the intensity of post-operations.

If the complete operation is noiseless, one can simply use the global object:

iqsdk::k_iqs_ideal_op = {0, 0, 0, 0, {}, "ideal", 0, 0, 0, 0}

already defined in the header quantum_full_state_simulator_backend.h.

Custom operation specification

While the subsection above explained how to define a single custom operation, we still need to specify the behavior of a custom action. For example, one may want to return different IqsCustomOp objects for the same gate type depending on the simulated physical qubit as a way of having the noise reflect that of a realistic, inhomogeneous device.

The user needs to write a function for every quantum operation returning the appropriate IqsCustomOp object for the given parameters of the quantum operation. For example, one may want to use a simplified noise model for the one-qubit gates by expressing them as ideal gates followed by depolarization. At the same time, they may want to use a process matrix describing the action of the two-qubit CZ gates. One may even use different process matrices depending on the qubits involved in the gate.

In a simple example, a custom CPhase operation with a 10% chance of a dephasing error prior to the gate executing would be defined as:

iqsdk::IqsCustomOp CustomCPhaseRot(unsigned q1, unsigned q2, double g) {
  return {0.1, 0, 0, 0, {}, "cphase_dephasing", 0, 0, 0, 0};
}

Using Custom IQS Noise Models in a Program

To enable the IQS with a customizable noise model, an IqsConfig should be declared with "custom".

iqsdk::IqsConfig custom_iqs_config(N, "custom");

where N is the number of qubits. Then, associate the desired functions to the customizable actions:

custom_iqs_config.PrepZ = CustomPrepZ;
custom_iqs_config.RotationXY = CustomRotXY;
custom_iqs_config.CPhaseRotation = CustomCPhaseRot;

Here, custom_iqs_config.<name> are set to user-defined functions with the following signatures:

iqsdk::IqsCustomOp PrepZ(unsigned qubit);
iqsdk::IqsCustomOp MeasZ(unsigned qubit);
iqsdk::IqsCustomOp RotationXY(unsigned qubit, double phi, double gamma);
iqsdk::IqsCustomOp RotationZ(unsigned qubit, double gamma);
iqsdk::IqsCustomOp ISwapRotation(unsigned qubit_1, unsigned qubit_2, double gamma);
iqsdk::IqsCustomOp CPhaseRotation(unsigned qubit_1, unsigned qubit_2, double gamma);

Not all of the functions need to be defined. If they are not defined, they will default to the ideal operation. Since the customizable noise model is compatible with full-state simulators, the IqsConfig is passed to an instantiation of a full-state simulator.

iqsdk::FullStateSimulator custom_iqs_device(custom_iqs_config);

if (iqsdk::QRT_ERROR_SUCCESS != custom_iqs_device.ready()) return 1;

A complete code example can be found in the custom_backend.cpp sample described in Code Samples.

Important Points on Performing Noisy Simulations with IQS

The Intel® Quantum SDK allows noisy simulations of qubits with the Intel® Quantum Simulator as the backend. Noise is incorporated during a simulation via stochastic injection of noise based on the specified noise intensity parameter. Thus, it is necessary to aggregate results from multiple simulations to accurately simulate a noisy qubit system. Given that the stochastic nature is realized via the initial seed, it is imperative that the user instantiates the backend with a different seed each time the same quantum circuit is run during sample collection. By processing the resulting samples, the probabilities from noisy simulations can be reconstructed. This sampling process can be made efficient by using the asynchronous mode of simulations, whereby multiple simulator backends initialized with different seeds are used to simultaneously perform simulations depending on the available memory and processing capability.