Advanced

Device

Select a simulation method to execute the quantum algorithm on QURI simulator.

The following two methods are available:

State vector simulator

If selected, calculations are performed by directly using the quantum state vector simulator.

In this simulation, instead of calculating sample averages of expectation values, the exact expectation values of energies or other physical quantities are returned.

Note that the results from this method correspond to the results from Sampling simulator with an infinite number of sampling.

Sampling simulator

If selected, calculations are performed by sampling the quantum state vector on the simulator, subject to the effects of statistical fluctuations by the sampling.

Similarly to the real quantum devices, in which the state vectors are not directly accessible, physical quantities are statistically estimated by repeatedly executing and measuring quantum circuits.

With this method, you can perform simulations under conditions closer to those of actual quantum devices.

The number of sampling shots used for a single calculation of physical quantities is specified in the Number of shots field.

Noise

When running QURI by sampling simulation, it is possible to also include the effect of noise to more accurately reflect the performance of actual quantum hardware. Noise may be added to simulations by toggling on the Noise option. Doing so enables the selection of noise presets which are based on commonly available superconducting and ion-trap devices. The gate error rate is indicated for each of these. For fine tuning and experimentation it is also possible to enter a specific error rate manually.

Gate error rate

QURI uses a noise model in which all gate errors are represented by a depolarizing channel and only simulates 2-qubit gate error, where it is assumed that each 2-qubit gate has the same error rate. Additionally, readout errors are not incorporated into this noise model.

This noise model was chosen because it is very fast and user friendly, but it is important to note that it does not accurately model real device performance in every situation. In addition it is important to note that while quantum error plays a crucial role in device characterization, there are many other characteristics that are important to device performance in general. These include device connectivity, gate speeds, T1 and T2 times, etc. We do not recommend using this noise model as a tool to assess the performance of actual quantum devices based on their publicly available calibration data.

Excited states

Settings for calculation of electronic excited states.

Num excited states

The number of excited states is specified with an integer.

The ground state should not be included in this value.

Solver

The Solver specifies the method used to calculate excited states.

SSVQE

If selected, the Subspace-search VQE (SSVQE) method is used.

SSVQE weights : the weight $w_i (>0)$ for the $i$'th electronic state in the SSVQE cost function

$\mathcal{L}(\theta) = \sum_{i=0}^k w_i \langle \psi_i(\theta) |\hat{H}| \psi_i(\theta) \rangle$

is specified in this field as a series of integers, w_0, w_1, .... When the value in the Number of excited states field is $k$, the number of the weight coefficients should be $k+1$. The weights should also satisfy $w_0 > w_1 > ... > w_k > 0$; an example of the input for this field is 4.0, 3.0, 2.0, 1.0 when the value in the Number of excited states is 3.

VQD

If selected, the Variational Quantum Deflation(VQD) method is used.

VQD Weights : the weight $w (>0)$ for the VQD cost function

$\mathcal{L}(\theta_k) = \langle\psi(\theta_k)|H|\psi(\theta_k)\rangle + w \sum^{k-1}_{i=0} \left| \langle\psi(\theta_i)|\psi(\theta_k)\rangle \right|^2$

is specified in this field.

Penalty term weights

Contribution from a physical quantity $\hat{O}$ is included as a penalty term

$\sum_i w_i \langle \psi_i(\theta) |(\hat{O}-o_i)^2| \psi_i(\theta) \rangle$

into the cost function for parameter optimization. Here, $w_i (>0)$ is the weight for the penalty term, $\hat{O}$ is the operator corresponding to the target quantity, and $o_i$ is the fixed value that the quantity should take.

In the following fields, the weight $w_i$ and the expected value $o_i$ are specified.

Number of electrons

The weight for the penalty term that restricts the number of electrons in the active space to the value of Number of electrons in the Active space field.

Spin $S^2$

The weight for the penalty term that restricts the expectation value of the square of the total spin operator $\hat{S}^2$. The expected value of $\hat{S}^2$ is restricted to $S(S+1)$ if the value of Multiplicity in the SCF Settings field is $2S+1$ .

Spin $S_z$

The weight for the penalty term that restricts the expectation value of the $\hat{S}_z$ operator. The expected value is specified in the Sz target value field.

A valid input for the Sz target value field is determined by the value of Multiplicity specified in the SCF Settings section and the value of Number of electrons specified in the Active space section.

Chemical properties

Select the physical quantities to be calculated from obtained electronic states, and specify each parameter.

Number of electrons

If selected, the expectation value of the electron number operator in the active space is calculated.

Spin $S^2$

If selected, the expectation value of the square of total spin operator $\hat{S}^2$ is calculated.

Spin $S_z$

If selected, the expectation value of the $\hat{S}_z$ operator is calculated.

Dipole moment

If selected, the expectation value of the dipole moment $\langle \Psi | \hat{\mu} | \Psi \rangle$ is calculated. The target states are specified in the States field as 0, 1, ....

Transition dipole moment

If selected, the expectation value of the transition dipole moment $\langle \Psi_j | \hat{\mu} | \Psi_i \rangle$ is calculated. The pairs of target states are specified in the State pairs field as (i,j), (i,k), ....