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Quantum simulation for material science, chemistry and physics

This scenario describes the how quantum computing can be used for material science, chemistry and physics.

It has the following specification:

  • Input: molecule specification
  • Output: ground state energy
  • Used in:
    • material science
    • battery design
    • catalyst research

Application Layer - Downwards

  1. Simulation App:

    • The Simulation App is the entry point for this scenario.
    • It takes the molecule specification and passes it down to the Hartree-Fock algorithm

  2. Hartree-Fock:

    • The Hartree-Fock algorithm is the first transformation step to get from the molecule input to a quantum ready representation
    • Its input is the molecular geometry in our scenario
    • The output are the electron integrals.

  3. Hamiltonian Formulator:

    • The Hamiltonian formulation maps the electron integrals into a fermonic Hamiltonian.

  4. Jordan-Wigner:

    • The Jordan-Wigner Transformation allows a qubit representation using a fermonic Hamiltonian and turns it into a spin Hamiltonian, which is equivalent to a set of qubits.

  5. VQE (Variational Quantum Eigensolver):

    • The VQE Algorithm is a hybrid algorithm, which uses the qubit Hamiltonian to create a parameterised quantum circuit.

  6. VQE Program Generator

    • With the parametrised circuit the program generator creates a program for the transpilation pipeline in the system layer.

System Layer - Downwards

The Qiskit Transpilation Pipeline consists of 6 steps:

  1. Initialization Stage

    • Using the quantum program from the Application Layer, the transpilation pipeline can start.
    • The first step of the transpilation pipeline is breaking down multi- and custom made qubit- gates into one- or two-qubit operations.

  2. Layout Stage

    • This stage maps the input circuit's virtual qubits to the target's physical hardware qubits.
    • The algorithm's goal is to map the qubits in such a way that frequently-interacting virtual qubits end up next to each other in the physical hardware.

  3. Routing Stage

    • As described in the step before, a perfect connectivity between the qubits can not always be achieved. Therefore this stage adds additional operations to adapt to these constraints.
    • Using the circuit and hardware topology as inputs, it can create a physically compatible circuit by inserting SWAP gates to move information between previously disconnected qubits.

  4. Translation Stage

    • This stage rewrites all previously chosen gates into the specific native gates supported by the target hardware's Instruction Set Architecture (ISA).

  5. Optimization Stage

    • This stage executes low-level, hardware-aware refinements on circuits that are already compatible with the target's Instruction Set Architecture (ISA) to reduce redundancy.

  6. Scheduling Stage

    • The scheduling stage receives an ISA-compatible circuit and inserts explicit delay instructions to accurately reflect qubit idle periods, hardware timing constraints and to reduce error rate.
    • It ensures the final output remains ISA-compatible while updating start-time metadata and optionally applying walltime-sensitive transformations.
    • This concludes the Qiskit transpilation pipeline.

  7. Circuit-Command Mapping

    • Using the ISA-compatible circuit, additional information like number of measurements demanded and a translation table, which translated the commands into backend compatible commands, this steps gives a list of operations to the device and firmware of the hardware.

Physical Layer

  1. Superconducting Device and Firmware:

    • Using digital hardware instructions and pulse definitions, this process converts these commands into physical signals to control operations on the quantum chip.
    • It outputs a microwave signal list directly to the quantum hardware, translating digital instructions into executable physical actions.

  2. Molecule Laser:

    • The molecule laser uses the microwave signal list to execute the quantum operations on the physical hardware.
    • When all operations are done, the molecule Laser sends a status flag to the energy sensor

  3. Energy Sensor:

    • When the molecule laser has completed its job and updated its status, this step measures the qubit energy levels

System Layer - Upwards

  1. Transpilation
    • In this step, the qubit energy levels are transformed into an expectation value.
    • To do this, additional backend data is needed to interpret the measured results.

Application Layer - Upwards

  1. COBYLA

    • COBYLA is a classical optimizer which needs an expectation value as input.
    • It compares the expectation value to the last one (if it exists) and tries to optimize the parameters of the VQE algorithm.
    • After an local optimal solution is found or the maximum of iterations is reached, the classical optimizer terminates

  2. VQE Program Generator

    • The Program Generator updates the parameters of the COBYLA algorithm and starts the process again.
    • When the classical optimizer terminates, the Program Generator gives the optimal result towards the Error Mitigation Method.

  3. Zero Noise Extrapolation

    • Zero Noise Extrapolation (ZNE) is a error mitigation method, which can reduce the error rate by using an expectation value and a circuit has input
    • It creates a program to measure a new expectation value with a circuit, which has still the same function but uses more gates.
    • This process is repeated multiple times and lead towards a noise pattern, which allows to reduce the error rate by extrapolation.

  4. Simulation App

    • The error-optimized expectation value is given towards the simulation app, which then visualize it as ground state energy for the user.