Quantum register

Abstract

A method of encoding quantum information into a quantum dot in a magnetic field, the quantum dot comprising a confined qubit and a nuclear ensemble, the confined qubit comprising a confined electron or a confined hole, the nuclear ensemble comprising a first atomic species and a second atomic species, the method comprising the steps of: (a) adjusting the net polarisation of the nuclear ensemble comprising sensing the net polarization of the nuclear ensemble and performing a first polarization transfer process on the confined qubit and the first atomic species to adjust the net polarisation from the sensed net polarization to a target net polarization; (b) preparing a target state of the nuclear ensemble comprising performing one or more second polarization transfer processes on the confined qubit and second atomic species to adjust the total polarisation of the nuclei of second atomic species toward a first target polarisation; (c) encoding first quantum information into the second atomic species comprising performing a third polarization transfer process on the confined qubit and second atomic species.

Description

[0001] QUANTUM REGISTER STATEMENT OF GOVERNMENT SUPPORT This invention was made with government support under funder award number N62909- 19-1-2115 awarded by the Office of Naval Research Global. The government has certain rights in the invention. The project leading to this application has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 862035. TECHNICAL FIELD The present application relates to a method and system for encoding quantum information. BACKGROUND In a quantum communication system, quantum information may be encoded by single quanta, such as photons. A photon can carry a single bit of information, and by sending photons between a transmitter and a receiver quantum information may be transmitted. Quantum information may be encoded within a quantum node, which includes one or more physical quantum bits (qubits) serving as a quantum register. Multiple quantum nodes may be connected to form a quantum network, where each node serves to temporarily store quantum information before it is further propagated on the network. To form practical quantum nodes and quantum networks, quantum registers are required that demonstrate high quantum coherence and high quantum fidelity. BRIEF DESCRIPTION OF THE FIGURES Systems and methods in accordance with non-limiting embodiments will now be described with reference to the accompanying figures, in which: Figure 1A shows a schematic illustration of a quantum dot. Figure 1B shows a schematic illustration of a confined electron and nuclear ensemble within the quantum dot of Figure 1A. Figure 2 schematically illustrates a purification process for the nuclear ensemble. 14703377-1Figures 3A and 3B illustrate an energy level diagram of the state manifold of the quantumdot. Figure 4 illustrates an example light source apparatus. Figure 5A illustrates an example pulse sequence to perform a polarization transfer process. Figure 5B is an equivalent quantum circuit diagram for Figure 5A. Figure 5C illustrates another example pulse sequence to perform a polarization transfer process. Figure 6A illustrates a feedback pulse scheme for sensing a polarization state of the nuclear ensemble and performing a magnetization transfer process according to the sensed polarization state. Figure 6B is an equivalent quantum circuit diagram for Figure 6A.Figure 7 is a schematic diagram of a purification protocol.Figure 8A is a schematic illustration of an encoding and readout pulse scheme.Figure 8B is an equivalent quantum circuit for Figure 8A. Figure 9 is a schematic illustration of a quantum information protocol including purification, encoding and readout processes. Figure 10 is a schematic illustration of a quantum repeater. Figure 11 is a quantum circuit diagram illustrating a graph state generation protocol. DETAILED DESCRIPTION There is described herein a method of encoding quantum information into a quantum dot in a magnetic field, the quantum dot comprising a confined spin and a nuclear ensemble,the confined qubit comprising a confined electron or a confined hole, the nuclearensemble comprising a first atomic species and a second atomic species, the method comprising the steps of: (a) adjusting the net polarisation of the nuclear ensemble comprising sensingthe net polarization of the nuclear ensemble and performing one or more first polarizationtransfer processes on the confined spin and the first atomic species to adjust the netpolarisation from the sensed net polarization to a target net polarization; (b) preparing a ground state of the nuclear ensemble comprising performingone or more second polarization transfer processes on the confined spin and secondatomic species to adjust the total polarisation of the nuclei of second atomic species toward a first target polarisation; 14703377-1(c) encoding first quantum information into the second atomic speciescomprising performing a third polarization transfer processes on the confined spin andsecond atomic species.The present invention provides a system and method for a quantum encoding protocolthat enables encoding of quantum information into a nuclear ensemble of a quantum dot.The protocol purifies the nuclear ensemble of the quantum dot and encodes quantuminformation into the purified nuclear ensemble, thereby repurposing the existing nuclearspin ensemble of a quantum dot from a source of noise, and quantum state relaxation,into a reliable quantum register. The quantum dot comprises at least two atomic species,and is charged with a single electron or a single hole by adding or removing an electron(for example, through use of a diode), which functions as a proxy qubit. The protocoladdresses each of the atomic species independently via the proxy qubit, where oneatomic species is used to stabilise and lock the net polarization of the spin ensemble,and at least one other atomic species is used to store the quantum information. Due to the purification of the ensemble, the coherence of the nuclear mode is improved andthus enables any state transfer into the nuclear ensemble in an encoding process, andthus high coherence times for the information encoded into the purified spin ensemblecan be observed.The quantum register may be used in a variety of applications, including as part of anode in a quantum repeater. For a practical quantum repeater to be realised, one ormore quantum memories are required that are capable of storing quantum information for sufficiently long timescales to enable performance of the quantum repeater protocol. The systems and methods describe herein provide a practical quantum memory with the required qubit storage times to effect a quantum repeater apparatus. The use of the quantum register is not limited thereto; the quantum register may be deployed in any quantum apparatus in which quantum information is to be stored, such as a quantum memory in an encoder or decoder apparatus. In addition, the quantum register may be deployed in the generation of multi-dimensional cluster states, in which a multi-qubit register is deployed to store a plurality of quantum states within each qubit in the registerand the application of nuclear SWAP gates between the qubits.In some embodiments, the method further comprises performing a readout process on the second atomic species comprising performing a polarization transfer process 14703377-1 between the confined qubit and the second atomic species to transfer the encoded quantum information from the second atomic species to the confined qubit; and addressing the confined qubit with an optical pulse to generate an output photon. In some embodiments, the nuclear ensemble of the quantum dot further comprises a third atomic species, and wherein the preparing a target state comprises performing one or more third polarization transfer processes on the confined qubit and the third atomic species to adjust the total polarisation of the nuclei of the third atomic species toward a second target polarisation. In some embodiments, the first atomic species is As, the second atomic species is Ga71and the third atomic species is Ga69. In some embodiments, the method further comprises encoding second quantum information into the third atomic species comprising performing a polarization transfer process on the confined qubit and third atomic species. In some embodiments, the method further comprises performing a readout process on the second atomic species comprising performing a polarization transfer process between the confined qubit and the second atomic species to transfer the encoded quantum information from the second atomic species to the confined qubit; and addressing the confined qubit with an optical pulse to generate an output photon. In some embodiments, the encoding process and the readout process are separated by a storage time, and wherein the method further comprises inverting the polarization state of the confined qubit half way through the storage time. In some embodiments, steps (a) and (b) are repeated to produce a purified macrostate of the nuclear ensemble, wherein the purified macrostate has a net polarization of thenuclear ensemble, the second atomic species having the first target polarization and thethird atomic species having the second target polarization.In some embodiments, each first polarization transfer process comprises addressing the confined qubit with a light portion to drive the confined qubit in resonance with the Larmor frequency of the first atomic species, and each of the second and third polarization 14703377-1 transfer process comprises addressing the confined qubit with a light portion to drive the confined qubit in resonance with the Larmor frequency of the second atomic species. In some embodiments each polarization transfer process comprises: driving the confined qubit with a coherent microwave field at a Rabi frequency Ωand having a frequency detuned by δ from the confined qubit Larmor frequency suchthat √Ω^ + ^^ is equal to the Larmor frequency of the respective atomic species; orperforming a two-photon Raman process at a Rabi frequency Ω and having afrequency difference detuned by δ from the confined qubit Larmor frequency such that√Ω^ + ^^ is equal to the Larmor frequency of the respective atomic species.In some embodiments, each polarization transfer process further comprises addressing the confined qubit with a Rabi pulse having a frequency equal to a Larmor frequency of the confined qubit to perform a rotation of the confined qubit to a target state. In some embodiments, sensing the net polarisation of the nuclear ensemble comprises performing a Ramsey interferometry protocol, wherein, optionally, the Ramsey interferometry protocol includes addressing the confined qubit with a π / 2 pulse to perform a rotation, followed by a sensing period in which the confined qubit is not addressed. In some embodiments, the method further comprises initializing the confined qubit to an eigenstate in the Zeeman basis, wherein optionally the initializing of the confined qubit is performed at one or more of: (i) before step (a); (ii) after step (a); (iii) after step (b); and (iv) after step (c). In some embodiments, the initializing the confined qubit comprising performing an incoherent optical pumping process at a frequency equal to a trion excitation frequency of the quantum dot. In some embodiments, the method further comprises applying the magnetic field at a non-zero angle with respect of a crystallographic axis of the quantum dot; and / or applying strain to the quantum dot. 14703377-1 In some embodiments, the encoding further comprises performing a spin rotation on the confined qubit to place the confined qubit into a first quantum state comprising the quantum information. In some embodiments, the method further comprises performing a subsequent spinrotation on the confined qubit, after the encoding of the first quantum information into thesecond atomic species, to place the confined qubit into a second quantum statecomprising second quantum information; performing an entanglement process to entangle the quantum state of the second atomic species comprising the first quantum information and the second quantum state; and performing a first spin-photon entanglement process to generate a first photon entangled with the quantum state comprising the first quantum information and performing a second spin-photon entanglement process to generate a second photon entangled with the second quantum state. There is also described herein a quantum register, comprising: a quantum dot in a magnetic field, the quantum dot comprising a confined qubit and a nuclear ensemble, the confined qubit being a confined electron or a confined hole, the nuclear ensemble comprising a first atomic species and a second atomic species; and a light source apparatus, the light source apparatus configured to perform a method as described above. In some embodiments, the quantum register further comprises a magnet configured to apply the magnetic field, wherein the magnet is configured to applying the magnetic field at a non-zero angle with respect of a crystallographic axis of the quantum dot; and / or a pressure-imparting device configured to apply strain to the quantum dot. There is also described herein a quantum repeater comprising: a plurality of quantum registers, each quantum register being a quantum register as described above. The quantum repeater may further comprise at least one entanglement state measurement device, each entanglement state measurement devicearranged between two quantum register of the plurality of quantum registers.14703377-1 In some embodiments, the plurality of quantum registers comprises a first quantum register, second quantum register, third quantum register and fourth quantum register, and wherein the quantum repeater is configured to perform a quantum repeater protocol comprising: generating a first photon that is entangled with the confined qubit of the first quantum register and generating a second photon that is entangled with the confined qubit of the second quantum register; performing a first Bell state measurement of the first photon and the second photon to generate an entanglement between the confined qubit of the first quantum register and the confined qubit of the second quantum register; after performing the first Bell state measurement, performing a polarization transfer process on the confined qubit of the first quantum register and an atomic speciesof the first quantum register to place the atomic species of the first quantum register in afirst quantum state, and performing a polarization transfer process on the confined qubit of the second quantum register and an atomic species of the second quantum register such that the atomic species of the second quantum register is in a second quantum state; generating a third photon that is entangled with the confined qubit of the second quantum register and generating a fourth photon that is entangled with the confined qubit of the third quantum register; performing a second Bell state measurement of the third photon and the fourth photon to generate an entanglement between the confined qubit of the second quantum register and the confined qubit of the third quantum register; performing a spin-photon entanglement process to generate a fifth photon that is entangled with the quantum state of the atomic species of the second quantum register and performing a spin-photon entanglement process to generate a sixth photon that isentangled with the quantum state of the confined qubit of the second quantum register;and performing a third Bell state measurement of the fifth photon and the sixth photon to generate an entanglement between the first quantum register and the third quantum register.Figure 1A illustrates a quantum dot assembly 100 that can be implemented as a quantummemory / quantum register in accordance with embodiments herein. A quantum dot (QD) 14703377-1 is a structure configured to confine charged particles within a reduced volume, to provide a quantisation of energy levels of the charged particles. As shown in Figure 1, thequantum dot assembly 100 can be fabricated by embedding a first semiconductormaterial 110 having a first bandgap within a second semiconductor material 120 having a second bandgap larger than the first bandgap. The semiconductor material 110 thus forms the quantum dot having a potential well within the first semiconductor material 110in which electrons and holes can be confined. The quantum dot may be populated witha confined qubit, which may include populating the conduction band with a confinedelectron, or populating the valence band with a confined hole (also referred to ascharging the quantum dot). In either case, the charging results in a confined qubit with aplurality of spin states. In the example embodiments described herein, the confined qubit is described by reference to a single electron, having a spin S=1 / 2. However, it will be understood that the described embodiments apply equally to a confined hole, also havinga (quasi)spin S=1 / 2. In an alternative example, the confined qubit may be in the form ofa confined multi-particle molecule, such as a confined multi-electron molecule, as to be described below. (The QD 110 can further include additional layers, including a backgate 122, a top gate 124, a barrier layer 126 and Bragg diffraction layers 130. The backgate and top gate form a diode structure (e.g. a Schottky diode structure, or a p-i-n diodewhere the top gate 124 is p-doped and the back gate 122 is n-doped), which can be used to charge the QD. The back and top gates may be connected via Ohmic contacts (e.g. AuGeNi contacts). The barrier layer 126 forms a blocking barrier (e.g of AlGaAs) to prevent charge leakage. The Bragg diffraction layers 130 operate as a reflector to improve photon emission from the top surface. The QD can be fabricated by a processof molecular beam epitaxy (droplet-based or Stranski-Krastnov) or Metalorganic vapourphase epitaxy. In some embodiments the fabricated quantum dots are lattice-matched quantum dots.In the embodiments disclosed herein, the QD 110 is formed from a semiconductormaterial having at least two atomic species. For example, the QD 100 may be a GaAsquantum dot, in which the first semiconductor material 110 is GaAs, and the second semiconductor material 120 is AlGaAs. In these embodiments, the lattice matching between GaAs and AlGaAs means that nuclear spins experience a homogeneous electric-field gradient, which directly translates to homogeneity of the nuclear ensemble as seen from the confined qubit. The atomic species may include isotopes, and in someembodiments the QD 110 includes three atomic species including a first element and14703377-1 two isotopes of a second element. For example, the QD 110 is a GaAs quantum dotformed of As75, Ga69 and Ga71, with unit cell concentrations of 100%, 60% and 40%respectively, with a total number of nuclei at approximately ~ 5 x 104. In the embodiments described herein, the quantum dot may be selected from III-V materials (e.g. InGaAs, InP), II-V materials (CdSe, CdTe) or IV (SiGe) materials, each of which include a nuclear ensemble and thus may be used for the encoding of quantum information. As mentioned above, there exist a plurality of confined energy states for the confinedqubit (either the confined electron within the conduction band of the QD 110 or theconfined hole within the valence hand of the QD 110). The confined spin states can be further characterised by spin quantum number, which in the absence of a magnetic field, results in degenerate electron spin states. When an external magnetic field is applied, the confined spin will couple to the magnetic field, lift the degeneracy and undergoZeeman splitting. Given the electron / hole is a spin-1 / 2 / quasi-spin-1 / 2 particle, theZeeman splitting results in two energy levels, which may be addressed by the applicationof a coherent microwave field to transition the electron / hole spin between the two levels(the microwave field may take the form of a directly applied coherent microwave field or via a stimulated Raman transition). Similarly, the nuclei within the ensemble arecharacterised by their quantum numbers and will also couple to the applied magneticfield. The nuclear spins will each precess around the magnetic field, quantised by thespin value of the nucleus in the quantization axis of the individual spin (i.e. Iz).Within a charged quantum dot, the confined electron will couple to the spins of the nuclei of the QD, according to the hyperfine interaction. In embodiments described herein, spin-3 / 2 atomic species are chosen (such as As and Ga), resulting in the electron beingcoupled to an ensemble of ~ 5 x 104nuclear spins.As illustrated schematically in Figure 1B, the QD 110 can be approximated as a centralelectron spin 10 coupled to an ensemble 20 of N identical nuclear spins ^^^ in a magneticfield. The nuclear ensemble is described in the collective basis |j, m^ where j = 0.. NI isthe total angular momentum, I is the nuclear spin magnitude, and m = −j .. j is thepolarisation. In the absence of symmetry-breaking interactions, j is constant, leaving aladder of m-states separated in energy by the nuclear Larmor frequency ωn. The system evolves under the approximate Hamiltonian 14703377-1Where ^^ is the central spin, ^^^ = , aCLis the collinear hyperfine coupling term between the nuclei and the electron, aNCLis the non-collinear hyperfine coupling termbetween the nuclei and the electron, is the nuclear raising (lowering)operator resulting in changes of m provided that the energy cost ωn is overcome. ^^^^^^^is a term resulting from the drive of the electron by a coherent microwave field, whichprovides the energy to raise / lower the nuclear polarisation. In embodiments describedherein, the electron 10 of the QD may be driven by a coherent microwave field to drivetransitions between electron energy states. This drive is parameterised by the Hamiltonian term ^^^^^^^. The ensemble of nuclear spins collectively form a quantum state, characterised by the polarization net value Iztotof the ensemble, and information can be encoded into thequantum state of the nuclear ensemble by selectively driving the electron with a light fieldand transferring polarisation from the electron spin to the ensemble. The above Hamiltonian and Figure 1B describe a nuclear ensemble with a single spin species, but it will be understood that when multiple spin species are present the Hamiltonian can besuitably adjusted. For example, separate ^^^^^ terms for each atomic species, with eachatomic species having a different Larmor frequency. Changes in m can be actuated onspecific atomic species via the raising and lowering operators by resonantly driving the electron at the Larmor frequency of the chosen spin species. In QDs (such as GaAs QDs), a misalignment of electron and nuclear spin quantization axes results in the non-collinear coupling term aNCL. Increasing the non-collinearhyperfine coupling term increases the rate of the polarization transfer processes. Thevalue for aNCL can be modified through application of strain to the QD, such as by mounting the QD inside an anvil cell or other pressure-imparting device. Pressures ofup to a few hundred MPa (e.g. 300 MPa) may be applied. The value for aNCL mayalternatively by modified through varying the orientation of the applied magnetic field with respect to the crystallographic axes of the quantum dot unit cell. In some embodiments,the magnetic field is oriented at 45 degrees with respect to the

[0110] axis of the GaAslattice, where the magnetic field direction provides a degree of freedom for tuning the 14703377-1speed of polarization transfer (i.e. the aNCL due to the magnetic field is zero when themagnetic field is aligned with any of the crystallographic axes axes). Figure 2 shows schematically the preparation and encoding of a quantum state in the QD 110 in accordance with the present invention, with the quantum dot including anuclear ensemble 20 and an electron 10 coupled to the ensemble. The electron 10functions as a qubit and is used as an intermediary, or proxy, qubit through whichinformation can be transferred into the quantum register. The quantum informationencoding protocol first purifies the spin states of the nuclear ensemble to create a targetquantum state of the nuclear spins, and then encodes information within that targetquantum state. The nuclear ensemble 20 includes a plurality of atomic species. Figure 2 illustrates three atomic species, 20A, 20B and 20C, but embodiments are not limited thereto; the protocol may be performed on an ensemble including two atomic species,or three or more atomic species. For example, an InGaAs quantum dot may be used, inwhich there are four atomic species of In113, As75, Ga69 and Ga71. In this example, In113may be used to encode a third quantum state using polarization transfer processes acting on the Indium sub-ensemble in the same manner as quantum states are encoded onto each of the Gallium isotope sub-ensembles, to be described below. Prior to the purification, the ensemble 20 is in an un-purified configuration 200A. A magnetic field B is applied to the ensemble, resulting in the precession of the spin of each nuclei around the applied field, quantised by the Izvalue for each nuclei (-3 / 2, -1 / 2, 1 / 2, 3 / 2). As an example, Figure 2 shows the un-purified configuration 200A as a thermalground state where Iz values on each nuclear spin are randomly distributed. However,the purification protocol of the present invention can also be applied to purify an initial configuration that is at least partially purified. For example, an ensemble might have previously been purified, but due to natural spin relaxation processes the macrostate of the ensemble 20 drifts from the purified configuration to an un-purified confirmation by a small amount. The purification protocol can be applied prior to each encoding process to minimise impurities prior to the encoding, effectively locking the ensemble to a target polarization for the entire ensemble. After purification, the ensemble 20 is in a purified configuration 200B, in which theensemble exists in a target polarization macrostate for the entire ensemble, Iztot . Eachof the atomic species can exist in one of a plurality of spin states described in a collective14703377-1basis for the atomic species in the manner described above for the total ensemble - e.g.for atomic species A having NA nuclei in the ensemble, the species can exist in state|^^, ^^^, where j = 0.. NAI is the total angular momentum, I is the nuclear spin magnitude,and mA = −jA .. jA is the polarisation. In the absence of symmetry-breaking interactions, jA is constant, leaving a ladder of m-states for each species, separated in energy by thenuclear Larmor frequency ωn for the atomic species. The purification process can includemultiple steps of single-unit polarization transfer to pump / drive the nuclear ensemble 20 toward the purified state, in which the total net polarization Iztotof the entire ensemble isfixed and at least one of the atomic species is in a “dark state”, being a ground state forwhich there are no permitted spin transitions to a lower or higher energy level. Forexample, an atomic species of the nuclear register may exist in an upper spin dark state|^^^, where no transitions to a higher energy level are permitted (i.e. Φ^|^^^ = 0), ormay exist in a lower spin dark state |^^^, where no transitions to a lower energy level arepermitted (i.e. = 0). One atomic species may be in the upper spin dark state andanother may be in the lower spin dark state. The purified state is prepared such that anencoding process using a polarization transfer process is used to transfer an encodedquantum state to the spin ensemble. For example, in configuration 200B, the secondatomic species 20B has been driven to a dark state with the same Iz value of -3 / 2, and the third atomic species has been driven to a dark state with the same Iz value opposite in magnitude to that of the first atomic species (i.e. +3 / 2). The first atomic species maybe configured with a total polarization value resulting from a mixture of Iz values on eachnuclei. As outlined above in the Hamiltonian, the electron spin will be coupled to all the nuclear spins via the collinear hyperfine coupling term. For a given Iztotmacrostate, the electronspin splitting will be pinned at a specific value. Thus, by fixing Iztot to a particular value,the electron spin splitting is well-defined and polarization transfer can be deterministically transferred from the electron spin to a specific nuclear species. Furthermore, if the atomic species state deviates from a target dark state, then any information encoded would not be encoded within the dark state, resulting in reduced coherence times for the encoded quantum state.A polarization transfer process is a process by which the polarization state is transferredfrom one qubit to another, coupled qubit (such as between an electron and nuclei, asdescribed in examples herein). The purification process outlined above deploys14703377-1 polarization transfer processes to purify the nuclear ensemble 20 to repeatedly transfer units of magnetization from the electron to the nuclei until the purified state is achieved. A polarization transfer process is also used to swap a quantum state from the electron to the nuclear ensemble. An example polarization transfer process within the quantum dot is illustrated byreference to Figures 3A, 3B, and 4, with example microwave pulse schemes shown inFigures 5A – 5C. Figure 3A shows schematically the atomic energy level system in anegatively charged quantum dot in the presence of a magnetic field. The magnetic fieldmay be applied in a Voigt geometry (i.e. the magnetic field is applied in any directionperpendicular to the QD growth axis in which the quantum confinement is greatest. Forexample, the magnetic field is applied within the plane of the quantum dot andperpendicular to propagation direction of the incident light). However, embodiments disclosed herein are not limited to the Voigt geometry. The energy levels of the confinedelectron are Zeeman-split and defined by the spin quantisation axis, resulting in a two-level system of |↑^ and |↓^. The quantization axis may be along the magnetic fielddirection or, in the case of electron g-factor anisotropy, the electron spin quantisation axisis along a vector defined by responses to an angled field to two crystallographic axes that respond differently.In addition to the confined spin, the quantum dot 110 may additionally be populated withan electron-hole pair by exciting an electron from the valence band of the QD into the conduction band of the QD. The bound state of the populated electron and electron-holepair is referred to as a trion (or negatively charged exciton). The accessible electronexcited state and trion states form a manifold of states that can be addressed with photons to populate or depopulate the states within the manifold. The QD energy level system of Figure 3A includes a plurality of high level excited trion states. The spin states of the electron and trion are again quantised by the spin quantisation axis in the directionof the magnetic field. The lowest level trion states include two trion states |⇓↑↓^ and|⇑↑↓^. The transition between the electron state |↓^ and one of the two trion states canbe optically addressed by a photon of linearly polarised (H- or V- polarized) light havinga frequency resonant with the trion energy splitting. For example, the first trion transitionbetween |↓^ and |⇓↑↓^ can be addressed with light having a V polarised light withfrequency ^^, and the second trion transition between |↑^ and |⇓↑↓^ can be addressedwith light having a H-polarised light with frequency ^^. In alternative examples the firsttrion transition may be addressed by H polarized light and the second trion transition 14703377-1 may be addressed with V polarized light. Whether each transition is addressed by H or V will depend on the sign of the electron g-factor and the level of strain in the quantum dot. Through selection of the polarisation and frequency of incident light, an electron canbe pumped between states |↓^ and |↑^.As explained above, the confined spin may be addressed by a microwave drive field. The microwave drive field is selected to have a frequency ωµw, which is detuned by anamount δ from the Larmor frequency ωe between the spin states of the confined spin (i.e.spin-up and spin-down states), such that δ = ωe - ωµw. The presence of the microwavedrive field “dresses” the bare states of the confined spin (i.e. |↓^ and |↑^) to create dressedelectron spin states and |↓^^, which are split in energy and are eigenstates in a dressedelectron basis. These dressed eigenstates can be represented as a superposition of the bare electron states, and are within the plane transverse to the Overhauser field (whichis predominantly along the z-direction, and thus within the plane in which the electronspin is coupled to the spins of the nuclear ensemble. Thus, the dressed states are coupled to the nuclear ensemble via the non-collinear hyperfine interaction. When the energy splitting between the dressed states is tuned to be equal to the Larmor frequencyωn of an atomic species of the nuclear ensemble (i.e. χ = ωn), the dressed states aredriven on resonance with the separated nuclear spin states (i.e. the microwave drive field fulfils the Hartmann-Hahn condition and are driven at the Hartmann-Hahn resonance). The coherent microwave drive with Rabi frequency Ω, when having a Rabi vector aligned with the dressed state quantization axis and on resonance with the nuclear Larmor frequency, causes oscillations between the dressed states due to the non-collinearhyperfine coupling, the oscillations having a Rabi frequency ^^^^, and the separation ofenergy between the dressed states being defined as χ = √Ω^ + ^^. This results in Rabioscillations between the dressed states that couple resonantly with oscillations between two nuclear spin states separated by a single unit of polarization (i.e. the microwave drivecauses Rabi oscillations between a state |↓^^|^^^ and a state |↑^^|^^ − 1^).Therefore, when driven resonantly at the Larmor frequency of a selected atomic species of the ensemble, a transition between the two dressed states of the electron resonateswith a polarisation spin flip on the selected atomic species, which correspond tooscillations between two states within the atomic species sub-ensemble separated by asingle unit of polarization, as shown schematically in Figure 3B. This polarization changecorresponds to a polarization change of the opposite sign taking place on the confined 14703377-1 spin. Thus, by driving the confined spin on resonance with the Larmor frequency of an atomic species of the nuclear ensemble, a polarization transfer process can take place. By timing the duration of the electro-nuclear Rabi oscillations, a single unit of polarization can be transferred from the confined spin to the atomic species of the nuclear ensemble. In some embodiments, the properties of the coherent microwave drive field are chosensuch that Ω » δ, in which case the Hartmann-Hahn resonance condition is met when theRabi frequency Ω is equal to the Larmor frequency of the nuclear ensemble (i.e. Ω = ωn).As a result, fastest polarization transfer can be performed and the polarization transferprocess is less sensitive to imperfect locking of Iztot. In alternative embodiments, theproperties of the coherent microwave drive field can be chosen such that δ » Ω, in whichcase the Hartmann-Hahn resonance condition is met when δ= ωn.Prior to performing the polarization transfer process, the electron can be initialized intoa state within the dressed basis. This initialization process includes the incoherent optical pumping of the confined spin by an optical laser into a chosen spin state in thebare basis (i.e. the Zeeman basis in the z-axis direction, which is the direction of theapplied magnetic field), followed by a Rabi rotation of the confined spin from the z-basisinto the plane of y-z plane of the Bloch sphere. The confined electron rotations into they-z plane are performed by driving the confined spin with a frequency on resonance withthe Larmor frequency ωe of the spin-state separation of the confined spin (i.e. ω = ωe).The duration of the Rabi pulse determines the degree of rotation, and the phase of theRabi pulse determines the axis of rotation. For example, a rotation can be performed byperforming a π / 2 rotation around the x axis of the Bloch sphere to rotate the confinedspin from state |↓^ to state |↓^^.After completion of the polarization transfer process the confined spin can be returnedto the original non-dressed eigenstate via a further Rabi rotation. The confined spin mayalso be reset to any chosen Zeeman basis state by performing an incoherent opticalpumping process via the trion state as described above. The polarization transferprocess can then be repeated. Thus, the polarization transfer technique can beperformed multiple times to repeatedly adjust the polarization Iztotof the nuclear ensemble. 14703377-1Figure 4 illustrates an example light source apparatus 400, that may be used to driveand optically address the confined qubit to perform the protocol as described herein. Thelight source apparatus 400 includes a first laser 402, a second laser 408, two beam splitters 403, 405, an electro-optical modulator (EOM) 404, an arbitrary wave form generator (AWG) and a local oscillator (LO).The light source apparatus 400 is configured to perform a two-photon Raman process toachieve the polarization transfer process. In this process, the second laser 408 isconfigured to output light at a frequency detuned from the trion transition frequency ^^by an amount Δ. Δ may be tuned to be a variety of values, such as 600 GHz, 700GHzor 800GHz. The output of the second laser 408 is passed through an electro-opticalmodulator (EOM) 404 that modulates the laser signal. As shown in Figure 4, The EOM is driven by an IQ mixer 406 that mixes the output of an arbitrary wave form generator(AWG) with a local oscillator (LO) to produce an output having an amplitude V0,frequency = 2^^^ − ^^^^ , and phase ^^^. However, in some embodiments theAWG directly synthesises the microwave signal, and the mixer 406 and the LO is not required. By operating the EOM 404 in the regime where the microwave field linearly modulatesthe input optical field, a signal + Δ^^^) produces a control field output bythe EOM, the control field comprising two sideband frequencies at the twoside band frequencies having a relative phase offset of 2Δ^^^. These sideband frequencies are then used to drive the two-photon Raman transitions between the energylevels of the negatively charged QD, as shown in Figure 3A, with ^^ = ^^ − and^^ = ^^ + ^^^. The optical output provides a Rabi vector of [Ω cos(^), Ω sin(^) , ^],which can be fully controlled by via the Rabi frequency (which is varied according to thepower of the EOM output, i.e. Ω ∝ ^ ^^), its phase ^ = 2Δ^^^, and the two-photondetuning ^ = ^^ − 2^^^ . The AWG can be programmed to modulate the EOM togenerate a pulse sequence to provide full 3-axis control around the Bloch sphere. Thelight source of Figure 4 can be used to perform any desired protocol sequence ofrotations around the Bloch sphere for the central electron spin, and drive of the centralspin along a chosen axis within the Bloch sphere, facilitating any required control protocolfor polarization transfer methodologies described herein.14703377-1 As an alternative to a light source configured to perform a two-photon Raman process described above, alternative light source configurations may be deployed to provide full control over the Rabi vector and perform the control protocols as described herein. As a second example, there may be provided a light source apparatus configured to perform a direct microwave drive of the quantum dot. In the second example, the light sourceincludes first laser 402, but instead of generating a microwave signal using an EOM asdescribed above, the light source of the second example includes a microwave generator. The microwave generator is configured to generate a microwave signal thatis delivered to the QD directly (for example, the microwave field delivered to the QDdevice using coaxial microwave lines and an antenna close to the QD). For example,the microwave generator may include an arbitrary wave form generator (AWG)configured to generate the signal, or the combination of an AWG and microwave LO configured to provide input into IQ mixer to produce the microwave signal. The output of the microwave generator is used to provide a controllable Rabi vector[Ω cos(^), Ω sin(^) , ^], which is fully controlled by via the Rabi frequency (via power ofthe microwave generator output), frequency and phase of the microwave generatoroutput. The laser of the second example is configured in the same manner as the secondlaser 408 of the first example. For each light source apparatus example, the light source apparatus operates to performoptical operations on the QD using first laser 402. The first laser 402 is configured togenerate light resonant with a trion excitation The optical operations can includeinitialization and reset of the confined qubit (e.g. in the polarization or cooling processes to be described below) or to readout quantum information from the electron (as described below).In each example, the first laser 402 is configured to output light that is resonant with atrion transition to enable incoherent pumping of the electron state to reset the electron spin, and to enable readout of the quantum dot. When performing readout, the quantum dot emits a photon that can be received by a single-photon detector 410.Each light source apparatus example (and as illustrated in Figure 4 for light source 400)further comprises a controller 401. The controller is arranged to control the componentsof the apparatus, including first laser 402 and second laser 408 to perform the methodsdescribed herein. For example, the controller comprises one or more processors that 14703377-1 are configured to control operations of the laser 402, by execution of a computer program. The computer program may be stored in a non-transitory medium. The controller may be part of a computer system, server or other user device that may include an input interface allowing the user to specify a control program for the light source apparatus.The quantum dot may be cooled to a low temperature to ensure exciton trapping andquantum light emission for spin initialization and readout. For example, the quantum dot is placed within a cryostat comprising an electromagnet, where the cryostat is configured to cool the quantum dot below a target temperature (e.g. 4K). The electromagnet is configured to apply a target magnetic field (e.g.4.5T). The target temperature and target magnetic field results in an electron spin resonance frequency of at least ωe / 2π = 1.0GHz, but may be up to 40GHz (any value may be used that is larger than the trionlinewidth to allow spin pumping). The parameters of the microwave generator may beadjusted accordingly (e.g. to generate microwaves at a frequency between 1 GHz and 40GHz). The above-described apparatus and method for performing a polarization transferprocess is by way of example only. Alternative polarization transfer schemes may bedeployed by which the electron spin is addressed to modify a net polarization of the nuclear ensemble.Figure 5A illustrates an example pulse scheme in which the electron can be driven by acoherent microwave field (e.g. via Raman fields) to perform a polarization transferprocess based on the processes described above. Figure 5B shows the equivalentquantum circuit to the pulse process of Figure 5A. The process of Figure 5A is a NOVEL(Nuclear Spin Orientation via Electron Spin Locking) process, which comprises two microwave pulses 510 and 520. The first microwave pulse 510 is a rotation pulse, inwhich incident microwave rotates the initialised electron spin into the plane of theprecessing field of the nuclear spin. The second pulse 520 is a polarization transferpulse, being a locking pulse to resonantly drive the electron spin at the Larmor frequencyof the nuclear spins. The QD starts in an initial state where the ensemble has polarization Iztotand the spinelectron has an initial spin state (e.g. |↑^). For example, an initialization pulse may be14703377-1 directed at the electron, being an optical pulse to pump the electron into a chosen spinstate in an incoherent optical process. The first microwave pulse 510 is provided as acoherent rotation pulse directed at the QD. The pulse has a duration of T = π / (2Ω) (i.e.the pulse is a π / 2 pulse) with phase and amplitude selected to effect an Rx rotation around the Bloch sphere. This has the effect of rotating the spin state by π / 2 around theBloch sphere to place the spin within the plane transverse to the Overhauser field (whichis predominantly along the z-direction, and thus within the plane in which the electronspin is coupled to the spins of the nuclear ensemble and ready to be driven by thesubsequent locking pulse. The choice of phase to effect an Rx rotation is by exampleonly, and other microwave pulse phases may be selected. The effect of the π / 2 rotation is to place the spin vector into the plane of the effective field of the nuclear spin ensemble, with the choice of phase determining where in the plane the rotated vector will be.A second microwave pulse 520 is provided as a locking pulse after the rotation pulse,which drives the electron spin in the plane plane of the transverse field of the nuclearspins. The locking pulse is driven resonantly with a target atomic species having acorresponding Larmor frequency, and thus operates at a Hartmann Hahn resonance.This couples the oscillations in electron spin to oscillations in the nuclear spin states, which has the effect of transferring the polarization from the electron to the nuclear spins. For example, and as shown in Figure 4, the second pulse may be a two-photon Ramanpulse or coherent microwave field pulse as described above, tuned such that ^ =√^^ + Ω^ = ^^ as described above, with an amplitude and phase selected to effect anRy drive (or, in the limit Ω » δ, a Rabi frequency Ω is chosen to be equal to the Larmorfrequency of the atomic species). This rotation has the effect of resonantly driving thecoupled electron and the nuclear spins to transfer magnetization between the electronand the nuclear spins. This is represented by a SWAP gate in the equivalent quantumcircuit of Figure 5B. The phase of the microwave pulse 520 is selected to be 90 degreesout of phase with the phase chosen for the rotation pulse 510. As a result, the microwave pulse 510 rotates the electron onto the same axis of the drive of microwave pulse 520. As illustrated in Figure 5A, the phase of the second microwave pulse 520 is selected to effect a Ry drive, since the pulse 510 is provided as an Rx pulse. However, this is again by way of example only, and the drive axis of the second pulse may be along anyalternative direction that is orthogonal to the axis of the rotation pulse 510, and within thex-y plane (the plane orthogonal to the applied magnetic field). 14703377-1 The duration of the pulse is chosen such that the polarization is fully transferred from the electron to the nuclear spins. For example, of duration of T = π / (Ωmag) (i.e. the pulse is a π-pulse, driven at a Rabi frequency resonant with the nuclear ensemble Larmorfrequency). Since the dressed states are resonantly coupled to the nuclear spinensemble, the pulse 520 results in change in polarisation of the ensemble opposite to the change in the spin of the dressed state. Thus, pulse 520 transfers a single unit of polarization to the spin ensemble. The pulse 520 can adjust the ensemble magnetizationby +1 or by -1 by changing the phase of the Raman pulse to instead perform a R(y)(π)or a R(-y)(π) rotation. The NOVEL microwave pulse sequence thus results in the positiveinjection or negative injection of magnetization into the spin ensemble. Thus, the pulsecan be referred to as a + injection pulse scheme or a – injection pulse scheme.Following completion of the microwave pulse sequence 510 and 520, the electron can be addressed by optical pulse 530 to pump the electron back into the initial spin state. The optical pumping scheme is an incoherent process, such that the confined spin is always reset to a chosen state (e.g. spin-up in the Zeeman basis) regardless of the spin state of the confined spin prior to optical pumping. The above described apparatus and process relate to the addressing and purification of a target atomic species within a quantum dot by tuning the direct microwave drive or the two-photon Raman process to the Larmor frequency of the target atomic species. Through repeated applications of the polarization transfer pulse sequence of Figure 5A,the net polarization for the target atomic species can be driven to a target value.While a microwave driving process resonant with the nuclear Larmor frequency isdescribed above for transferring polarization, it will be understood that alternativeprocesses may be used to resonantly drive the electron with an atomic spin species having a Larmor frequency. For example, an electron spin echo process may beperformed. In another example, as illustrated in Figure 5C, the “PulsePol” sequencemay be applied. In a PulsePol sequence, a series of short pulses (much shorter thanthe Nuclear Larmor period) are provided in sequence, with waiting periods between eachpulse that refocus the electron-nuclear interaction such that polarization transfer is achieved through the accumulated dynamics between pulses. The duration of the pulses is based on Larmor frequency of the atomic species into which polarization is to be transferred. 14703377-1 The pulses are provided in a sequence to allow the confined qubit to evolve under the effect of different nuclear-electron dynamics for different periods of time to ‘engineer’ thesystem Hamiltonian to provide an effective flip-flop Hamiltonian. Namely, the nuclear-electron coupling within the QD is determined by the term ^^⃗ ⋅ ^⃗, where A is the hyperfinetensor. The electron can first be rotated around the y-axis and allowed to precess for a first time period. During this first time period, the effective Hamiltonian is ^^^^= ^^^^^^^^^, where ^^^^is the x component of the hyperfine vector and α < 1 is a constant determined by the configuration of the light source. A second pulse is then provided torotate the electron around the x-axis, which is then allowed to precess for a second timeperiod. During this second time period, the effective Hamiltonian is ^^^^ = ^^^^^^^^^ .Repeating this sequence yields a time evolution that is governed by an effective flip-flip Hamiltonian: For times exceeding 1 / ωn and for ^^^^« ωn. The evolution of the electron under this flip-flop Hamiltonian over time has the result of transferring a unit of polarization from theelectron to the nuclear spin ensemble. The above described sequence is showed schematically in Figure 5C. Each pulse of the sequence is driven with microwave signal having a frequency on resonance with the electron Larmor frequency and having a Rabi frequency that is not tuned to be on resonance with the Larmor frequency. The phase of the microwave signal can be adjusted to effect a rotation around a chosen axis in the rotating frame of the microwave drive. The pulse sequence includes, in order, a first pulse, a first delay period, a second pulse, a second delay period, a third pulse, a fourth pulse, a third delay period, a fifth pulse, a fourth delay period and a sixth pulse. The pulse sequence is repeated N times, where the first pulse of the next sequence immediately follows the sixth pulse of the preceding sequence.In one example implementation, the first pulse is a π / 2 pulse around the Y-axis, thesecond pulse is a –π pulse around the x-axis the third pulse is a π / 2 pulse around the Y- axis, the fourth pulse is a π / 2 pulse around the x-axis, the fifth pulse is a π pulse around 14703377-1 the y-axis, and the sixth pulse is a π / 2 pulse around the x-axis. However, these represent only example directions within x-y plane of the Bloch sphere; alternative axes of rotation within the x-y plane of the Bloch sphere may be chosen for each pulse that fulfil the relative change in axis direction as described. Each of the first, second, third and fourth delay period are each chosen to be the same, and equal to ^^^ / 4. The pulse sequence achieves polarization transfer for pulse spacing ^^ ^^^=^^ . Full polarization transfer is achieved for a time ^ = ^^^^, where N is thenumber of repetitions of the pulse sequence. Thus, the N repetitions of the pulse sequence together form one polarization transfer process 540. N may be selected to optimise the pulse transfer to transfer a single unit of polarization from the electron to the ensemble. After completion of the polarization transfer, the spin may be re-initialized into a chosenspin state with optical pulse 530 as previously described.In Figure 5C, the first through sixth pulses are illustrated with finite width for ease of understanding. However, it will be understood that these pulses are much shorter intimescale than the delay period between the pulses. The PulsePol scheme provides fora fast polarization transfer process that is robust to noise and small pulse imperfections. Embodiments described herein relate to systems and methods for encoding quantuminformation onto a quantum dot, where the quantum dot includes at least two atomicspecies. Each atomic species is a sub-ensemble of the nuclear ensemble, and there is minimal exchange interaction coupling between the different atomic species. As a result, each atomic species is characterised by a corresponding macrostate for that species according to the degree of magnetization of the spins in the sub-ensemble in an applied magnetic field. The electron will couple to all spins across all atomic species, and the properties of the electron is thus affected by the macrostate of the entire nuclear ensemble. However, due to different atomic properties of each atomic species, each atomic species will have a different Larmor frequency and thus a different ladder of states. Thus, in embodiments of the present invention, each atomic species may be separately addressed by the driving light field. For example, the second atomic species (e.g. Ga71) may be driven to the dark state via repeated application of the NOVEL pulse scheme as described above for Figure 5, with 14703377-1 repeated transfer of polarization to lower the net magnetization value. The third atomic species (e.g. Ga69) may also be driven to a dark state via repeated application of the NOVEL pulse scheme as described above for Figure 5, with repeated transfer of polarization to increase the net magnetization value. Each of the dark states of the second atomic species and the third atomic species may be subsequently addressedseparately for encoding of quantum information.For example, as shown in energy level diagram 210 of Figure 2, the dark state of the second atomic species can be represented as first atomic species ground state|0^^^, above which there exists a first excited state |1^^^, which corresponds to the reversal of a single spin in the ensemble of the first atomic species. An arbitrary quantum state canbe prepared as a superposition of these two states – for example, |^^^^ = ^|0^^^ +^|1^^^. The arbitrary quantum state may be encoded by polarizing the electron spin intoa corresponding superposition of dressed states (i.e. and performingthe polarization transfer process to swap the spin states between the electron and the ensemble.The first atomic species 20A may also be repeatedly addressed via the NOVEL schemeto provide an initial macrostate for a target macrostate for the first atomic species. The target macrostate for the first atomic species is selected such that the total net polarization for the nuclear ensemble is at a target value.Thus, while each individual spin species is addressed separately to adjust the totalpolarization value for each sub-ensemble, each adjustment will also affect the total polarization value for the entire spin ensemble. Figures 6A and 6B illustrate a feedback pulse scheme 600, which is a variation on the NOVEL scheme of Figures 5A and 5B. In embodiments described herein, the step of adjusting the total net polarization of the nuclear ensemble includes the feedbackscheme to lock the total Iztot value of the entire ensemble to a target value.The feedback scheme 600 includes a sensing period 615 following an actuation period620. In the sensing period 615, the QD is configured to sense the current Iztot state ofthe ensemble (i.e. the current net polarization of the ensemble). In the actuation period 14703377-1 620, the QD is driven to adjust the net polarization of the ensemble toward a target value, based on the sensed state of the ensemble. A sensing mechanism for the macrostate is a linear energy shift on the central spin Hsense, where Hsense is a term in the system Hamiltonian due to the coupling between the central qubit and the mean Overhauser field. This energy shift can be measured by a Ramseyinterferometry measurement, comprising addressing the electron / hole with a rotationpulse 610, followed by a free evolution period 615. The rotating pulse 610 rotates theelectron / hole spin away from the Zeeman quantisation axis into the plane of the effectivefield of the nuclear ensemble, in same manner as described above for pulse 510 of Figure 5A. For example, the pulse is an Rx(π / 2) rotation. In the free evolution period, the electron spin is then allowed to freely evolve in the presence of the coupling with thenuclear ensemble, under Hsense. In the actuation period 620 the central qubit is driven bya microwave field having frequency and detuning to fulfil the conditions for polarization transfer. In the rotating frame of the drive, the coupling between the central spin and the nuclearensemble, and thus Hsense, is (^ + ^^^^^ + ^^^^^^)^^. A primary setpoint for thealgorithm, Izlock is chosen by selecting an ESR drive detuning value ^ ≡ −^^^^^^^^^. A difference in macrostate from Izlockwill have the effect of precessing the central spin qubit around the z-axis (Zeeman axis). The projection of the Bloch vector along the xdirection will be the error signal for a deviation Δ^^ = ^^^^^ − ^^^^^^. The error signal isgiven by which for a single spin flip ΔIz = 1 reaches a maximumat τ = 1 / 4A0. In the equivalent quantum circuit of Figure 6B, an evolution period for amaximum error signal corresponds to a R±z(π / 2) rotation conditional on the state of the spin system. In the actuation pulse 620, the spin is driven by a polarization transfer pulse, as describedabove. Pulse 620 to evolve the system under the non-collinear term of the Hamiltonian + Φ^ ^^). The evolution under this flip-flop Hamiltonian is produced by drivingthe spin resonantly at the Larmor frequency of a target atomic species with a spin lockingpulse, as described above. Due to the free evolution under the effect of the mean nuclear ensemble field, at the end of τsense, the spin vector direction is rotated to align along the same axis on the Bloch sphere along which the spin was rotated by pulse 610. Thus, the phase of the microwave pulse 620 is selected to be the same as the phase chosen for 14703377-1 the rotation pulse 610, such that the confined spin is driven along the same axis as the axis of rotation of the microwave pulse 510. In the example of Figures 6A and 6B, the rotation pulse 610 and the actuation pulse are Rx pulses, but alternative microwave phases may be chosen to rotate and actuate along any direction within the x-y plane ofthe Bloch sphere. The Rabi polarization transfer pulse is driven for a time period T asdescribed above in order to perform a π pulse. As a result, depending on the sensedmacrostate, the polarization transfer pulse will increment or decrement the total macrostate by one unit of polarization.In the equivalent quantum circuit of Figure 6B, this pulse is equivalent to a SWAP gatebetween the electron spin and the nuclear ensemble. It is to be noted that the feedback procedure of steps 610, 615 and 620, no measurement is required between the sensing period 615 and actuation period 620, meaning the feedback operation is autonomous. Following completion of the feedback sequence 610, 615 and 620, the electron can beaddressed by optical pulse 630 to incoherently pump the electron back into the initialspin state. The above feedback process can be applied repeatedly to iteratively increase the purity of the spin ensemble. The feedback process may be applied to a spin ensemble that is already close to the target ensemble macrostate (e.g. a spin ensemble that has already been purified and deployed as a quantum repeater) to correct minor deviations from the target macrostate. In this manner the feedback can be used to make adjustments to correct natural error as the system is deployed over time. The feedback process may also be deployed to purify a spin ensemble from the thermal state configuration of 200A.As mentioned above, the error signal reaches a maximum at τ = 1 / 4A0 for a single spinflip ΔIz = 1. For larger differences from the target Itotz state (e.g. where ΔIz = M, M>1), themaximum error signal is reached for τ = 1 / 4MA0. A smaller sensing time will sense alarger M deviation from the target macrostate, and a larger sensing time will sense asmaller deviation from the target macrostate (e.g. a single unit deviation).In order to sense and correct for polarization deviations across a range of magnitudes, the feedback process may comprise multiple feedback blocks, where each block comprises one feedback sequence 610, 615, 620 and 730 of Figure 6A, and wherein the 14703377-1 sensing period in each feedback block is different in duration. The blocks may beprovided successively, where the sensing time for each successive sensing period isincrementally increased by a selected sensing interval to sense and correct for larger deviations. For example, the first repetition in the series has a sensing time ^^^^ofabout 1 / 4^^√^, where N is the total number of nuclei (across all atomic species) in theensemble, and the last in the series has a sensing time of ^^^^of about 1 / 4A0.The macrostate of the entire spin ensemble (i.e. Iztot) exists as a probability distributionp(Iz), initially with a broad distribution when in the thermal macrostate and thus thesensing step will sense a net polarization Iz with probability p(Iz). As a result of performing the above-described feedback process to correct deviations from a target macrostate, the width of the probability distribution is successively narrowed as the feedback process is performed. Repeated application feedback process can stabilise the net polarization of the entire spin ensemble to within single-spin fluctuations. By narrowing the probability distribution of the macrostate, the efficiency and speed of the polarization transfer process between the proxy spin and the nuclear ensemble can be improved. The above described feedback procedure is detailed in document “Optimal purification of a Spin Ensemble by Quantum Algorithmic Feedback” by D. Jackson et al., Physical Review X, 12, 031014 (2022), the contents of which are incorporated by reference.In the feedback scheme of Figure 6A and 6B, the macrostate of the entire ensemble issensed during the sensing period, but only one of the plurality of atomic species isaddressed during the feedback step to inject a unit of polarization into that one atomicspecies, by addressing the electron at the Larmor frequency of the selected atomic species. Any atomic species may be chosen for the feedback process by driving the electron at the chosen Larmor frequency. In accordance with the present invention, the polarization injection process of Figures5A and 5B (or 5C) and the feedback process of Figures 6A and 6B are performed on aquantum dot having a plurality of atomic species, with each process performed on a different atomic species. The resulting purification process produces a high purity spin ensemble in which quantum information can be stored in high coherence times. 14703377-1Figure 7 shows a purification protocol in accordance with the present invention. Thepurification protocol comprises a series of steps including at least one feedback step 710followed by at least one injection step 720. The feedback and injection steps mayalternate, as illustrated in Figure 7. Each feedback step 710 comprises one or morefeedback processes as described above in connection with Figures 6A and 6B (forexample, the feedback step 710 may include the plurality successive feedback blocks, and the plurality of successive feedback blocks may be repeated multiple times). Eachinjection step 720 comprises one or more injection processes as described above inconnection with Figures 5A and 5B. Each feedback process 710 is configured to sense the entire Iztotmacrostate of the nuclear ensemble and to address the first atomic species of the plurality of atomicspecies to effect a change of ΔIz = ±1 on the first atomic species to adjust the totalensemble state. For example, when the nuclear ensemble comprises Arsenic andGallium, the feedback process operates on the Arsenic (As) nuclei within the atom as the first atomic species, since Arsenic has the lowest Larmor frequency well-separated from the higher frequencies of isotopes of Gallium. As such, As is easier to distinguish in ensembles at low Iztotpurity with minimal cross-talk to higher frequencies. As illustrated in Figure 7, each injection step 720 includes a first injection process 720-A and a second injection process 720-B. The first injection step 720-A is configured to address the electron at a Larmor frequency of the second atomic species to increase the net polarization of the second atomic species by ΔIz= +1, and the second injection step720-B is configured to address the electron at a Larmor frequency of the third atomicspecies to increase the net polarization of the second atomic species by ΔIz= -1. For example, when the nuclear ensemble comprises Arsenic and Gallium, the injection processes operates on the Gallium (Ga) nuclei within the atom, with Ga69as the second atomic species and Ga71as the third atomic species. By choosing Ga69and Ga71for the second atomic species and third atomic species, the hyperfine shifts to the ESR frequency from each atomic species cancel out when the polarization of each atomic species is adjusted in opposite directions. The repeated injection of magnons into the Ga isotopes will affect the overall net polarization, which may shift it away from the desired target spin state Iztot. However,since the feedback process (acting on As exclusively) is provided to lock the spin state14703377-1 at a target Iztot, these deviations can be compensated for during the purification protocol. In some embodiments, multiple feedback steps may be provided prior to the first injection step 720 to purify the Iztotstate from the thermal state to purify the first atomic species, thereby generating a partially purified state. Additional feedback steps may then be repeated between each injection step 720 to adjust for the effect of magnon injection. By partially purifying the ensemble toward the target macrostate Iztot(e.g. by repeated application of the feedback process 710 until a target macrostate Iztotis reached) prior to the first injection step, the protocol provides for improved resolution when addressing thesecond and third atomic species during the injection steps and more efficient polarizationstate transfer. The accessible ensemble spin states for each of the second and third atomic species are provided as a ladder of states, where each injection step will inject a positive or negative unit of polarization to move the ensemble up or down the ladder. At each endof the ladder exists a “dark state” – i.e. a state for which a transition is allowed in onlyone direction. The second atomic species is progressively pumped toward a first dark state and the third atomic species is progressively pumped toward a second dark state. The dark states do not necessarily correspond to complete, 100% polarization of the atomic species; a dark state may be achieved by lower polarization amounts (e.g.60% polarization). Thus, the steps of the purification protocol are repeated multiple times to pump the quantum dot into a purified spin state, in which the net polarization of the entire ensembleis locked to a target Iztot value, and at least one of the atomic species is in a dark stateinto which a magnon can be injected.While injection steps on different atomic species are illustrated, it will be understood thatonly a single injection step on one atomic species is required for the invention. In thisembodiment, the feedback step operates on one species (e.g. As) and the injection operates on the second atomic species (e.g. Ga), thereby still locking the ensemble at a target Iztot, and creating a dark state for one atomic species. However, by using twoatomic species for the injection locking, the injected polarization into the second atomicspecies and the injected polarization into the third atomic species can produce a netpolarization corresponding to the difference in net polarization in each sub-ensemble(e.g. a difference corresponding to the relative concentrations of the second and third 14703377-1atomic species in a unit cell). Since positive and negative polarization injections areprovided in succession, the injection process into the second and third atomic speciesdoes not affect the feedback process being conducted on As, leading to a more preciseand efficient stabilization of total ensemble Iztot. In some embodiments, the netpolarization can be set to zero by equal injection of magnons into the second and thirdatomic species and performing the feedback process on the first atomic species to produce a net zero polarization. This is in contrast to repeatedly injecting a single unitof polarization of the same magnitude (i.e. + all +1 or all -1), which would result in a largeESR shift and the quenching of the anisotropic coupling between the electron and thenuclear ensemble in a quantum dot where the non-collinear coupling is present due tothe electron g-factor anisotropy (where a large ensemble nuclear polarization would pull the electron towards the nuclear axis, thus reducing non-collinearity). Alternatively, in cases where a non-collinear coupling arises from strain, and thus nuclear quadrupolar effects, a large nuclear ensemble would not result in quenching of the non-collinearcoupling resulting from strain. In such cases a target macrostate of Iztot may be chosenin which all atomic species are repeatedly injected with polarizations of the same magnitude. Following purification of the ensemble, the protocol includes encoding and readout steps,as illustrated in Figures 8A and 8B. Figure 8A illustrates a pulse sequence to encode achosen quantum state into the nuclear ensemble, and to read out the encoded quantum state from the nuclear ensemble. Figure 8B illustrates an equivalent quantum circuit diagram for the pulse sequence of Figure 8A. The encoding step comprises a first rotation pulse 810, which is directed at the electron system to perform a generalised electron spin rotation ^^^to prepare the electron into an input quantum state |^^^, which is a superposition of spin states in the undressedbasis. Any arbitrary state has a representation in the dressed state basis and thecoherences defining this state will be transferred onto the nuclei. Providing ^^^is fortomographic purposes (to characterise the state representation and coherences, byinjecting an arbitrary state into the quantum state transfer protocol). The encoding step further comprises a second pulse 820, which is a polarization transfer pulse as previously described (e.g. a two-photon detuned Raman pulse or direct microwave drive), configured to resonantly drive the electron at the Larmor frequency of 14703377-1 an atomic species of the nuclear ensemble, thereby swapping the input quantum state from the electron to the atomic species of the nuclear ensemble. The pulse 820 is represented as a SWAP gate on the equivalent quantum circuit of Figure 8B. The nuclear ensemble is thereafter encoded with an ensemble excited state |^^^. The spin dark state of the atomic species corresponds to a polarized ground state of the atomic species, with excited states of the atomic species corresponding to single spin flips. However, the nuclear ensemble comprises many nuclear spins (e.g. approximately ~ 5 x 104), thus providing correspondingly many single spin-flip excitations at different ensemble locations that are degenerate. Upon excitation, therefore, the single-unit spin flip can thus be distributed across multiple nuclei to form a coherent, zero-momentum ‘spin wave’, or ‘magnon’. The ensemble excited state will remain stored within the nuclear ensemble for a storage time Tstore, during which time the excitation will precess around the applied magnetic field. During this precession, the ensemble excited state will continue to be coupled to the spin of the charged electron within the quantum dot. The ensemble excited state will experience an effective field from the presence of the electron (the Knight field). The Knight field is different in sign (+ or -) depending on the spin state of the electron, which causes a shift in the Larmor frequency of the precession of the ensemble excited state. For example, the ensemble excited state has a first Larmor frequency of ^↓= 59.060(8)MHz when the electron is in a |↓^ state, and has a second Larmor frequency of ^↑ =58.560(9) MHz when the electron is in a |↑^ state, with = 0.500(12) MHz.Prolonged exposure to a Knight field gradient during storage times can dephase the ensemble excited mode. Thus, in embodiments, the electron can be driven with a re-focusing pulse 830 halfway through the storage time Tstore. The storage time Tstore maybe selected depending on the desired application for the quantum encoded information (e.g. during asynchronous operation of a quantum repeater protocol). The refocusingpulse inverts the electron state (e.g. a π x-rotation pulse is performed). Thus, for the firsthalf of the storage time the ensemble excited state will be subjected to a first Knight field gradient from a first electron spin state, and for the remaining half of the storage time, the ensemble excited state will be subjected to a second Knight field gradient from a second electron spin state that is opposite to the first Knight field gradient. The dephasing effect of the electron can thus be cancelled out over the storage time. 14703377-1Due to the highly purified polarization value, the encoded magnon will maintaincoherence for longer timescales, and will have a much higher fidelity than in unpurifiedensembles. A quantum dot purified and encoded according to the embodiments described herein can provide storage times of T = 130 µs. After the ensemble excited state has been stored for a storage time Tstore, a readout process may be performed. The readout process comprises performing a furtherpolarization transfer process to swap the ensemble excited state back to the electron.For example, and as shown in Figure 8A, the polarization transfer process includesdriving the electron with a pulse 840 that is a two-photon Raman pulse. The electron can then be addressed with an incident optical pulse 860 to stimulate emission of a photon. For example, the readout 860 takes the form of a pulse resonantwith the |↓^ − |⇓↑↓^ trion frequency, meaning the |↓^ state is a bright state, The populationof the |↓^ state can thus be probed using the first laser 402. The population of the |↑^can instead be read out by performing an Rx(π) rotation prior to the readout pulse 860. After performance of the polarization transfer process 840, the electron may be in any quantum state formed of a superposition of the bare electron states. This superpositionmay be rotated back to the |↓^ state by an appropriately configured rotation pulse 850.For example, rotation ^^^ may be performed to rotate the state from |^^^ into |↓^ forreadout. However, in some examples the state of the register (and thus the electronafter process 840) will not be known and is to be measured. In which case, the rotation850 can be selected based on a desired decoding basis.In some embodiments, the confined qubit may be entangled with a photon by means ofa spin-photon entanglement process. In this process, a photon is generated that is entangled with the confined qubit. The quantum information in the confined qubit maysubsequently be transferred into the nuclear ensemble as a magnon, as describedabove. This process results in entanglement between the magnon in the nuclear ensemble and the photon. This process may be used in quantum information protocols, including a repeater protocol as described below. A spin-photon entanglement process may comprise addressing the confined qubit withoptical pulses (e.g. from the first laser 402 of Figure 4), resonant with the |↓^ − |⇓↑↓^transition. If the electron spin is initially prepared in the |↓^ state, a single laser pulse as14703377-1described above will populate the |⇓↑↓^ state, which will decay with equal probability tothe |↓^ state and |↑^ state, in each case emitting a photon with a different polarization(e.g. P1 and P2) and frequency and ^^), generating an entangled spin-photon Bellstate (|↓, ^^, ^^^ + |↑, ^^, ^^^) / √2. Entangled states generated by this process may beused, for example, in the quantum repeater applications to be described below. Apolarization or frequency measurement of the emitted photon will collapse the state to|↓^ or | ↑^.Alternatively, an arbitrary electronic spin state ^|↓^ + ^|↑^ may be entangled with anarbitrary number of emitted photons using a time-bin encoding. Here, an entangledphoton is generated by exciting the electron spin with an early pulse |^^ and a late pulse|^^, each resonant with the |↓^ − |⇓↑↓^ transition. Between the early pulse and the latepulse a ^ −rotation of the electron spin is performed, swapping the |↓^ and |↑^ states,resulting in an entangled spin-photon Bell state (^|↑^|^^ + ^|↓^|^^) / √2. Entangled statesgenerated by this process may be used, for example, in the quantum repeaterapplications to be described below. This alternative spin-photon entanglement protocolrequires the trion state to preferentially decay via the spin conserving the |↓^ − |⇓↑↓^transition. This can be achieved using a magnetic field aligned along the QD growth axis or by selectively enhancing a single optical transition with a cavity or waveguide structure. The pulse sequence described above may be repeated k times, leading to the emission of k photons and the generation of a spin multi-photon GHZ state, ^|↓^|^^⊗^) / √2. The above described spin-photon entanglement protocols are provided by way of example. Alternative spin-photon entanglement processes may be performed, and in each case leaving a single electron in the QD and emitting a single photon, the spin and photon being entangled with one another. In some embodiments, the readout process may include performing a spin-photon entanglement process to generate a photon entangled with the magnon within the quantum register. The photon may then be output for use in quantum information protocols. For example, the quantum register may be used to generate a plurality ofentangled photons in a graph state, as described below in connection with Figure 11.14703377-1 Figure 9 illustrates an entire quantum information protocol 900 in accordance with the present invention. The protocol includes a purification process 910 (also called a “cooling process”) to create a target Iztotmacrostate of the nuclear ensemble 20 of the QD 110. The target Iztotmacrostate has a total Iztotvalue locked to stable point and whereat least one of the atomic species within the QD 110 has a net Iz state that is a dark spinstate, and optionally where multiple atomic species within the QD110 have net Iz statesthat are dark spin states. The purification process 910 can be repeated multiple times until the target macrostate is obtained. The purification process is fully autonomous and does not require intermediate measurement to confirm the state of the system. The purification process may be repeated multiple times over a given purification timescale, which is long enough to allow for purification. After completion of an initial purification process (e.g. from a thermal state to a target macrostate), the purification process may only be repeated occasionally to maintain the nuclear ensemble in the purified state.The purification process 910 can include a feedback process 912 and a polarizationprocess 914 as described above. The feedback process can be performed on one ofthe plurality of atomic species, being an atomic species that is not used for storage of quantum information. Thus, the first atomic species can be driven to a macrostate that is not a dark state, providing flexibility in achieving a target net polarization without compromising the fidelity of a quantum state encoded into the nuclear ensemble. The feedback process may be repeated multiple times before the next polarization process is performed. The polarization process may comprise separate polarization processes each targeting any atomic species of the plurality of atomic species that is not addressed during the feedback stage. The polarization processes may be repeated multiple times before the next feedback process is performed. After the nuclear ensemble has been purified, an encoding process 920 is performed, as described above, followed by a readout process 930. After the readout has been completed, the process returns to the purification stage to re-purify the ensemble in preparation for further encoding. The encoding process 920 may comprise multiple encoding steps, wherein for each encoding step quantum information is encoded within a different nuclear sub-ensemble of the quantum dot. In this example, the decoding process 930 may comprise multiple readout steps, in which a readout is performed on each nuclear sub-ensemble. In some embodiments, quantum information may also be encoded within the confined qubit. 14703377-1 As mentioned above, the described examples are detailed by reference to a single electron as the confined qubit, and in alternative examples the confined qubit may be a multi-particle molecule, such as a multi-electron molecule. In this alternative, thequantum dot 110 is one of a plurality of quantum dots within the quantum register, whereeach quantum dot includes a confined electron, and the confined electrons are coupled across the multiple quantum dots via exchange interaction to form the molecule. The exchange interaction coupling of the spins of the multi-particle molecule result in a netspin state having two or more Sz states that functions as the qubit states |0^ and |1^. Forexample, singlet / triplet states may be formed by two paired electrons having one state S = 0 and three S = 1 states, with the S = 1 states quantized by Sz = 0 or ±1, or a doubletstate may be formed from three electrons, having a net spin of S = ½. In each case, themulti-electron state is coupled to the nuclear ensembles of all quantum dots forming part of the quantum register, with the above-described macrostate including all nuclei across all quantum dots to which the multi-electron molecule is coupled. The purification and polarization processes are performed as described above, resulting in a purified plurality of quantum dots. The encoding process is also performed as described above, resulting in a quantum state being encoded on a single magnon within one of the plurality of quantum dots, or alternatively delocalised among the plurality of quantum dots. The confined qubit may also be formed as a multi-hole molecule from confined holes across multiple quantum dots within a register which may be used as a quantum register in the same manner as described above for a register with a multi-electron molecule as the confined qubit. In embodiments described herein, the quantum register is deployed as part of a quantum repeater apparatus and addressed as part of a quantum repeater protocol. Figure 10 illustrates an example of a quantum repeater 1000. Quantum repeater 1000 includes aplurality of quantum registers 11-1 to 11-5, a plurality of Bell state measurement devices12-1 to 12-4. Each quantum register may be connected to one or more Bell statemeasurement devices by fiber optic cable or other photon-transmitting medium, or the quantum registers may be configured to transmit photons to each Bell statemeasurement device over free space. Each of the quantum registers 11-1 to 11-5 is aquantum register according to embodiments as described above. As illustrated forregisters 11-2 to 11-4, the register can include multiple qubits, which include the confinedqubit and each nuclear sub-ensemble within the nuclear ensemble. The quantum14703377-1repeater apparatus 1000 can be used to generate entanglement between two remoteparties according to a quantum repeater protocol. The described quantum repeater andquantum repeater protocol utilizes Bell states as the entanglement basis, but this is by way of example only; alternative entanglement state bases and measurement devices may be used depending on the quantum repeating protocol deployed. The quantum registers are provided in sequence such that each quantum register is separated from its neighbouring quantum registers by a distance and the first and last quantum registers in the sequence are remote from one another. While five quantum registers are shown, it will be understood that many more quantum registers may be provided to increase the separation between the first and last quantum registers in the series. The example quantum repeater protocol using the quantum repeater 1000 of Figure 10 includes a first memory entanglement operation. In the first memory entanglement operation, a spin-photon entangled state is generated, via an optical pulse directed atthe confined qubit of the first register 11-1, in which the first register 11-1 generates afirst photon 13-2 that is entangled with the confined qubit of register 11-1. The sameprocess is simultaneously performed at the second register 11-2 to generate a secondphoton 13-2 entangled with the confined qubit of the second register 11-2. The firstphoton 13-1 and second photon 13-2 are then directed toward the first Bell state measurement device 12-1. A measurement is performed in the Bell basis that destroys the first photon and second photon, but results in an entanglement between the electronin the first register 11-1 and the electron in the second register 11-2.In an example operation of the first memory entanglement operation, the first photon and the confined qubit of register 11-1 are generated to share a maximally entangled state, such as Bell state , where Q1 indicates theconfined qubit of the first register and P1 indicates the first photon. In this example, the second photon and the confined qubit of the second register are generated to share the same maximally entangled Bell . The initialstate of both confined spins and qubits is The Bell state measurement of the first and second photons may result in a detection of any one of the four Bell states with equal probability. Depending on what Bell state outcome 14703377-1is detected for the first and second photon, a different entangled state results betweenthe confined qubits of the first and second registers: In each case, after the Bell State Measurement, the confined qubits of the first and second register have established a maximally entangled state between themselves. Depending on the observed Bell state in the Bell State Measurement, one or more transformations may be performed on the confined qubit of the second quantum register to place the entangled state shared by the confined qubit into the original entangled state of the spin-photon pairs. The result of the Bell state measurement may be communicated by means of a classical channel to the controller (or computer system implementing the controller) of the second quantum register to control the light source apparatus to effect the transformations.Following this first entanglement generation, the quantum information within theentangled electron of the first register 11-1 may be transferred into nuclear ensemble of the first register 11-1 by means of an encoding process via polarization transfer as described above. The quantum information within the entangled electron of the second register 11-2 may be transferred into the nuclear ensemble of the second register 11-2 in the same manner. The nuclear ensembles of each quantum register thus store theentangled states for later use, with high coherence times. The transfer of the quantuminformation from the confined qubit of the second register to the nuclear ensemble of thesecond register frees the electron of the second register for use in a second memory entanglement operation that forms part of the repeater protocol. In the second memory entanglement operation, a spin-photon entangled state isgenerated, via an optical pulse directed at the confined qubit of the second register 11-2. The second register 11-2 generates a third photon 13-3 that is entangled with theconfined qubit of register 11-2. The same process is simultaneously performed at thethird register 11-3 to generate a fourth photon 13-4 entangled with the confined qubit ofthe third register 11-3. The third photon 13-3 and fourth photon 13-4 are then directed14703377-1toward the second Bell state measurement device 12-2. A measurement is performedin the Bell basis that destroys the third photon and fourth photon, but results in anentanglement between the electron in the second register 11-2 and the electron in thethird register 11-3. The same example process described above for the first memoryentanglement process may be performed for the second memory entanglement process. The second memory entanglement operation may be performed to generate an entangled state between the confined qubits of the second and third register such thatthe entangled state shared between the confined qubits of the second and third registeris the same entangled state shared by the confined qubits of the first and second register. For example, the result of the Bell state measurement in the first memory entanglement operation may be sent, via classical channel, to the second register and the third register and the second memory entanglement operation may be performed based on the received measurement. Following this second entanglement generation, the quantum information within theentangled electron of the second register 11-2 may be transferred into the nuclearensemble of the second register 11-2 by means of an encoding process via polarizationtransfer as described above, wherein the quantum information is transferred to a different nuclear sub-ensemble to the sub-ensemble currently storing the entangled quantum information generated following the first entanglement operation. Alternatively, no polarization transfer process is performed and the quantum information may be retainedwithin the confined qubit of the second register following the second memoryentanglement operation. The quantum information within the entangled electron of thethird register 11-3 may be transferred into a selected nuclear sub-ensemble of the thirdregister 11-3. The nuclear ensembles of each quantum register thus store the entangled states for later use, with high coherence times. The transfer of the quantum informationfrom the confined qubit of the third register to the nuclear ensemble of the third registerfrees the electron of the third register for use in a subsequent memory entanglement operation that forms part of the repeater protocol. The steps of the second memory entanglement operation, and the subsequent transferof entangled quantum information that results, is repeated for sequential quantumregisters to create a first sequence of entanglements 1010 between successive quantum registers. For example, as shown in Figure 10, a first qubit of register 11-1 is entangled with a first qubit of register 11-2, a second qubit of register 11-2 is entangled with a first 14703377-1 qubit of register 11-3, a second qubit of register 11-3 is entangled with a first qubit of register 11-4 and a second qubit of register 11-4 is entangled with a qubit of register 11- 5. As mentioned above, for each of registers 11-2, 11-3 and 11-4, the first and second qubits may each be two different nuclear sub-ensembles within the same quantum dot,or may be the confined qubit and a single atomic species within the same quantum dot.Each entangled state shared by each pair of entangled qubits may be the same maximally entangled state. For example, each pair may be entangled into the same oneof the four Bell states (which of the four Bell states does not matter, so long as the Bellstate is known; this may be achieved by classical communication channels between the components of the quantum repeater). The quantum repeater protocol 1000 further comprises performing a plurality of entanglement swapping operations, each entanglement swapping operation comprising performing a Bell state measurement. In a first entanglement swapping operation, a Bell State Measurement is performed on the two qubits within the second quantum register 11-2, and a Bell state measurement is performed on the two qubits within the fourth quantum register 11-4. This can be performed, for example, by performing a spin-photon entanglement process on each of the two qubits in the register to generate two photons, and performing a Bell state measurement on the two generated photons. In alternative examples, the entanglement may be performed using a CZ gate, which is beimplemented by using sqrt(SWAP) gates and single qubit rotations (where both CZ andsqrt(SWAP) gates are universal two-qubit gates related to each other by single qubit rotations). The sqrt(SWAP) operation is performed by stopping the above-describedSWAP operation half-way (i.e. a π / 2 rotation rather than a π rotation under the Hartmann-Hahn resonance condition). In this way, entanglement between the electron and nuclear spin register can be produced deterministically. Following the Bell state measurements of the first entanglement swapping operation, thequantum repeater is in a second entanglement sequence 1020, in which the qubit of thefirst register 11-1 is entangled with the first qubit of the third register 11-3, and the qubitof the fifth register 11-5 is entangled with the second qubit of the third register 11-3.In a second entanglement swapping operation of the plurality of entanglement swapping operations, a Bell State Measurement is performed on the two qubits within the second quantum register 11-3. Following the Bell state measurement of the second 14703377-1 entanglement swapping operation, the quantum repeater is in a third entanglementsequence 1030, in which the qubit of the first register 11-1 is entangled with the qubit ofthe fifth register 11-5.Each of the above-described memory entanglement operations and memory entanglement swapping operations have a finite probability of success. Thus, the entanglement swapping protocol comprises performing each memory entanglement operation and memory entanglement swapping operation multiple times until a Bell state measurement is successfully observed. If a Bell state measurement fails (e.g. between photons 13-3 and 13-4), the photon generation and Bell state measurement can simply be repeated. The entanglement between other registers (e.g.11-1 and the first register in 11-2) is unaffected, as their entangled state is stored in a memory. The high coherence times achieved by the quantum memories / registers described herein provide practical long-term storage, thereby facilitating more entanglement repetitions, and therefore a quantum repeater that is more practical and of higher performance. The above-described quantum repeater protocol is one example, but other repeater protocols may be deployed on a quantum repeater comprising a plurality of the quantum registers as described herein, in order to generate an entangled state shared betweentwo remotely located quantum registers. Due to the presence of a high coherence andhigh fidelity quantum memory, the quantum registers as described herein allow for practical and effective implementation of quantum repeater protocols, such as the example described above. In embodiments described herein, the quantum register may be used to generate multi- dimensional photonic cluster states. Multi-dimensional photonic cluster states are usefulin measurement-based quantum computing (MBQC), comprising a single qubitmeasurement and feedforward, in which the results from the single qubit measurement dictates the choice of measurement basis for the remaining qubits. Multi-dimensional photonic cluster states can also be deployed in all-photonic quantum repeaters for long- range quantum communication.Figure 11 illustrates an example embodiment for generation of a multi-dimensionalphotonic cluster state (graph state), in the form of a quantum circuit diagram of a graphstate generation protocol 1100. In this embodiment, a quantum register according to the 14703377-1 above described embodiments is used to generate multidimensional photonic cluster state. The graph state generation protocol 1100 comprises an initialization process. In the initialization process, the quantum dot 110 of the quantum register is prepared such that each of the sub-ensembles are prepared in a polarized ground state (or other dark state), labelled as |0^^and |0^^, in accordance with the embodiments described above (e.g. implementing purification protocol 910). The confined spin is prepared in a ground state |0^^(e.g. spin-up), for example by optical pumping. After the initialization process, the graph state generation protocol comprises a preparation process 1100, in which each of the confined spin, and each nuclear sub-ensemble is prepared in an identical superposition state of a ground state and excitedstate. This is performed by sequential operation of single qubit gates on the confined spin and SWAP gates between the nuclear sub-ensemble and the confined spin. The single qubit gate comprises performing a Ry rotation by addressing the confined spin with a microwave pulse, and the SWAP gates are performed by a polarization transfer process via the hyperfine interaction as described above. For example, a first Ry rotation is performed on the confined spin to generate the superposition state. A SWAP gate is performed to transfer the ground state of the first nuclear sub-ensemble A to the confined spin, following which a further rotation Ry is performed to rotate the state into the superposition state. The ground state of the second nuclear sub-ensemble B is thentransferred to the confined spin, following which a rotation Ry is performed to rotate thestate into the superposition state. Finally, a SWAP gate is performed between thesecond nuclear sub-ensemble B and the confined spin. The sequence of Ry gates andSWAP gates are examples only, and other arrangements may be provided to achieve the same result. Following the preparation process 1100, one or more graph state generation processes 1120 are performed. Each graph state generation process 1120 comprises an entanglement process 1130, a photon emission process 1140 and a rotation process 1150. The entanglement process 1130 comprises performing a first hyperfine-enabled controlled-phase gate (CZ) between the confined spin and the first nuclear sub-ensemble 14703377-1 A, and a second hyperfine-enabled controlled-phase gate (CZ) between the confined spin and the second nuclear sub-ensemble B. This results in the state encoded in the first nuclear sub-ensemble being entangled with the state encoded in the second nuclear sub-ensemble. For example, the controlled-phase gate may be implemented by means of two spin-photon entanglement processes followed by a Bell State Measurement, where a first spin-photon entanglement process is performed on the confined qubit, generating a first photon, followed by a SWAP gate to swap the confined qubit state and the state of a first nuclear sub-ensemble, which is followed by a further spin-photon entanglement process to generate a second photon entangled with the magnon of the first nuclear sub-ensemble. A Bell State Measurement is performed on the first and second photons, resulting in an entanglement between the confined qubit and the state of the first nuclear sub-ensemble. A further SWAP gate may then be performed to swap the states of the confined qubit and the first nuclear sub-ensemble. An identical entanglement process may then be performed to entangle the confined qubit and the magnon of the second nuclear sub-ensemble.In alternative examples, the CZ gate maybe implemented by using sqrt(SWAP) gates and single qubit rotations (where both CZand sqrt(SWAP) gates are universal two-qubit gates related to each other by single qubit rotations). The sqrt(SWAP) operation is performed by stopping the above-describedSWAP operation half-way (i.e. a π / 2 rotation rather than a π rotation under the Hartmann-Hahn resonance condition). In this way, entanglement between the electron and nuclear spin register can be produced deterministically The photon emission process 1140 comprises performing a plurality of spin-photon entanglement processes on the confined spin, and a plurality of SWAP gates to transfer the state of each nuclear sub-ensemble to the confined spin prior to each spin-photon entanglement process. As illustrated in Figure 11, the photon emission process may comprise, in sequence, a SWAP gate between the confined spin and first nuclear sub- ensemble, a spin-photon entanglement operation of the confined spin, a SWAP gate between the confined spin and first nuclear sub-ensemble, a spin-photon entanglement operation of the confined spin, a SWAP gate between the confined spin and second nuclear sub-ensemble, a spin-photon entanglement operation of the confined spin and finally a SWAP gate between the confined spin and second nuclear sub-ensemble. Under this operation, the quantum dot 110 emits a multi-qubit photonic state 1160 in which the first photon is entangled with the second photon and with the confined spin, the second photon is entangled with the third photon and the first nuclear sub-ensemble, 14703377-1 and the third photon is additionally entangled with the second nuclear sub-ensemble. In this way, a two-dimensional graph state is produced where three photons, a confined spin, and two sub-ensembles are in an entangled graph state. Each repetition of the entanglement process and the photon emission described above adds another three photons to the entangled graph state. The generation process can be ended by measuring the state of the confined spin, and of the two sub-ensembles, as made possible by SWAP gates, leaving behind a purely photonic entangled state which together with the information obtained from measuring the spins constitute a resource state for MBQC. The sequence of gates and photon emission processes are by way of example only, and alternative sequences may be deployed to generate a series of photons. The rotation process 1150 is the same as preparation process 1110, and provided to regenerate the plurality of identical superposition states encoded on each of the nuclear sub-ensembles and the confined spin. The graph state generation protocol may comprise more than one graph state generation process 1120 in sequence. That is, after performance of one graph state generation process, the protocol immediately performs another entanglement process 1130, another photon emission process 1140 and another rotation process 1150, which results in an additional 3 entangled photons being output by the quantum dot. In some embodiments, M sequential repetitions of the graph state generation process are performed, resulting in M groups of three entangled pulses. Finally, a measurement process 1170 is performed on the confined spin and nuclear sub-ensembles in the z-basis, which results in a purely photonic cluster state of 3 x M.Figure 11 illustrates a quantum register in which two qubit sub-ensembles, A and B,together with the electron (or other confined qubit), S, are used to generate a 3 x M cluster state, but embodiments herein are not limited to. For example, a single ensemble A may be used, which is used to generate a 2 x M cluster state, or a quantum dot havingN atomic species (as described above) may be used to generate a (N + 1) x M clusterstate. 14703377-1 While certain embodiments have been described, these embodiments have been presented by way of example only and are not intended to limit the scope of the invention. Indeed, the novel methods, devices and systems described herein may be embodied in a variety of forms; furthermore, various omissions, substitutions and changes in the form of the methods and systems described herein may be made without departing from the scope of the invention as claimed. 14703377-1

Claims

CLAIMS:

1. A method of encoding quantum information into a quantum dot in a magneticfield, the quantum dot comprising a confined qubit and a nuclear ensemble, the confinedqubit comprising a confined electron or a confined hole, the nuclear ensemble comprisinga first atomic species and a second atomic species, the method comprising the steps of:(a) adjusting the net polarisation of the nuclear ensemble comprising sensingthe net polarization of the nuclear ensemble and performing a first polarization transferprocess on the confined qubit and the first atomic species to adjust the net polarisationfrom the sensed net polarization to a target net polarization; (b) preparing a target state of the nuclear ensemble comprising performingone or more second polarization transfer processes on the confined qubit and secondatomic species to adjust the total polarisation of the nuclei of second atomic species toward a first target polarisation; (c) encoding first quantum information into the second atomic speciescomprising performing a third polarization transfer process on the confined qubit andsecond atomic species.

2. The method of any preceding claim, further comprising performing a readoutprocess on the second atomic species comprising performing a polarization transferprocess between the confined qubit and the second atomic species to transfer theencoded quantum information from the second atomic species to the confined qubit; andaddressing the confined qubit with an optical pulse to generate an output photon.

3. The method of claim 1 or claim 2, wherein the nuclear ensemble of the quantumdot further comprises a third atomic species, and wherein the preparing a target statecomprises performing one or more third polarization transfer processes on the confinedqubit and the third atomic species to adjust the total polarisation of the nuclei of the thirdatomic species toward a second target polarisation.

4. The method of claim 3, wherein the first atomic species is As, the second atomicspecies is Ga71and the third atomic species is Ga69. 14703377-15. The method of claim 3 or claim 4, further comprising encoding second quantuminformation into the third atomic species comprising performing a polarization transferprocess on the confined qubit and third atomic species.

6. The method of claim 5, further comprising performing a readout process on thesecond atomic species comprising performing a polarization transfer process betweenthe confined qubit and the second atomic species to transfer the encoded quantuminformation from the second atomic species to the confined qubit; and addressing theconfined qubit with an optical pulse to generate an output photon.

7. The method of claim 6, wherein the encoding process and the readout processare separated by a storage time, and wherein the method further comprises inverting thepolarization state of the confined qubit half way through the storage time.

8. The method of any one of claims 3 – 7, wherein steps (a) and (b) are repeated toproduce a purified macrostate of the nuclear ensemble, wherein the purified macrostate has a net polarization of the nuclear ensemble, the second atomic species having thefirst target polarization and the third atomic species having the second target polarization.

9. The method of any preceding claim, wherein each first polarization transferprocess comprises addressing the confined qubit with a light portion to drive the confinedqubit in resonance with the Larmor frequency of the first atomic species, and each of thesecond and third polarization transfer process comprises addressing the confined qubitwith a light portion to drive the confined qubit in resonance with the Larmor frequency ofthe second atomic species.

10. The method of claim 9, further comprising, wherein each polarization transferprocess comprises: driving the confined qubit with a coherent microwave field at a Rabi frequency Ωand having a frequency detuned by δ from the confined qubit Larmor frequency suchthat √Ω^ + ^^ is equal to the Larmor frequency of the respective atomic species; orperforming a two-photon Raman process at a Rabi frequency Ω and having afrequency difference detuned by δ from the confined qubit Larmor frequency such that√Ω^ + ^^ is equal to the Larmor frequency of the respective atomic species.14703377-111. The method of claim 9 or claim 10, wherein each polarization transfer processfurther comprises addressing the confined qubit with a Rabi pulse having a frequencyequal to a Larmor frequency of the confined qubit to perform a rotation of the confinedqubit to a target state.

12. The method of any preceding claim, wherein sensing the net polarisation of thenuclear ensemble comprises performing a Ramsey interferometry protocol,wherein, optionally, the Ramsey interferometry protocol includes addressing theconfined qubit with a π / 2 pulse to perform a rotation, followed by a sensing period inwhich the confined qubit is not addressed.

13. The method of any preceding claim, further comprising initializing the confinedqubit to an eigenstate in the Zeeman basis, wherein optionally the initializing of theconfined qubit is performed at one or more of: (i) before step (a); (ii) after step (a); (iii)after step (b); and (iv) after step (c), wherein, optionally, the initializing the confined qubit comprising performing an incoherent optical pumping process at a frequency equal to a trion excitation frequency of the quantum dot.

14. The method of any preceding claim, further comprising applying the magneticfield at a non-zero angle with respect of a crystallographic axis of the quantum dot; and / or applying strain to the quantum dot.

15. The method of any preceding claim, wherein the encoding further comprisesperforming a spin rotation on the confined qubit to place the confined qubit into a first quantum state comprising the first quantum information.

16. The method of any preceding claim, further comprising performing a subsequentspin rotation on the confined qubit, after the encoding of the first quantum informationinto the second atomic species, to place the confined qubit into a second quantum statecomprising second quantum information; performing an entanglement process to entangle the quantum state of the secondatomic species comprising the first quantum information and the second quantum state;and performing a first spin-photon entanglement process to generate a first photonentangled with the quantum state comprising the first quantum information and14703377-1performing a second spin-photon entanglement process to generate a second photon entangled with the second quantum state.

17. A quantum register, comprising:a quantum dot in a magnetic field, the quantum dot comprising a confined qubitand a nuclear ensemble, the confined qubit being a confined electron or a confined hole,the nuclear ensemble comprising a first atomic species and a second atomic species; and a light source apparatus, the light source apparatus configured to perform amethod according to any one of claims 1 – 15.

18. The quantum register of claim 17, further comprisinga magnet configured to apply the magnetic field, wherein the magnet is configured to applying the magnetic field at a non-zero angle with respect of a crystallographic axis of the quantum dot; and / or a pressure-imparting device configured to apply strain to the quantum dot.

19. A quantum repeater comprising:a plurality of quantum registers, each quantum register being a quantum registeraccording to claim 17 or claim 18.

20. The quantum repeater of claim 19, wherein the plurality of quantum registerscomprises a first quantum register, second quantum register, third quantum register andfourth quantum register, and wherein the quantum repeater is configured to perform aquantum repeater protocol comprising: generating a first photon that is entangled with the confined qubit of the firstquantum register and generating a second photon that is entangled with the confinedqubit of the second quantum register;performing a first Bell state measurement of the first photon and the secondphoton to generate an entanglement between the confined qubit of the first quantumregister and the confined qubit of the second quantum register;after performing the first Bell state measurement, performing a polarization transfer process on the confined qubit of the first quantum register and an atomic speciesof the first quantum register to place the atomic species of the first quantum register in afirst quantum state, and performing a polarization transfer process on the confined qubit 14703377-1of the second quantum register and an atomic species of the second quantum registersuch that the atomic species of the second quantum register is in a second quantum state; generating a third photon that is entangled with the confined qubit of the secondquantum register and generating a fourth photon that is entangled with the confined qubit of the third quantum register; performing a second Bell state measurement of the third photon and the fourth photon to generate an entanglement between the confined qubit of the second quantum register and the confined qubit of the third quantum register; performing a spin-photon entanglement process to generate a fifth photon that isentangled with the quantum state of the atomic species of the second quantum registerand performing a spin-photon entanglement process to generate a sixth photon that isentangled with the quantum state of the confined qubit of the second quantum register;and performing a third Bell state measurement of the fifth photon and the sixth photon to generate an entanglement between the first quantum register and the third quantum register. 14703377-1

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