code review

.gitignore

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+quest_link*
+gates_synthesis
+others
+sdbells
+*.gif
+

LICENSE.txt

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+# Released under MIT License
+
+Copyright (c) 2013 Mark Otto.
+
+Copyright (c) 2017 Andrew Fong.
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

NVCenter/README.md

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+<div align="center">
+ <img src="../supplement/web/nvc.png" width="150" alt="Alt text">
+</div>
+
+# Nitrogen-vacancy center qubits
+
+There is currently one virtual NV-center device, namely NV-center diamond that is inspired from devices in the University of Delft. This device is instantiated with command ``NVCenterDelft[]``.
+
+**Table of contents**
+1. [Characteristics](#characteristics)
+2. [Native operations](#native-operations)
+3. [Parameters and usage](#parameters-and-usage)
+
+## Characteristics
+
+NV-center has star-shaped connectivity, where the NV<sup>-</sup>  electron spin is sitting in the center, surrounded by the nuclear spins <sup>13</sup>C &mdash; and may also involve <sup>14</sup>Nq spin.
+We set the electron spin to be indexed 0 in the program. See the picture below, where q0 is the electron spin and the rest are nuclear spin. The green circle represents nitrogen spin if you want to use it; this is decided in the setting up the parameters, e.g.,  particular fidelities and coherence time.
+
+
+<div align="center">
+ <img src="../supplement/web/conn_nvc.jpg" width="150" alt="Alt text">
+</div>
+
+Therefore, two-qubit gates operations can be done (directly) between the center spin to the surrounding spin.
+
+
+## Native operations
+
+Here are the operators defined in the virtual NV-center qubits, together with their commands.
+
+- Direct initialisation is the NV electron spin only, can be performed anytime.
+$$\mathtt{Init_0}$$
+- Direct measurement is the NV electron spin only, can be performed anytime, and is projective measurement in the computational basis.
+$$\mathtt{M_0}$$
+- Single qubit gates are Pauli rotations that can be operated upon any qubit $q$.
+$$\mathtt{Rx_q[\theta]}, \mathtt{Ry_q[\theta]}, \mathtt{Rz_q[\theta]}$$
+- Two-qubit gates are conditional rotation between electron and nuclear spin $q>0$
+$$\mathtt{CRx_{0,q}[\theta]}, \mathtt{CRy_{0,q}[\theta]}$$
+where  $$\mathtt{CR\sigma[\theta]}=\|0\rangle\langle0\|\otimes R\sigma(\theta)+\|1\rangle\langle1\|\otimes R\sigma(-\theta)$$
+- Doing nothing; remember it will introduce passive noise
+$$\mathtt{Wait_q[\Delta t]}$$
+
+## Parameters and usage
+
+The following configuration takes inspiration from devices at the University of Delft: a virtual NV-center contains six qubits without considering the nitrogen spin. 
+
+- Time unit is **second (s)**
+- Frequency unit is **Hertz (Hz)**
+- 0 is the index of NV<sup>-</sup> electron spin
+
+The code below can be directly copied and executed. 
+```Mathematica
+Options[NVCenterDelft] = {
+   QubitNum -> 6
+   ,
+   (* T1 of each qubit *)
+   T1 -> <|0 -> 3600, 1 -> 60, 2 -> 60, 3 -> 60, 4 -> 60, 5 -> 60 |>
+   ,
+   (* T2 of each qubit; we assume dynamical decoupling is actively applied *)
+   T2 -> <|0 -> 1.5, 1 -> 10, 2 -> 10, 3 -> 10, 4 -> 9, 5 -> 9|>
+   ,
+   (* dipolar interaction among nuclear spins: cross-talk ZZ-coupling in order of a few Hz on passive noise *)
+   FreqWeakZZ -> 5
+   ,
+   (* direct single rotation on Nuclear spin is done via RF, put electron in state -1 leave out the Rx Ry on nuclear spins ideally. *)
+   FreqSingleXY -> <|0 -> 15*10^6, 1 -> 500 , 2 -> 500, 3 -> 500,  4 -> 500, 5 -> 500|>
+   ,
+   (* usually done virtually *)
+   FreqSingleZ -> <|0 -> 32*10^6, 1 -> 400*10^3, 2 -> 400*10^3, 3 -> 400*10^3, 4 -> 400*10^3, 5 -> 400*10^3|>
+   ,
+   (* Frequency of CRot gate, conditional rotation done via dynamical decoupling or dd+RF. The gate is conditioned on electron spin state *)
+   FreqCRot -> <|1 -> 1.5*10^3, 2 -> 2.8*10^3, 3 -> 0.8*10^3, 4 -> 2*10^3 , 5 -> 2*10^3|>
+   ,
+   (* Fidelity of CRot gate  *)
+   FidCRot -> <|1 -> 0.98, 2 -> 0.98, 3 -> 0.98, 4 -> 0.98 , 5 -> 0.98|>
+   ,
+   (* fidelity of x- and y- rotations on each qubit *)
+   FidSingleXY -> <| 0 -> 0.9995, 1 -> 0.995, 2 -> 0.995, 3 -> 0.99, 4 -> 0.99, 5 -> 0.99 |>
+   ,
+   (* fidelity of z- rotations on each qubit *)
+   FidSingleZ ->  <| 0 -> 0.9999, 1 -> 0.9999, 2 -> 0.99999, 3 -> 0.9999, 4 -> 0.999, 6 -> 0.99 |>
+   ,
+   (* Error ratio of 1-qubit depolarising:dephasing of x- and y-rotations  *)
+   EFSingleXY -> {0.75, 0.25}
+   ,
+   (* Error ratio of 2-qubit depolarising:dephasing of CRot gate *)
+   EFCRot -> {0.9, 0.1}
+   ,
+   (* initialization fidelity on the electron spin *)
+   FidInit -> 0.999
+   ,
+   (* initialization duration on the electron spin *)
+   DurInit -> 2*10^-3
+   ,
+   (* measurement fidelity on the electron spin *)
+   FidMeas -> 0.946
+   ,
+   (* measurement duration on the electron spin *)
+   DurMeas -> 2*10^-5
+   };
+```
+
+In practice, dynamical decoupling is constantly applied to passive qubits to mitigate unwanted interaction. For instance, let ``circuit`` be a circuit comprises native operations. The following command obtain noisy version of running ``circuit`` on the virtual NV-center defined above.
+
+```Mathematica
+noisycircscheduled = InsertCircuitNoise[Serialize @ circuit, NVCenterDelft[], ReplaceAliases -> True];
+noisycirc = Extractcircuit @ noisycircscheduled;
+ApplyCircuit[rho, noisycirc]
+```
+First, variable ``noisycircscheduled`` contains noise-decorated ``circuit`` together with its schedule.
+Command ``Serialize @ circuit`` imposes serial implementation, 
+turning every element into a set, i.e., maps a set {a,b,c,...} to {{a},{b},{c}...}. 
+Therefore, passive noise becomes more prevalent; however, given that dynamical decoupling is assumed, 
+the coherence values (T1 and T2) supposed to be high with this implementation.
+Note that, option ``ReplaceAliases`` replaces gate aliases/custom gates into standard **QuESTlink** operations:
+for instance ``Init`` gate here is defined as an amplitude damping.
+Variable ``noisycirc`` contains noise-decorated ``circuit`` that is ready for simulation. 
+Second, the command ``ExtractCircuit[]`` basically removes the schedule information.
+Finally, command ``ApplyCircuit`` operates ``noisycirc`` upon the density matrix ``rho``. 

NeutralAtom/README.md

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+<div align="center">
+ <img src="../supplement/web/rydberg.png" width="150" alt="Alt text">
+</div>
+
+# Neutral atoms
+
+There is currently one virtual neutral atom device, namely Rydberg atom device that is inspired by devices in the University of Strathclyde and the University of Harvard. This device is instantiated with the command ``RydbergHub[]``.
+
+**Table of contents**
+1. [Characteristics](#characteristics)
+2. [Native operations](#native-operations)
+3. [Parameters and usage](#parameters-and-usage)
+
+## Characteristics
+
+
+Rydberg atoms/qubits are arranged inside a vacuum chamber. The atoms' configuration can be arbitrary for 2D and 3D geometries. Every atom is identical; they have the same noise characteristics and blockade radius.  Qubits connectivity is fully connected, as multi-qubit gates operations can be done to any set of atoms as long as they lie within their overlapping radii. The user needs to reconfigure the atoms in order to fulfil the requirement; this is achieved by swapping and shifting the locations of the atoms.
+
+Since atoms configuration is important, we provide a visualisation function ``PlotAtoms[]`` that will show the register/atoms configuration. 
+
+The following example generates a Rydberg device ``dev`` and plots its configuration. 
+
+```Mathematica
+dev = RydbergHub[]
+PlotAtoms[dev]
+```
+ <img src="../supplement/web/na1.png" width="250" alt="Neutral atom default">
+
+``PlotAtoms`` has options &mdash; with their default values &mdash; ``ShowBlockade->{}`` and ``ShowLossAtoms->False``; the first option shows the blockade radii of a set of atoms (empty by default) and the second option will show the last location of atoms that are lost to the environment (False by default). In addition, you can input the options from graphics as well to modify the visualisation style. 
+
+For instance, the following commands perform a circuit composing shifting location of atoms 5 and 7, followed by measurement on them.  For instance, in this device, the atoms are lost to the environment with a high chance after measurement. Then, we plot the configuration of the register afterwards.
+```Mathematica
+circuit = {Subscript[ShiftLoc, 5, 7][{1, 0, 0}], Subscript[M,5], Subscript[M,7]}
+InsertCircuitNoise[circuit, dev];
+PlotAtoms[dev, ShowBlockade->{0,4}, ShowLossAtoms->True, LabelStyle->"Section", BaseStyle->Directive[14, FontFamily->"Times"]]
+```
+ <img src="../supplement/web/na2.png" width="300" alt="Neutral atom default">
+
+In the ``PlotAtoms[]`` command, option ``ShowBlockade->{0,4}`` shows blockade radii of atoms 0 and 4 which are overlapping, option ``ShowLossAtoms->True`` displays the last locations of atoms 5 and 7 before lost to the environment, indicated with grey colours, and the rest of options change style of the plots, i.e., font styles.
+
+
+## Native operations
+
+Below are the operators defined in the virtual Rydberg atom qubits, together with their commands.
+
+- Initialisation can be done on any atom $q$, at anytime
+$$\mathtt{Init_q}$$
+- Measurement in the computation basis can be done anytime on any atom $q$; this process induces the atom lost to the environment.
+$$\mathtt{M_q}$$
+- Single-qubit gates comprise Pauli rotations, (frequently used) Hadamard, and arbitrary drive (single rotation ``SRot``)
+$$\mathtt{Rx_q[\theta], Ry_q[\theta],Rz_q[\theta],H_q,SRot_q[\Phi, \Delta, dt]}$$,
+where given that  $\tilde\Omega=\sqrt{\Omega^2+\Delta^2}$, and $\Omega$ indicates the Rabi frequency,
+
+$$\mathtt{SRot[\Phi,\Delta,dt]}=\begin{pmatrix}\cos(\frac{\tilde\Omega t}{2})-i \frac{\Delta}{\tilde\Omega}\sin(\frac{\tilde\Omega t}{2})&-i\frac{\Omega}{\tilde\Omega}\sin(\frac{\tilde\Omega t}{2})e^{i\phi}  \\\\ -i\frac{\Omega}{\tilde\Omega}\sin(\frac{\tilde\Omega t}{2})e^{-i\phi} &\cos(\frac{\tilde\Omega t}{2}) +i\frac{\Delta}{\tilde\Omega}\sin(\frac{\tilde\Omega t}{2})\end{pmatrix}$$
+
+- Two-qubit controlled-Z, given that atoms $\mathtt{q1}$ and $\mathtt{q2}$ lie within their overlapping radii.
+$$\mathtt{CZ_{q1,q2}}$$
+- Multi-qubit gates on atoms multiple-controlled Z, given that atoms $\mathtt{q1,q2,q3,...,qt}$ lie within their overlapping radii.
+$$\mathtt{C_{q1,q2,q3,...}}[Z_{qt}]$$ 
+- Multi-qubit gates on atoms one-control multiple-Z, given that atoms $\mathtt{q1,q2,q3,...,qc}$ lie within their overlapping radii.
+$$\mathtt{C_{qc}}[Z_{q1,q2,q3,...}]$$ 
+- Register reconfiguration: swap the location of atoms $\mathtt{q1}$ and $\mathtt{q2}$
+$$\mathtt{SWAPLoc_{q1,q2}}$$
+- Register reconfiguration: shift location of atoms $\mathtt{q1,q2,q3,...}$ by a vector $v$
+$$\mathtt{ShiftLoc_{q1,q2,q3,...}}[v]$$
+- Doing nothing; remember it will introduce passive noise
+$$\mathtt{Wait_q[\Delta t]}$$
+
+## Parameters and usage
+
+The following configuration takes inspiration from a device at Harvard University: seven-qubit Rydberg atom device based on this [reference](https://doi.org/10.1038/s41586-022-04592-6), in the Steane code stabiliser measurement experiment.
+
+- Time unit is **microseconds** ($\mu s$)
+- Frequency unit is **megahertz (MHz)**
+- Length/distance unit is **micrometer** ($\mu m$) 
+
+The code below can be directly copied and executed. 
+
+```Mathematica
+Options[RydbergHub] = {
+   (* The total number of atoms/qubit*)
+   QubitNum -> 7
+   ,
+   (*Physical location on each qubit described with a 2D- or 3D-vector*)
+   AtomLocations -> <|6 -> {0, 1}, 5-> {1, 1}, 2 -> {2, 1}, 1 -> {4, 1}, 4 -> {2, 0}, 0 -> {4, 0}, 3 -> {5, 0}|>
+   ,
+   (* It's presumed that T2* has been echoed out to T2 *)
+   T2 -> 1.5*10^6
+   ,
+   (* The lifetime of vacuum chamber, where it affects the T1 time, T1=Tvac/N, where N=number of atoms  *)
+   VacLifeTime -> 48*10^6
+   ,
+   (* Rabi frequency of the atoms. We assume the duration of multi-qubit gates is as long as 4$\pi$ pulse of single-qubit gates *)
+   RabiFreq -> 1
+   ,
+   (* Asymmetric bit-flip error probability; the error is acquired during single qubit operation *)
+   ProbBFRot -> <|10 -> 0.001, 01 -> 0.03|>
+   ,
+   (* This will be the unit of the lattice and coordinates *)
+   UnitLattice -> 3
+   ,
+   (* blockade radius of each atom *)
+   BlockadeRadius -> 1
+   ,
+   (* Leakage probability during initialisation process *)
+   ProbLeakInit -> 0.001
+   ,
+   (* Leakage probability during initialisation process *)
+   DurInit -> 5*10^5
+   ,
+   (* Duration of moving atoms; we assume SWAPLoc and ShiftLoc take this amount of time *)
+   DurMove -> 100
+   ,
+   (* The factor that estimates accelerated dephasing due to moving the atoms. Ideally, it is calculated from the distance and speed. *)
+   HeatFactor -> 10
+   ,
+   (* Fidelity of qubit readout *)
+   FidMeas -> 0.975
+   ,
+   (* Duration of readout *)
+   DurMeas -> 10
+   ,
+   (* The increasing probability of atom loss on each measurement. The value keeps increasing until being initialised *)
+   ProbLossMeas -> 0.0001
+   ,
+   (* leak probability of implementing multi-qubit gates *)
+   ProbLeakCZ -> <|01 -> 0.01, 11 -> 0.0001|>
+   }; 
+```
+To allow efficient gates implementation that also reflects to what happen in practice, we provide gates arrangement command
+``CircRydbergHub[]`` with option to implement parallel (``CircRydbergHub[circuit, device, Parallel -> True]``) or serial implementation.
+(``CircRydbergHub[circuit, device, Parallel -> False]``). 
+
+Parallelisation in neutral atoms is atomic configuration-dependent, where concurrent operations can be performed if
+the corresponding atoms operated upon do not have their blockade radii overlapped.
+This means, if two atoms have their blockade radii overlapping, then parallel gates cannot be performed upon them. 
+On the other hand, serial implementation imposing gates to be performed one at a time, but initialisations are done simultaneously.
+This reflects the initialisation process in practice comprises loading and rearranging the atoms. 
+
+Here is an example of implementing a ``circuit`` in parallel fashion, on a virtual netural atoms. Note that ``circuit`` contains legitimate operations
+taking into account requirement on the atomic configurations, e.g., two-qubit gates are legit to atoms within their overlapping blockade radii.
+
+```Mathematica
+mydev = RydbergHub[];
+noisycircscheduled = InsertCircuitNoise[CircRydbergHub[circuit, mydev, Parallel -> True], mydev, ReplaceAliases -> True];
+noisycirc = ExtractCircuit @ noisycircscheduled;
+ApplyCircuit[rho, noisycirc];
+```
+First, ``mydev`` contains an instance of ``RydbergHub[]``.
+Second, ``noisycircscheduled`` contains noise-decorated of parallel implementation of ``circuit``. 
+Note that, ``InsertCircuitNoise`` command modifies ``mydev``; for instance, the arrangement of atoms, loss probabilities
+due to measurements are updated and stored in ``mydev``.
+Parallel arrangement is taken care by command ``CircRydberghub[Parallel -> True]``,
+which takes into account register reconfiguration operations in ``circuit``.
+Third, ``noisycirc`` contains the noise-decorated ``circuit`` without schedule information. 
+Finally, ``ApplyCircuit`` command operates the noisy circuit ``noisycirc`` to a density of states ``rho``.