diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..1ed16b0 --- /dev/null +++ b/.gitignore @@ -0,0 +1,6 @@ +quest_link* +gates_synthesis +others +sdbells +*.gif + diff --git a/LICENSE.txt b/LICENSE.txt new file mode 100644 index 0000000..1d938e9 --- /dev/null +++ b/LICENSE.txt @@ -0,0 +1,11 @@ +# 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. diff --git a/NVCenter/NVCenterDelft.nb b/NVCenter/NVCenterDelft.nb new file mode 100644 index 0000000..7bc4e49 --- /dev/null +++ b/NVCenter/NVCenterDelft.nb @@ -0,0 +1,3085 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 13.1' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 135069, 3077] +NotebookOptionsPosition[ 125931, 2940] +NotebookOutlinePosition[ 126677, 2965] +CellTagsIndexPosition[ 126634, 2962] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ 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+ Alt text +
+ +# 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- electron spin is sitting in the center, surrounded by the nuclear spins 13C — and may also involve 14Nq 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. + + +
+ Alt text +
+ +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- 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``. diff --git a/NeutralAtom/README.md b/NeutralAtom/README.md new file mode 100644 index 0000000..54f32e1 --- /dev/null +++ b/NeutralAtom/README.md @@ -0,0 +1,156 @@ +
+ Alt text +
+ +# 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] +``` + Neutral atom default + +``PlotAtoms`` has options — with their default values — ``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"]] +``` + 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``. \ No newline at end of file diff --git a/NeutralAtom/RydbergHub.nb b/NeutralAtom/RydbergHub.nb new file mode 100644 index 0000000..9d38b0d --- /dev/null +++ b/NeutralAtom/RydbergHub.nb @@ -0,0 +1,8961 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 13.1' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 446040, 8953] +NotebookOptionsPosition[ 427741, 8698] +NotebookOutlinePosition[ 428454, 8723] +CellTagsIndexPosition[ 428411, 8720] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell["Neutral atoms/Rydberg qubits", "Title", + 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+ Alt text +
+ +# Virtual Quantum Devices + +**VQD** is a **Mathematica** package that contains a collection of virtual quantum devices that are based on or inspired by actual quantum devices. **VQD** is built atop [**QuESTlink**](https://github.com/QTechTheory/QuESTlink), a Mathematica extension of [**QuEST**](https://github.com/QuEST-Kit/QuEST): a powerful open-source emulator of quantum computers developed in **C**. + **QuESTlink** combines **Mathematica**’s powerful symbolic operations with **QuEST**’s high-performance backend, enabling virtual devices to be highly configurable through an intuitive interface, and able to leverage powerful visualisation facilities, without compromising performance! + + +[![Mathematica version](https://img.shields.io/badge/Mathematica-v12-brightgreen)](https://www.wolfram.com/mathematica/) [![Mathematica version](https://img.shields.io/badge/Mathematica-v13-brightgreen)](https://www.wolfram.com/mathematica/) [![MIT license](https://img.shields.io/badge/license-MIT-lightgrey.svg)](LICENCE.txt) +[![Depends on](https://img.shields.io/badge/Depends%20on-QuESTlink-blue)](https://github.com/QTechTheory/QuESTlink) [![Backend](https://img.shields.io/badge/Backend-QuEST-blue)](https://github.com/QuEST-Kit/QuEST) + + +This package is developed by [Cica Gustiani](https://github.com/cicacica) within the University of Oxford, in [Simon Benjamin](https://qtechtheory.org/) group. + +[![Email](https://img.shields.io/badge/email-cicacica13@pm.me-red.svg)](mailto:cicacica13@pm.me) +[![Paper](https://img.shields.io/badge/Paper-Quantum%202025-blue?style=flat-square&logo=readthedocs)](https://doi.org/10.22331/q-2025-02-25-1642) + + + +## Our goal + +We aim to facilitate the creation of virtual quantum devices with ease. We have developed an environment in which users can readily input parameters commonly mentioned in experimental papers such as **T1, T2, T2*, qubit frequency, coupling strength, blockade radius, leakage probability, gate fidelities, initialisation fidelities**, and so forth. + +We've designed this to function as a user-friendly, plug-and-play platform. This empowers users to test their concepts and estimate their performance on actual devices, even across different noise scales. Not only useful for testing, this platform can also assist experimentalists in making estimates of certain parameters. All of these factors contribute to making quantum exploration more accessible. + + +## Five families of virtual quantum devices + +Currently, we provide five types of quantum devices. Navigate to the corresponding folder in which a short guide is provided for each device. + +Our current devices includes: +1. Ion traps +2. Nitrogen-vacancy-center (NV-center) +3. Neutral atoms +4. Semiconductor spin qubits +5. Superconducting qubits. + + +Each type of quantum device is unique and is based on or inspired by actual devices. For more in-depth information on the architecture and used error models, refer to our [**paper**](https://doi.org/10.22331/q-2025-02-25-1642). + +## Quickstart + + +Our virtual device is designed to reflect a close approximation to the physical reality. It achieves this by offering access solely to native operations and parameters that are physically feasible and tailored specifically to the quantum device in question. Therefore, users will find it beneficial to have some understanding of the devices they're interested in. But don't worry if you're not there yet — you can get up to speed quickly by diving into our [**paper**](https://doi.org/10.22331/q-2025-02-25-1642), or follow the steps below. + + +### **1. Navigate to the Desired Folder** + +We categorise devices into five separate folders, that correspond to the family of quantum devices. Select the folder of your interest: +- `TrappedIon` - For ion trap devices +- `NVCenter` - For NV-center devices +- `NeutralAtom` - For neutral atom devices +- `SemiconductorSpin` - For semiconductor spin qubits in quantum dots devices +- `SuperconductingQubit` - For superconducting qubit devices + +### **2. Review the Quick Documentation** + +After you've selected and entered the appropriate folder, take a moment to read the quick documentation provided. This brief overview will introduce you to the function that generates the corresponding virtual device. + +### **3. Run the Example Notebooks** + +Inside every folder, you'll find an example notebook. These notebooks serve to demonstrate the functionality of each respective device. We recommend running these notebooks to get a hands-on understanding of how the devices operate. + +### **4. Compare the Results** + +Once you've run the notebooks, you should have generated outcomes. To verify the accuracy of your results, compare your outcomes with those depicted in the corresponding PDF file, which is included in each folder. + +By following these steps, you'll get a feeling of how various quantum devices operate, as each device type has unique capabilities and requirements. + + +## General usage + +The **VQD** functionalities are neatly packaged within the `vqd.wl` file, where you can instantiate virtual quantum devices. As it is built atop **QuESTlink**, one must first load the **QuESTlink** package. + +Here's how you can do this in Mathematica: + +```Mathematica +Import["https://qtechtheory.org/questlink.m"] +CreateDownloadedQuESTEnv[]; +``` + +The above commands perform two tasks. The first imports the **QuESTlink** package and the second downloads a *link binary* named `quest_link`. This link binary contains the protocols for linking the **QuEST** code to your Mathematica environment. + +If you wish to leverage parallelisation features such as multi-threading or GPU processing, you'll need to perform a manual compilation on the link binary. You can find step-by-step instructions in the [QuESTlink documentation](https://github.com/QTechTheory/QuESTlink/tree/main/Doc). + +Finally, load the **VQD** package, + +```Mathematica +Get["vqd.wl"] +``` +and access the API of **VQD** +```Mathematica +?VQD`* +``` + + +### Virtual device instantiation and customisation + +A virtual device in our system holds descriptions of various physical quantum devices, encapsulating the characteristic of devices like architecture, legitimate operations, and every error that comes with every operation. Our noise descriptions generally have complete-positive map forms. + +To create these device descriptions, we provide functions that align with specific quantum device types + +- ``TrappedIonOxford[]`` for the multi-node ion traps based on the University of Oxford devices. +- ``NVCenterDelft[]`` for the NV-center diamonds based on the University of Delft devices. +- ``RydbergHub[]`` for the Rydberg neutral atoms based on the University of Strathclyde devices. +- ``SiliconDelft[]`` for the Si/SiGe spin qubits based on the University of Delft devices. +- ``SuperconductingHub[]`` for the superconducting transmon qubits based on the University of Oxford devices. + + +These functions do not come with default parameters. Users must set these parameters, reflecting the fundamental characteristics of their devices. Here is an example of how to set parameters for the `TrappedIonOxford` function: + +```Mathematica +Options[TrappedIonOxford] = +{ +QubitNum -> 6 +, +T1 -> <|0 -> 3600, 1 -> 60, 2 -> 60, 3 -> 60, 4 -> 60, 5 -> 60 |> +, +T2 -> <|0 -> 1.5, 1 -> 10, 2 -> 10, 3 -> 10, 4 -> 9, 5 -> 9|> +, +FreqWeakZZ -> 5 +, +FreqSingleXY -> <|0 -> 15*10^6, 1 -> 500 , 2 -> 500, 3 -> 500, 4 -> 500, 5 -> 500|> + +... (and so on) + +} +``` +In the corresponding folder, we offer a set of examples on how to configure these parameters, as well as the range of numbers that are typically based on actual, approximately realistic, devices. These examples provide a practical view of realistic parameters that you can easily modify according to your needs or your devices. + +The following command instantiates a virtual ion trap with the default parameters set above. + +```Mathematica +TrappedIonOxford[] +``` +Overriding default parameters devices can be done on the fly; for example +```Mathematica +TrappedIonOxford[FreqWeakZZ -> 10] +``` +which overrides the default parameter ``FreqWeakZZ``. + + + + +## Build your own virtual device + +Want to build a virtual device from scratch? follow the QuESTlink guide [here](https://github.com/QTechTheory/QuESTlink/blob/main/Doc/guide_creating_device_spec.pdf) to create your own device. + + +## Acknowledgements + +The development of this package would not have been possible without the significant contributions and collaborations of many individuals. + +- **Scientific Contributors:** +Mohammed Alghadeer, Mohamed Abobeih, Simon Benjamin, Alessandro Ciani, Shuxiang Cao, Andrew Daley, Joseph Goodwin, Fernando Gonzalez-Zalba, Tomas Kozlej, Peter Leek, David Nadlinger, Natalie Pearson, Gerard Pelergi, Cody Poole, Jonathan Pritchard, Mark Saffman, Jason Smith, and Joanna Zajac, for designing error models and describing their quantum devices as well as the processes happening. + +- **Software Contributors:** +Tyson Jones, for providing essential support on the QuESTlink part. + +✨THANK YOU✨ + diff --git a/SemiconductorSpin/README.md b/SemiconductorSpin/README.md new file mode 100644 index 0000000..283e339 --- /dev/null +++ b/SemiconductorSpin/README.md @@ -0,0 +1,140 @@ +
+ quantum dots +
+ +# Semiconductor spin qubits + +There is currently one virtual spin qubit in semiconductor quantum dots device, where quantum dots are defined in the 28Si quantum well of the 28Si/SiGe heterostructure. This device is based on a quantum device in the University of Delft and is instantiated with the command ``SiliconDelft[]``. + +**Table of contents** +1. [Characteristics](#characteristics) +2. [Native operations](#native-operations) +3. [Parameters and usage](#parameters-and-usage) + + +## Characteristics + +The device has 1D linear architecture with nearest neighbour connectivity. There is favoured direction on the two-qubit gates implementation and direct measurement is only possible on the pair edge qubits, which is parity measurement. + +For instance, the architecture below is based on a silicon device in Delft [here](https://doi.org/10.1038/s41586-022-05117-x), and consists of six qubits. + +
+ quantum dots +
+ +The arrows in the architecture denote the connectivity of CNOT gates, with each arrow directed towards the target qubits. The dashed lines, on the other hand, represent the symmetric connectivity of the controlled-phase gates. The regions marked in yellow perform the function of parity measurement, specifically, they measure the parity between qubits 0,1 and 4,5. This architecture can be straightforwardly extended to incorporate any even number of qubits. With such a mechanism, initialisations are constrained to start from the edge qubits. + +The parity measurement operator distinguishes even ($\|01\rangle,\|10\rangle$) and odd outcomes ($\|00\rangle,\|11\rangle$) followed with fast decay of state $\|01\rangle$ into $\|10\rangle$. We describe such parity measurement with the following operations: +$$\mathcal{M}=\mathcal{K}(M)$$ +where $M$ is the parity measurement projector and $\mathcal{K}$ is a CPTP map describing the state decay, +$$M=\\{ (\|01\rangle\langle01\|+\|10\rangle\langle10\|,\mathtt{0}),(\|00\rangle\langle00\|+\|11\rangle\langle11\|,\mathtt{1}) \\}$$ +$$\mathcal{K}=\\{\|00\rangle\langle00\|,\|11\rangle\langle11\|,\|10\rangle\langle10\|,\|10\rangle\langle01\|\\}$$ + +## Native operations + +Below are the operators defined in the virtual silicon spin qubits, together with their commands. + +- Initialisation must be done from edge qubits at any time. For example, in the case of the six-qubit device shown above, here are the legitimate initialisation commands. +$$\mathtt{Init_{0,1}, Init_{0,1,2}, Init_{4,5}, Init_{3,4,5}}$$ +- Parity measurement can be done only on the edge qubits. For example, in the case of the six-qubit device shown above, legitimate parity measurements are shown below. +$$\mathtt{MeasP_{0,1},MeasP_{4,5}}$$ +- Single-qubit gates comprise Pauli rotations. +$$\mathtt{Rx_q[\theta], Ry_q[\theta],Rz_q[\theta]}$$ +- The controlled-Z and controlled-phase gates can be operated upon nearest-neighbour qubits; here $\mathtt{p}$ and $\mathtt{q}$ are nearest neighbours +$$\mathtt{C_{p}[Z_q], C_{p}[Ph_q[\theta]]}$$ +- The CNOT gates can be operated upon nearest-neighbour qubits with certain directions (see **Characteristics** section above). +$$\mathtt{C_p[X_q]}$$ +- 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 the University of Delft: six-qubit silicon device based on this [reference](https://doi.org/10.1038/s41586-022-05117-x). Device architecture is pictured above (see **Characteristics**). + + +- Time unit is **microseconds** ($\mu s$) +- Frequency unit is **megahertz (MHz)** + + +The code below can be directly copied and executed. +```Mathematica +Options[SiliconDelft] = + { + (* The number of qubits *) + QubitNum -> 6 + , + (* T1 of every qubit *) + T1 -> 10^4 + , + (* We assume T2* is echoed out to T2 *) + T2 -> <|0 -> 14, 1 -> 21.1, 2 -> 40.1, 3 -> 37.2, 4 -> 44.7, 5 -> 26.7|> + , + (* Qubit frequency of each qubit *) + QubitFreq -> <|0 -> 15.62*10^3, 1 -> 15.88*10^3, 2 -> 16.3*10^3, 3 -> 16.1*10^3, 4 -> 15.9*10^3, 5 -> 15.69*10^3|> + , + (* Rabi frequency of single rotations on each qubit *) + RabiFreq -> <|0 -> 5, 1 -> 5, 2 -> 5, 3 -> 5, 4 -> 5, 5 -> 5|> + , + (* Set the noise form of off-resonant Rabi oscillation. This takes RabiFreq information to produce the noise.*) + OffResonantRabi -> True + , + (* Set the standard depolarising and dephasing passive noise using T1 and T2 *) + StdPassiveNoise -> True + , + (* Fidelities of X- and Y- rotations by random benchmarking *) + FidSingleXY -> <|0 -> 0.9977, 1 -> 0.9987, 2 -> 0.9996, 3 -> 0.9988, 4 -> 0.9991, 5 -> 0.9989|> + , + (* Error fraction/ratio {depolarising, dephasing} sum is either one or zero (off) *) + EFSingleXY -> {0, 1} + , + (* The rabi Frequency and fidelities of controlled-Z(C[Z]), nearest-neighbors. Keys are the smallest qubit number. This applies to controlled-Ph gates *) + FreqCZ -> <|0 -> 12.1, 1 -> 11.1, 2 -> 6.6, 3 -> 9.8, 4 -> 5.4|> + , + (* Fidelity of controlled-Z, the numbers below indicate the lower number of qubits *) + FidCZ -> <|0 -> 0.9374945614729504`, 1 -> 0.9339691831083574`, 2 -> 0.9286379436705322`, 3 -> 0.9967228426036524`, 4 -> 0.9793017377403548`|> + , + (* Fidelity of CROT(CNOT) rotation *) + FidCRot -> 0.9988 + , + (* Rabi frequency of CROT(CNOT), obtained by conditional microwave drive *) + FreqCRot -> 5 + , + (* Error fraction/ratio {depolarising, dephasing} of controled- Ph(Pi) or controlled-Z. The error for other angles is scaled from Pi. *) + EFCZ -> {0, 1} + , + (* Crosstalks error (C-Rz[ex])on the passive qubits when applying CZ gates; square matrix with dims nqubit-2 *) + ExchangeRotOn -> {{0, 0.023, 0.018 , 0.03, 0.04}, {0.05 , 0, 0.03, 0.03, 0.04}, {0.05, 0.03 , 0, 0.07, 0.042}, {0.038 , 0.03 , 0.031, 0 , 0.25}, {0.033, 0.03 , 0.02, 0.03, 0}} + , + (* Crosstalks error (C-Rz[ex])on the passive qubits when no CZ gates applied; the qubits below indicate the controlled-qubit *) + ExchangeRotOff -> <|0 -> 0.039, 1 -> 0.015 , 2 -> 0.03 , 3 -> 0.02, 4 -> 0.028|> + , + (* Parity readout fidelity/charge readout fidelity between Q0,Q1 or Q4,Q5 *) + FidRead -> 0.9997 + , + (*Parity readout duration *) + DurRead -> 10 + }; +``` + +It is common to apply gates in serial manner in practice, which adds an asumption that +some dynamical decoupling sequences are constantly applied to passive qubits. +The following command obtain the noisy version of ``circuit`` running on a virtual silicon spin qubit, +e.g., virtual device with configuration above. + +```Mathematica +noisycircscheduled = InsertCircuitNoise[Serialize @ circuit, SiliconDelft[], ReplaceAliases -> True]; +noisycirc = ExtractCircuit @ noisycircscheduled; +ApplyCircuit[rho, noisycirc]; +``` +First, variable ``noisycircscheduled`` contains noise-decorated circuit together with its schedule. +Command ``Serialize @ circuit`` imposes simple 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 will be replaced with a +series of operations involving parity measurements. +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``. + diff --git a/SemiconductorSpin/SiliconDelft.nb b/SemiconductorSpin/SiliconDelft.nb new file mode 100644 index 0000000..7e05717 --- /dev/null +++ b/SemiconductorSpin/SiliconDelft.nb @@ -0,0 +1,22409 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 13.0' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 1320136, 22401] +NotebookOptionsPosition[ 1312058, 22273] +NotebookOutlinePosition[ 1312740, 22297] +CellTagsIndexPosition[ 1312697, 22294] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell["Silicon qubits Delft", 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We assume the T2* is echoed out to T2\n\nThe standard passivenoise \ +(2) can be eliminated by setting", + StyleBox[" StdPassiveNoise \[Rule] False", + FontWeight->"Bold"], + ". The Cross-talk (1) can be set off by setting ", + StyleBox["ExchangeRotOff \[Rule] False", + FontWeight->"Bold"] +}], "Text", + InitializationCell->True, + CellChangeTimes->{{3.863702948818843*^9, 3.863702998776547*^9}, { + 3.863728630239959*^9, 3.863728632645852*^9}, {3.866618329845446*^9, + 3.866618497698738*^9}, {3.866618689914864*^9, 3.866618723446488*^9}, { + 3.866618840046075*^9, 3.866618947248354*^9}, {3.866619078477621*^9, + 3.866619087011146*^9}, {3.8666192112509527`*^9, 3.8666192706948338`*^9}, { + 3.866619330775076*^9, 3.866619343814622*^9}, {3.866619778050337*^9, + 3.866619839594288*^9}, {3.8666198790568857`*^9, 3.8666198873346777`*^9}, { + 3.866621079044393*^9, 3.866621094134581*^9}, {3.866622161062787*^9, + 3.8666221722322197`*^9}, {3.866631873960064*^9, 3.866631904130617*^9}, { + 3.8743126018065023`*^9, 3.8743126185447617`*^9}, {3.895568736025693*^9, + 3.8955687566585913`*^9}}, + Background->RGBColor[ + 0.87, 0.94, 1],ExpressionUUID->"91c81d20-c0b6-406f-9460-d4f2fb40ff37"], + +Cell[BoxData[{ + RowBox[{"InsertCircuitNoise", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + SubscriptBox["Wait", "0"], "[", "\[Pi]", "]"}], "}"}], ",", + RowBox[{"SiliconDelft", "[", "]"}]}], "]"}], "\[IndentingNewLine]", + RowBox[{"DrawCircuit", "[", "%", "]"}]}], "Input", + CellChangeTimes->{{3.868554708926196*^9, 3.868554742730074*^9}, { + 3.8685547769233437`*^9, 3.8685547930144463`*^9}, {3.868560283503166*^9, + 3.868560284741558*^9}, {3.868694292579809*^9, 3.868694309722279*^9}, + 3.8737303834493923`*^9, {3.887523406334545*^9, 3.887523408207644*^9}}, + CellLabel-> + "In[106]:=",ExpressionUUID->"bfdecc4a-3d95-4979-b2c5-a96358c26d0d"] +}, Open ]], + +Cell[CellGroupData[{ + +Cell["Single qubit gates", "Subsection", + CellChangeTimes->{{3.86370306345203*^9, 3.863703075147481*^9}, { + 3.8637297595242434`*^9, 3.863729766939557*^9}, {3.8666190523425503`*^9, + 3.866619055838517*^9}},ExpressionUUID->"e4995822-6d3f-4592-8284-\ +de2a010712f4"], + +Cell[TextData[{ + "Single qubit gates: x- and y- rotations have the same error \nThe noise \ +forms:\n1) Off-resonant Rabi Oscillation. This takes RabiFreq input and \ +applied when", + StyleBox[" OffResonantRabi\[Rule]True", + FontWeight->"Bold"], + ".\n2) Standard Dephasing and Depolarising noise. This takes ", + StyleBox["FidSingleXY", + FontWeight->"Bold"], + " and ", + StyleBox["EFSingleXY", + FontWeight->"Bold"], + " inputs to estimate the error parameters. Set ", + StyleBox["EFSingleXY\[Rule]{0,0}", + FontWeight->"Bold"], + " to set this off." +}], "Text", + CellChangeTimes->{{3.863702948818843*^9, 3.863702998776547*^9}, { + 3.863728630239959*^9, 3.863728632645852*^9}, {3.866618329845446*^9, + 3.866618497698738*^9}, {3.866618689914864*^9, 3.866618723446488*^9}, { + 3.866618840046075*^9, 3.866618947248354*^9}, {3.866619903594878*^9, + 3.8666199041921453`*^9}, {3.8668806639102163`*^9, 3.866880678248349*^9}, + 3.867141591800489*^9, {3.868553776753438*^9, 3.868553777382896*^9}, { + 3.895568795814522*^9, 3.895568813484728*^9}}, + Background->RGBColor[ + 0.87, 0.94, 1],ExpressionUUID->"77139c97-1303-4462-aef5-a336edc8c5f0"], + +Cell[BoxData[{ + RowBox[{"InsertCircuitNoise", "[", + RowBox[{ + RowBox[{"CircSiliconDelft", "[", + RowBox[{ + RowBox[{"{", + RowBox[{ + RowBox[{ + SubscriptBox["Rx", "0"], "[", + RowBox[{"\[Pi]", "/", "2"}], "]"}], ",", + RowBox[{ + SubscriptBox["Wait", "0"], "[", "1", "]"}]}], "}"}], ",", " ", + RowBox[{"Parallel", "->", "False"}]}], "]"}], ",", + RowBox[{"SiliconDelft", "[", + RowBox[{ + RowBox[{"StdPassiveNoise", "->", "True"}], ",", + RowBox[{"OffResonantRabi", "->", "True"}]}], "]"}]}], + "]"}], "\[IndentingNewLine]", + RowBox[{"DrawCircuit", "[", "%", "]"}]}], "Input", + CellChangeTimes->{{3.863700373553709*^9, 3.8637004053841553`*^9}, { + 3.8637027910241337`*^9, 3.863702836653534*^9}, {3.8637030394983397`*^9, + 3.863703042886256*^9}, {3.863703134219542*^9, 3.863703134821913*^9}, { + 3.863714286237688*^9, 3.863714343540049*^9}, {3.8637242288083067`*^9, + 3.863724267904917*^9}, 3.863724339932461*^9, {3.863725073189245*^9, + 3.8637250751033573`*^9}, {3.863725120276568*^9, 3.8637251218366737`*^9}, { + 3.863725166282064*^9, 3.863725186660061*^9}, {3.863725234381577*^9, + 3.863725255164744*^9}, {3.86372533912416*^9, 3.863725344870339*^9}, { + 3.863725392017466*^9, 3.8637253929121447`*^9}, {3.863725452172702*^9, + 3.863725452653985*^9}, {3.863725586850235*^9, 3.863725593285967*^9}, { + 3.863725772694718*^9, 3.8637257851725397`*^9}, 3.863725833235972*^9, { + 3.863725865527495*^9, 3.863725869533815*^9}, 3.863726460943598*^9, { + 3.863727256454788*^9, 3.863727258022772*^9}, {3.864809420523555*^9, + 3.86480942329453*^9}, {3.864964834800452*^9, 3.864964844149131*^9}, { + 3.8656791861998873`*^9, 3.865679186949088*^9}, {3.865896102554289*^9, + 3.8658961146183*^9}, 3.866618311688501*^9, {3.866619027769165*^9, + 3.866619045933983*^9}, {3.866620015496698*^9, 3.866620034957123*^9}, { + 3.866620320613103*^9, 3.866620343712743*^9}, {3.8666203858625097`*^9, + 3.866620398582757*^9}, 3.866620910587131*^9, {3.866621567177445*^9, + 3.866621579853125*^9}, {3.866622632879058*^9, 3.8666226392668047`*^9}, { + 3.866631987142173*^9, 3.8666320049024878`*^9}, {3.866633495050239*^9, + 3.866633495801289*^9}, {3.8668806058565283`*^9, 3.866880606615921*^9}, { + 3.8668806884908457`*^9, 3.866880688616033*^9}, {3.8668807626962423`*^9, + 3.866880797998846*^9}, {3.866891345140547*^9, 3.86689135105947*^9}, + 3.867386215330474*^9, {3.868554818976068*^9, 3.8685548364791527`*^9}, { + 3.868554886841674*^9, 3.868554890627323*^9}, {3.868555063993815*^9, + 3.868555064627152*^9}, {3.868555144043919*^9, 3.8685551755271893`*^9}, { + 3.868556942235899*^9, 3.8685569485370493`*^9}, {3.868558644815991*^9, + 3.8685586600776854`*^9}, {3.868561431276607*^9, 3.868561485190961*^9}, { + 3.868694379805399*^9, 3.868694390168824*^9}, {3.868694474055262*^9, + 3.8686944765037518`*^9}, {3.873797443238089*^9, 3.873797443677495*^9}, + 3.873797491680901*^9, {3.8738297599653873`*^9, 3.8738297658871117`*^9}, { + 3.873829817996234*^9, 3.8738298508003187`*^9}, {3.887691942114456*^9, + 3.887691944988179*^9}, 3.893925903554494*^9, 3.893928325679208*^9}, + CellLabel-> + "In[108]:=",ExpressionUUID->"c20a747f-e714-4920-9b47-871feb81cb78"], + +Cell[CellGroupData[{ + +Cell["Controlled - Z, Coltrolled-Phase", "Subsubsection", + CellChangeTimes->{{3.8714441188738003`*^9, 3.871444133039071*^9}, { + 3.874313789214643*^9, + 3.874313794471397*^9}},ExpressionUUID->"c5a89e96-51b9-459c-bc61-\ +745dad3e44bc"], + +Cell[TextData[{ + "The noisy forms:\n1) Standard 2-qubits dephasing and depolarising noise. \ +This takes information ", + StyleBox["FidCZ", + FontWeight->"Bold"], + " (fidelities) and ", + StyleBox["EFCZ", + FontWeight->"Bold"], + " (error fraction). 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+ Alt text +
+ +# Superconducting qubits + +There is currently one virtual superconducting qubit devices, which is superconducting transmon qubits connected with cpacitive coupling. This device is based on quantum device in the University of Oxford, which is instantiated by ``SupercondcutingHub[]``. + +**Table of contents** +1. [Characteristics](#characteristics) +2. [Native operations](#native-operations) +3. [Parameters and usage](#parameters-and-usage) + +## Characteristics + +Architecture of the device is entirely determined by the user, in particular, by setting up qubit frequencies and coupling strengths. Based on these user-defined settings, the program will generate the corresponding connectivity. + +The connectivity can be displayed by accessing key ``Connectivity``. For instance, the following command instantiates VQD and shows the connectivity. + +```Mathematica +dev = SuperconductingHub[]; +dev[Connectivity] +``` +The command above outputs the layout of the device architecture below +
+ Alt text +
+where nodes correspond to transmon qubits and edges indicate capacitive coupling between the qubits. The numbers displayed on the nodes represent the frequencies of the qubits, whereas those on the edges correspond to the coupling strength. All frequency values are expressed in MHz, and the edges are directed towards the higher qubit frequencies, which dictate the preferred direction, for a faster operation, of the cross resonance gate $\mathtt{ZX_{i,j}}$ — frequency of $\mathtt{Q_i}$ is higher than of $\mathtt{Q_j}$. + +In this model, gates application are modelled as perfect; primary contribution of noise during operations comes from passive noise and cross-talk. + +Typical device supports **full gates parallelisation**. + + +## Native operations + +The native operations of the virtual superconducting qubit are the following. + +- Initialisation must be done to the entire device; this prepare the qubits into their thermal state. +$$\mathtt{Init_{0,1,...,N-1}}$$ +- Measurement can be done anytime, which performs projective measurement in the computational basis. +$$\mathtt{M_q}$$ +- Single-qubit gates are Pauli rotations with angle $\theta\in[-\pi,\pi]$. +$$\mathtt{Rx_q[\theta]}, \mathtt{Ry_q[\theta]}, \mathtt{Rz_q[\theta]}$$ +- Two-qubit gate called siZZler (Stark-induced ZZ by level excursion). This gate is symmetric. +$$\mathtt{ZZ_{p,q}}:=Exp(-i\frac{\pi}{2}Z_p\otimes Z_q)$$ +- Cross-resonance gate. This gate has preference (frequency p > q) direction that is shown by the arrows in the layout. +$$\mathtt{ZX_{p,q}}:=Exp(-i\frac{\pi}{2}Z_p\otimes X_q)$$ +- Doing nothing; remember it will introduce passive noise +$$\mathtt{Wait_q[\Delta t]}$$ + +## Parameters + +The following configuration takes inspiration from a device at the University of Oxford. The code provided below can be directly copied and executed. + +- Time unit is **microseconds** ($\mu s$) +- Frequency unit is **Megahertz** (MHz) + +```Mathematica +Options[SuperconductingHub] = { + (* The number of qubits should match all assignments. Qubits are numbered from 0 to N-1 *) + QubitNum -> 6 + , + (* The T1 time *) + T1 -> <|0 -> 63, 1 -> 93, 2 -> 109, 3 -> 115, 4 -> 68, 5 -> 125|> + , + (* The T2 time with Hahn echo applied *) + T2 -> <|0 -> 113, 1 -> 149, 2 -> 185, 3 -> 161, 4 -> 122, 5 -> 200|> + , + (* Excited population probability in the initialisation, also the thermal state *) + ExcitedInit -> <|0 -> 0.032, 1 -> 0.021, 2 -> 0.008, 3 -> 0.009, 4 -> 0.025, 5 -> 0.007|> + , + (* Qubit frequency of each qubit *) + QubitFreq -> <|0 -> 4500, 1 -> 4900, 2 -> 4700, 3 -> 5100, 4 -> 4900, 5 -> 5300|> + , + (* Exchange coupling strength of the resonators on each edge. Use [Esc]o-o[Esc] for the edge notation *) + ExchangeCoupling -> <|0 \[UndirectedEdge] 1 -> 4, 0 \[UndirectedEdge] 2 -> 1.5, 1 \[UndirectedEdge] 3 -> 1.5, 2 \[UndirectedEdge] 3 -> 4, 2 \[UndirectedEdge] 4 -> 1.5, 3 \[UndirectedEdge] 5 -> 1.5, 4 \[UndirectedEdge] 5 -> 4|> + , + (* Transmon Anharmonicity *) + Anharmonicity -> <|0 -> 296.7, 1 -> 298.6, 2 -> 297.4, 3 -> 298.3, 4 -> 297.2, 5 -> 299.1|> + , + (* Fidelity of qubit readout *) + FidRead -> <|0 -> 0.9, 1 -> 0.92, 2 -> 0.96, 3 -> 0.97, 4 -> 0.93, 5 -> 0.97|> + , + (* Measurement duration. It is done without quantum amplifiers *) + DurMeas -> 5 + , + (* Duration of the Rx and Ry gates are the same regardless the angle. Rz is virtual and perfect. *) + DurRxRy -> 0.05 + , + (* Duration of the cross resonance ZX gate that is fixed regardless the angle. The error is sourced from the passive noise only. *) + DurZX -> 0.5 + , + (* Duration of the siZZle gate is fixed regardless the angle that is fixed regardless the angle. The error is sourced from the passive noise only. *) + DurZZ -> 0.5 + , + (* switches to turn on/off standard passive noise, i.e., T1 and T2 decay *) + StdPassiveNoise -> True + , + (* switches to turn on/off the cross-talk ZZ-noise *) + ZZPassiveNoise -> True + }; +``` + +Superconducting qubits devices typically allow full parallelism in practice. +Full parallel configuration is default implementation in **QuESTlink**. Therefore, +implementing a circuit in this virtual device is simpler than other virtual devices. +See the following example of usage, where we want to emulate running ``circuit`` that +comprises legitimate operations on to a virtual superconducting qubits, e.g., a device +with configuration given above. + +```Mathematica +noisycircscheduled = InsertCircuitNoise[circuit, SuperconductingHub[], ReplaceAliases -> True]; +noisycirc = ExtractCircuit @ noisycircscheduled; +ApplyCircuit[rho, noisycirc]; +``` +First, variable ``noisycircscheduled`` contains noise-decorated circuit together with its schedule. +Passing ``circuit`` directly will arrange gates implementation in full parallell; one can +see this in the schedule, use ``DrawCircuit[noisycircscheduled]``. +Note that, option ``ReplaceAliases`` replaces gate aliases/custom gates into standard +**QuESTlink** operations: for instance ``Init`` gate here replaces the state into the corresponding thermal state. +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``. + diff --git a/SuperconductingQubit/SuperconductingHub.nb b/SuperconductingQubit/SuperconductingHub.nb new file mode 100644 index 0000000..5178323 --- /dev/null +++ b/SuperconductingQubit/SuperconductingHub.nb @@ -0,0 +1,1757 @@ +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 0, 0] +NotebookDataLength[ 74070, 1756] +NotebookOptionsPosition[ 67704, 1643] +NotebookOutlinePosition[ 68514, 1671] +CellTagsIndexPosition[ 68471, 1668] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell["Superconducting qubits Hub", "Title", + CellChangeTimes->{{3.883715555188192*^9, 3.883715560920237*^9}, { + 3.8837156066949453`*^9, + 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+ Alt text +
+ +# Trapped Ions + +There is currently one virtual ion trap, which is multi-node ion traps. This device is based on a quantum device in the University of Oxford, which is instantiated with ``TrappedIonOxford[]``. + +**Table of contents** +1. [Characteristics](#characteristics) +2. [Native operations](#native-operations) +3. [Parameters and usage](#parameters-and-usage) + +## Characteristics + +The multi-node ion traps have local full connectivity within each trap/node. In this virtual device, the user specifies the number of traps and the number of ions in each trap. Each trap contains four "zones", with each zone assigned to perform specific tasks. For instance, remote entanglement must be conducted in zone 4, gate operations in zones 2 and 3, and so on. Given these characteristics, the user needs to take into account the location of ions to perform operations. + +We provide a command to check the position of ions. For instance, the following code instantiates a virtual ion trap and displays the position of ions. The user can freely specify the trap or node names, which are used in the operators. The following example shows two-node ion traps called **Alice** and **Bob**. + +```Mathematica +dev = TrappedIonOxford[]; +dev[ShowNodes] +``` + Alt text + +The picture above shows the initial configuration of two ion traps, in which all ions in the trap are combined (shown by the dashed lines). Before performing a two-qubit gate, the corresponding ions must be **combined**. +## Native operations + +The native operations of the virtual ion traps are the following. Note that, the user must specify the **node** name (**Alice** or **Bob** in the figure above) and the ion (indexed from **1** to **N**) in every operation. + +Every operator has designated zones; the user must shuttle the ions around to fulfil this requirement. + +- Initialisation must be done to all ion +$$\mathtt{Init_{1,...,N}[node]}$$ + +- Qubit readout must be done to a single ion sitting alone in the zone. +$$\mathtt{Read_q[node]}$$ + +- Single-qubit gates are +$$\mathtt{Rx_q[\theta]}, \mathtt{Ry_q[\theta]}, \mathtt{Rz_q[\theta]}$$ + +- Two-qubit gate is controlled-Z; qubits $\mathtt{q_1,q_2}$ must be **combined** before this gate. +$$\mathtt{CZ_{q_1,q_2}[node]}$$ + +- Remote gate between two different traps, generating entanglement gate. The following command initialises Bell pair $(\|01\rangle-\|10\rangle)/\sqrt{2}$ between qubit $\mathtt{q_1}$ in $\mathtt{node1}$ and $\mathtt{q_2}$ in $\mathtt{node2}$. +$$\mathtt{Ent_{q_1,q_2}[node1, node2]}$$ + +- Physical move: swap location between qubits $\mathtt{q_1}$ and $\mathtt{q_2}$; qubits $\mathtt{q_1,q_2}$ must be **combined** before this operator. +$$\mathtt{SWAPLoc_{q_1,q_2}[node]}$$ + +- Physical move: combine two qubits (physically means creating a sub-zone); both qubits must be sitting inside the same zone. This is required before applying any two-qubit operator, including physical swap. +$$\mathtt{Comb_{q_1,q_2}[node]}$$ + +- Physical move: split two combined qubits (physically means splitting the created sub-zone with Comb); both qubits must be sitting inside the same zone. This is required before moving the ion around. +$$\mathtt{Splz_{q_1,q_2}[node]}$$ + +- Physical move: shuttling the ions linearly to the destination zone **dzone**. All ions must be sitting inside the same zone. The move is linear, there is no ions in the path. +$$\mathtt{Shutl_{q_1,q_2,q_3,...}[node, dzone]}$$ + +- Doing nothing; remember it will introduce passive noise +$$\mathtt{Wait_q[\Delta t]}$$ + +### Zone and allowed operations + +- **Zone 1**: $\mathtt{Shutl, Init, Read, Splz, Comb, SWAPLoc}$ +- **Zone 2**: $\mathtt{Shutl, Init, Read, Splz, Comb, SWAPLoc, Rx, Ry, Rz, CZ}$ +- **Zone 3**: $\mathtt{Shutl, Init, Read, Splz, Comb, SWAPLoc, Rx, Ry, Rz, CZ}$ +- **Zone 4** : $\mathtt{Shutl, Ent}$ + + +## Parameters and usage + +The following configuration takes inspiration from a device at the University of Oxford. The code provided below can be directly copied and executed. + +- Time unit is **microseconds** ($\mu s$) +- Frequency unit is **Megahertz** (MHz) + +```Mathematica +Options[TrappedIonOxford] = { + (* the name of trap nodes name together and the number of ions on each node *) + Nodes -> <|"Alice" -> 4, "Bob" -> 4|> + , + (* the T1 time, exponential decay *) + T1 -> <|"Alice" -> 3*10^9, "Bob" -> 3*10^9 |> + , + (* the T2* time, Gaussian decay *) + T2s -> <|"Alice" -> 10^5, "Bob" -> 10^5 |> + , + (* Duration for moving operations: Split, Combine, and physical SWAP *) + DurMove -> <| "Alice" -> <|Shutl -> 25, Splz -> 50, Comb -> 50, SWAPLoc -> 10 |>, "Bob" -> <|Shutl -> 25, Splz -> 50, Comb -> 50, SWAPLoc -> 10 |> |> + , + (* fidelity and duration of initialisation on each qubit; the initialisation is done simultaneously on all ions *) + FidInit -> <|"Alice" -> 0.9999, "Bob" -> 0.9998|> + , + DurInit -> <|"Alice" -> 20, "Bob" -> 20|> + , + (* readout duration *) + DurRead -> <|"Alice" -> 50, "Bob" -> 50|> + , + (* Symmetric bit-flip error during readout *) + ProbBFRead -> <|"Alice" -> 10^-3, "Bob" -> 10^-3|> + , + (*Fidelity of single x- and y- rotations; z-rotation is instaneous (noiseless, virtual)*) + FidSingleXY -> <|"Alice" -> 0.99999, "Bob" -> 0.99999|> + , + (*fraction of depolarising:dephasing noise of the x- and y-rotations *) + EFSingleXY -> <|"Alice" -> {1, 0}, "Bob" -> {1, 0}|> + , + (* Rabi frequency on single rotations *) + RabiFreq -> <|"Alice" -> 10, "Bob" -> 10 |> + , + (* Frequency of CZ operation *) + FreqCZ -> <|"Alice" -> 0.1, "Bob" -> 0.1|> + , + (* Fidelity of CZ operation *) + FidCZ -> <|"Alice" -> 0.999, "Bob" -> 0.999|> + , + (* fraction of two-qubit depolarising: dephasing error after entanglement distillation *) + EFCZ -> <|"Alice" -> {0.1, 0.9}, "Bob" -> {0.1, 0.9}|> + , + (* rate of heralded remote entanglement generation *) + FreqEnt -> 0.1 + , + (* fidelity of the raw bell pair *) + FidEnt -> 0.95 + , + (* fraction of noise on the obtained raw bell pair, 2-qubit depolarising:dephasing *) + EFEnt -> {0.1, 0.9} + , + (* Switch on/off the standard passive noise: decays T1 and T2* *) + StdPassiveNoise -> True + }; +``` +In practice, gates parallelisation on ion traps is applicable to certain operations with +some configuration of zones, e.g., when qubits are in different zones concurrent +gates may be acted upon them. However, as this effort is still actively explored, +we do not implement parallelisation on this virtual ion traps for practical reasons. +However, the user must rearrange the gates as there are multiple nodes involved, +in which parallelisation is applicable on different nodes. This arrangement is +taken care by function ``CircTrappedIons[]``, with option ``MapQubits -> True`` +or ``MapQubits -> False``. + +The simulation of the multi-node ion trap is performed on the total density matrix. +Therefore, we partition the density matrix into the corresponding nodes. +The option ``MapQubits -> True`` will map the local indices within a node into +the global indices for the whole density matrix. This is useful to check the circuit +arrangement globally, for instance, command +```Mathematica +DrawCircuit @ CircTrappedIons[circuit, TrappedIonOxford[], MapQubits -> True] +``` +will draw the (noiseless) circuits arranged according to multi-nodes indices. +However, to obtain the noise-decorated ``circuit``, to simulate it on the noisy +ion traps, one must set ``MapQubits -> False``. See example below. +```Mathematica +mytraps = TrappedIonOxford[]; +noisycircscheduled = InsertCircuitNoise[CircTrappedIons[circuit, mytraps, MapQubits -> False], mytraps, ReplaceAliases -> True]; +noisycirc = Extractcircuit @ noisycircscheduled; +ApplyCircuit[rho, noisycirc] +``` +First, variable ``noisycircscheduled`` contains noise-decorated ``circuit`` together with its schedule. +Command ``CircTrappedIons[circuit, mytraps, MapQubits -> False]`` imposes serial implementation +locally to the node, but parallel with respect to different nodes. +Remark that command ``InsertCircuitNoise[]`` will update the state of the virtual device instance, namely, +``mytraps`` in this case; for example, the arrangement of the ions is updated. +Note that, option ``ReplaceAliases`` replaces gate aliases/custom gates into standard **QuESTlink** operations: +for instance ``Init`` gate here is defined as 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``. + + + + diff --git a/TrappedIon/TrappedIonOxford.nb b/TrappedIon/TrappedIonOxford.nb new file mode 100644 index 0000000..10e4c6e --- /dev/null +++ b/TrappedIon/TrappedIonOxford.nb @@ -0,0 +1,6361 @@ +(* Content-type: application/vnd.wolfram.mathematica *) + +(*** Wolfram Notebook File ***) +(* http://www.wolfram.com/nb *) + +(* CreatedBy='Mathematica 13.0' *) + +(*CacheID: 234*) +(* Internal cache information: +NotebookFileLineBreakTest +NotebookFileLineBreakTest +NotebookDataPosition[ 158, 7] +NotebookDataLength[ 316133, 6353] +NotebookOptionsPosition[ 261638, 5387] +NotebookOutlinePosition[ 308203, 6248] +CellTagsIndexPosition[ 308160, 6245] +WindowFrame->Normal*) + +(* Beginning of Notebook Content *) +Notebook[{ + +Cell[CellGroupData[{ +Cell["Trapped-Ions Oxford/Hub virtual device", "Title", + 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+Cell[CellGroupData[{ + +Cell["\<\ +Paper supplement: entanglement distillation strategies +(https://arxiv.org/abs/2306.07342)\ +\>", "Chapter", + CellChangeTimes->{{3.8955565755419188`*^9, 3.895556579150084*^9}, { + 3.8973770145576487`*^9, + 3.8973770351024942`*^9}},ExpressionUUID->"4d518824-3f83-4b77-a8e8-\ +2e70512d2626"], + +Cell[TextData[{ + "A 4-ions entanglement distillation on each node for up to 3 rounds \ +comprises sequences of phase-flip (0) and bit-flip (1)\n\n", + StyleBox["0 = phase-flip noise distillation\n", + FontWeight->"Bold"], + Cell[BoxData[ + GraphicsBox[ + TagBox[RasterBox[CompressedData[" +1:eJzsnQncTNUbx7Pve9lly5ItOwnJUiLZI0KFaJOkUEqLQiKtSrSqkC0lKpEt +kqKyhPpnjZItpGznP7+ruc69M3Pn3jvnzsw79/f9fJ7/P+8799wz88477/ee ++5znKX3rPR1uS3/BBRfclzXwPx1uGXLVoEG3DOuYN/CPzgPuu73fgL59rh0w +uG+/voPq35oh8MXd6S64YH3g8RkD/y0IIYQQQgghdlmV6AkQQgghhBCShlid +6AkQQgghhBCShqA/E0IIIYQQYh/6MyGEEEIIIfahPxNCCCGEEGIf+jMhhBBC +CCH2oT8TQgghhBBiH/ozIYQQQggh9qE/E0IIIYQQYh/6MyGEEEIIIfahPxNC 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