Quantum systems and methods

Abstract

1. A method for performing a quantum gate operation using a quantum system including two or more neutral atoms, each atom of the two or more neutral atoms configured to transition between atomic states including a first hyperfine ground state of the atom, a second hyperfine ground state of the atom, a Rydberg state, and at least one intermediate excited state, the quantum system further including an interaction between the Rydberg states in the two or more neutral atoms, the method comprising: generating a pulse sequence; and providing the generated pulse sequence to the two or more neutral atoms to transition the atoms between the atomic states, the pulse sequence taking into account at least a portion of the hyperfine structure of the at least one intermediate atomic state.

Description

[Technical field]

[0001] The present invention relates to quantum computing methods and apparatus, and in particular to methods for performing quantum gate operations. [Background technology]

[0002] Quantum computing devices for performing quantum information processing can be based on quantum circuit principles, where quantum bits or "qubits" encode quantum information. Similar to digital circuits, these quantum circuits can use quantum logic gates (also called quantum gates) as building blocks. A variety of physical quantum systems or phenomena can be used to implement such quantum gates.

[0003] An example of a physical quantum system that can be used to implement quantum gates is the neutral atom. Indeed, over the past decade, trapped neutral atoms have emerged as one of the most promising platforms for quantum information processing. It has been demonstrated that reliable filling, initialization and readout of single atoms in configurable 1D, 2D and 3D optical arrays formed by up to several hundred sites can be achieved without fundamental limitations for further upscaling.

[0004] [Problem to be solved by the invention] Neutral atomic qubits can mediate entanglement with Rydberg states. It is known to control quantum gates implemented using such Rydberg quantum systems with laser pulses. For example, in Non-Patent Document 1, two separate approaches to perform high-fidelity gates using Rydberg quantum systems are outlined. One of these approaches is based on adiabatic rapid passage (ARP) with analysis based on single-photon transitions. In this approach, optimized analysis pulses were reported to yield Bell-state fidelity F>0.999 for one-photon transition schemes. Such approaches in alkali atoms may cause problems such as the need to use stable high-power ultraviolet lasers and / or the presence of significant recoil backscattering. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] "Symmetric Rydberg controlledZ gates with adiabatic pulses" by Saffman et.al (Physical Review A 101, 2021) Summary of the Invention [Means for solving the problem]

[0006] According to a first aspect, there is provided a method of performing a quantum gate operation using a quantum system including two or more neutral atoms, wherein each atom of the two or more neutral atoms is configured to transition between atomic states including a first hyperfine ground state of the atom, a second hyperfine ground state of the atom, a Rydberg state, and at least one intermediate excited state, the quantum system further including an interaction between the Rydberg states in the two or more neutral atoms, and the method comprises the steps of generating a pulse sequence and supplying the generated pulse sequence to the two or more neutral atoms to transition the atoms between the atomic states, wherein the pulse sequence takes into account at least a portion of the hyperfine structure of the at least one intermediate atomic state.

[0007] The pulse sequence may be generated according to a two-photon excitation protocol. The at least one intermediate state includes at least one hyperfine component state. The at least one intermediate state may include a complete hyperfine structure of the intermediate state. The pulse sequence may include at least one pulse. The at least one pulse of the pulse sequence may include at least one property that takes into account at least a portion, optionally all, of the complete hyperfine structure of the at least one intermediate state.

[0008] The method may further comprise the step of preparing a quantum state. The prepared quantum state may be an entangled quantum state. The quantum gate may be a CNOT gate. The quantum gate may be a controlled phase gate. The quantum information may be encoded in first and second hyperfine basis states of the two or more neutral atoms. The quantum gate operation may be a controlled quantum gate operation. The pulse sequence may be designed to include a complete hyperfine structure or at least a portion of the hyperfine structure of the intermediate atomic state.

[0009] At least one intermediate state of each atom has the atomic number, total angular momentum quantum number J e and a fixed angular momentum quantum number I. At least one hyperfine component of the intermediate state may be represented by a set f eSome f in e and a set f e teeth,

number

[0010] The one or more pulses of the pulse sequence may be delivered to each atom of the two or more neutral atoms substantially simultaneously. The one or more pulses may be applied symmetrically to the two or more neutral atoms. The one or more pulses may be delivered to each atom of the two or more neutral atoms such that the one or more pulses are incident on each atom of the two or more neutral atoms substantially simultaneously. The two or more neutral atoms may be nearest neighbor atoms.

[0011] The two or more neutral atoms may include at least a first neutral atom and a second neutral atom configured to transition between said atomic states. The two or more neutral atoms may include a first neutral atom and a second neutral atom configured to transition between said atomic states.

[0012] The first neutral atom may correspond to or represent a first quantum qubit. The second neutral atom may correspond to or represent a second quantum qubit. The first quantum qubit may be a control qubit and the second quantum qubit may be a target qubit. The first and second hyperfine ground states in the first and second neutral atoms may correspond to the first and second computational states. The first and second quantum qubits may be encoded in the hyperfine ground states.

[0013] The two or more neutral atoms may include a third neutral atom configured to transition between a corresponding set of atomic states, and the generated pulse sequence is provided to each of the first, second, and third neutral atoms. The third neutral atom may correspond to or represent a third quantum qubit.

[0014] The two or more neutral atoms may include a third and a fourth neutral atom configured to transition between a corresponding set of atomic states, and the generated pulse sequence is provided to each of the first, second, third and fourth neutral atoms. The third and fourth neutral atoms may correspond to or represent a third and fourth quantum qubit. The two or more neutral atoms may include more than four neutral atoms. The two or more neutral atoms may include a plurality of neutral atoms corresponding to or representing a plurality of quantum qubits.

[0015] The first and second hyperfine ground states of the two or more neutral atoms may correspond to the first and second computational states. The first and second quantum qubits may be encoded in the hyperfine ground states.

[0016] The quantum gate operation may correspond to an evolution of at least two neutral atoms between said atomic states. The pulse sequence may include at least one property based on a calculation or application of a model of the quantum system including an effect of at least one hyperfine component of at least one intermediate state on said evolution. The quantum gate operation may correspond to at least two neutral atoms transitioning between a sequence of atomic states. The at least one property may be based on a calculation or application of a model of the quantum system including an effect of at least one hyperfine component of at least one intermediate state in a sequence of states. The at least one property may be based on a calculation or application of a model of the quantum system including an effect of at least one hyperfine component of at least one intermediate state on the dynamics of the quantum system.

[0017] At least one property may be determined using a model of the quantum system, the model including a portion including all effects of at least one hyperfine component, optionally at least one intermediate state. The model may include a portion that models the influence of at least one hyperfine component of at least one intermediate state on transitions between atomic states. The portion of the model may include elements or terms of mathematical objects.

[0018] The model may include a dynamical model of the quantum system. The model may represent a relationship between at least one parameter of the pulse sequence and interactions between said atomic states. The dynamical model may take into account dynamical properties of the quantum system, including hyperfine components of intermediate states.

[0019] The quantum gate operations may correspond to a desired progression between atomic states in the quantum system. At least one property of the pulse sequence may provide the desired progression between atomic states in the quantum system. The dynamical model may be used to calculate at least one property of the pulse sequence that provides the desired progression of the quantum system.

[0020] The quantum gate operation may correspond to a desired evolution of an atomic state of the quantum system via an atomic transition. The at least one pulse may include at least one characteristic such that the pulse sequence results in a desired evolution of the atomic state. The method may include providing the generated pulse sequence to two or more neutral atoms to distribute and / or transition an electron population between at least a hyperfine ground state and an excited Rydberg state via a hyperfine component of the intermediate state. The pulse sequence may include providing the generated pulse sequence to transition an electron population to a desired quantum state via a hyperfine component of at least one intermediate state.

[0021] The model may include at least one portion based on frequency splitting of hyperfine states to vary at least one or more characteristics of the pulse sequence by including at least one term or portion. The dynamic model may include at least one term or portion that models the dynamics of the transition from the ground state to the Rydberg state via at least one hyperfine component of at least one intermediate state.

[0022] The at least one characteristic includes at least one of a shape, a size, an amplitude, a frequency, or a duration of the pulse.

[0023] The method may further include generating the pulse sequence having the at least one characteristic by selecting and / or modifying operating parameters of a pulse generator.

[0024] The pulse sequence may be generated by a pulse generator. The pulse generator may include one or more lasers, preferably at least two lasers. The pulse generator may include associated optical devices, such as steering optics or optical modulation devices. Selecting and / or modifying operating parameters of the pulse generator may include selecting and / or modifying operating parameters of the lasers and / or associated optical devices and / or optical modulation devices.

[0025] At least one characteristic of the pulse sequence may be represented by one or more pulse parameters, and the method comprises obtaining values ​​of the one or more pulse parameters based on said calculation or applying a model.

[0026] The pulse sequence may include one or more adiabatic pulses. The pulse sequence may include an adiabatic rapid pulse. The pulse sequence may include a chirped laser pulse characterized by a change in frequency. The pulse sequence may include performing an adiabatic sweep across the frequency. Generating the pulse sequence may include varying at least one of the frequency and / or intensity of the laser.

[0027] The calculation or application of the model may consider quantum transitions from hyperfine ground states of two or more neutral atoms to respective Rydberg states of those neutral atoms that include a superposition of all allowed transitions to hyperfine components of at least one intermediate atomic state, which may be decomposed into a plurality of intermediate hyperfine states.

[0028] At least one pulse of the sequence of pulses may be characterized by a frequency detuning curve, the frequency detuning curve including at least one compensation feature for compensating for a perturbation effect on one or more hyperfine components of the intermediate state. The perturbation effect may be a result of application of an external laser. The perturbation effect may be an AC Stark shift. The compensation feature may include at least one of a discontinuity, a rate of change, an adjustment in the rate of change, a maximum, a minimum or turning point, a peak and / or a minimum.

[0029] The shape of the detuning curve may be constrained by an adiabatic condition. The detuning curve may have features that compensate for the AC shift such that the effective two-photon detuning is smooth. The detuning curve may be selected such that the effective two-photon detuning is approximately smooth.

[0030] Generating the pulse sequence may comprise controlling the at least one laser to generate at least one chirped excitation pulse, the chirped excitation pulse including a sweep over a range of frequencies that includes at least a two-photon resonance frequency that is between the second hyperfine ground state and the Rydberg state.

[0031] Generating the pulse sequence comprises generating a first pulse including a range of frequencies sufficient to non-resonantly couple at least one intermediate atomic state with the Rydberg state, and generating a second pulse including a sweep over a range of frequencies including a resonant frequency between a first hyperfine ground state and the Rydberg state.

[0032] The range of frequencies may depend on the effective linewidth of the two-photon excitation. The pulse sequence may include a two-photon adiabatic rapid passage (ARP) protocol.

[0033] The quantum system may be represented by a first model having a first number of dimensions, and the pulse sequence is generated as part of a time-dependent detuning process over a sufficiently large frequency range such that the quantum system can be effectively represented by a second model having a second, lower number of dimensions.

[0034] The pulse sequence may correspond to a detuning of at least one intermediate state that is sufficiently large to allow an effective two-level description of the quantum system to be obtained by adiabatic removal of the intermediate state. The pulse sequence may be such that the detuning of the at least one intermediate state has a value approximately greater than the Rabi frequency between the ground state and the at least one intermediate state. The pulse sequence may be such that the at least one intermediate state is resonantly far enough apart to allow removal of the intermediate state via adiabatic removal.

[0035] The detuning process may be such that the quantum system can be characterized by a single effective Rabi frequency and a single detuning parameter.

[0036] The quantum system may be a three-level quantum system that can be effectively described using an effective Rabi frequency and a two-photon detuning. The method may include controlling one or more lasers to produce the desired variation in these quantities.

[0037] The pulse sequence may be characterized by a time-dependent change in at least an effective Rabi frequency and a two-photon detuning parameter. The range of the effective Rabi frequency and the two-photon detuning parameter may be constrained by one or more adiabatic conditions.

[0038] The method may further comprise the step of performing a further modulation on the generated pulse sequence.

[0039] Further modulation may be based on quantum optimal control processes.

[0040] The further modulation may include varying at least one characteristic of at least one pulse in the pulse sequence. The at least one characteristic may include pulse shape, amplitude, intensity, frequency and duration. The further modulation may include modulating the time-dependent change of the single effective Rabi frequency and the single detuning parameter by varying the pulse parameters. The method may further comprise determining at least one characteristic or parameter of the pulse sequence based on a calculation or model that takes into account the complete hyperfine structure of at least one intermediate atomic state, and further modulating the determined at least one pulse parameter based on an optimal quantum control process.

[0041] The optimal quantum control process may comprise obtaining pulse parameters that optimize a function representing a quantum gate operation. The optimal pulse parameters may be determined by performing a numerical optimization process to find the optimal parameters. The numerical optimization process may comprise applying a numerical solver to find the values ​​of the pulse parameters. The optimal quantum control process may comprise obtaining the pulse parameters by numerically optimizing parameters of an envelope function expanded as a sum of orthogonal functions. The optimized parameters may correspond to parameters representing at least one characteristic including shape, size, amplitude, frequency, duration, Rabi frequency and detuning. The optimal parameters may be based on a Fourier expansion control.

[0042] 10. The method of any preceding claim, wherein the generated pulse sequence comprises a first excitation pulse and a second excitation pulse, the first excitation pulse comprising a first continuous wave laser light and the second excitation pulse comprising a second continuous wave laser light.

[0043] The transitions between atomic states may involve Rabi oscillations.

[0044] The method may further include symmetrically providing the generated pulse sequence to two or more neutral atoms.The method may include symmetrically providing the generated pulse sequence to each of the two or more neutral atoms.

[0045] The two or more neutral atoms may include alkali atoms.

[0046] The two or more neutral atoms may include one of sodium (Na), rubidium (Rb), cesium (Cs), and potassium (K) atoms.

[0047] The atomic state may be selected based on one or more laser parameters, such as the linewidth and / or the maximum available laser power. The atomic state may be selected based on at least one of the laser operating parameters, the type of neutral atom, and the configuration of the neutral atom.

[0048] The method may further comprise maintaining the quantum system at a temperature approaching zero Kelvin. The quantum system may be maintained at a temperature such that the product of the Boltzmann constant and the temperature is lower than any relevant energy scale of the quantum system.

[0049] The generated pulse sequence may have energies based on the energy separation of the ground hyperfine level, the intermediate state and the Rydberg state, with a selected detuning value imposed.

[0050] The method may comprise applying a single qubit rotation as part of a pulse sequence. The method may comprise applying a single qubit rotation in addition to the pulse sequence. The pulse sequence may be part of a two-photon excitation scheme further comprising applying a global phase rotation.

[0051] Rydberg interactions between the Rydberg states of two or more neutral atoms can prevent the simultaneous excitation of two or more neutral atoms into their respective Rydberg states.

[0052] The quantum gate operation may include preparing an entangled quantum state, which may be provided as part of a quantum gate protocol.

[0053] One or more pulses of the pulse sequence may have a pulse duration in the range of 1 to 1000 microseconds.

[0054] The pulse sequence may be generated by first and second lasers of a pulse generator. The first and second lasers may have a maximum laser power in the range of 5 mW to 1000 mW, optionally in the range of 5 mW to 500 mW, optionally in the range of 5 mW to 300 mW. The first and second lasers may have a wavelength in the range of 300 nm to 1500 nm.

[0055] According to a second aspect, a quantum computing device is provided, the quantum computing device comprising: a quantum system including two or more neutral atoms, each atom of the two or more neutral atoms configured to transition between atomic states including a second hyperfine ground state of the atom, a Rydberg state, and at least one intermediate atomic state, the quantum system further including an interaction between the Rydberg states in the two or more neutral atoms; and a pulse generator configured to generate a pulse sequence and supply the generated pulse sequence to the two or more neutral atoms to transition the atoms between the atomic states, the pulse sequence including at least one pulse having a property that takes into account at least a portion of the hyperfine structure of the at least one intermediate atomic state.

[0056] The pulse generator may comprise at least one pulse source. The pulse generator may comprise first and second pulse sources. The first and second pulse sources may comprise first and second lasers, respectively. The quantum computing device may comprise a controller for controlling the excitation pulse generator.

[0057] According to a third aspect, there is provided a method comprising performing a calculation to determine a pulse sequence for a quantum system, the determined pulse sequence being such that a desired quantum gate operation is obtained, the quantum system comprising two or more neutral atoms, the two or more neutral atoms configured to transition between atomic states comprising a first hyperfine ground state of the atoms, a second hyperfine ground state of the atoms, a Rydberg state and at least one intermediate excited state, the quantum system further comprising an interaction between the Rydberg states in the two or more neutral atoms, and the calculation taking into account at least a portion of the hyperfine structure of the at least one intermediate state. The method may further comprise storing pulse sequence data representative of the determined pulse sequence.

[0058] The method may further comprise acquiring pulse sequence data and generating the determined pulse sequence using the acquired pulse sequence data.

[0059] The calculation may include using or applying a model of the quantum system. The calculation may include determining at least one property of at least one pulse of the pulse sequence. The model may comprise a portion including an effect of at least one hyperfine component of an intermediate state on the at least one property.

[0060] According to a fourth aspect, there is provided a data processing apparatus comprising a processor configured to perform the method of the third aspect.

[0061] According to a fifth aspect, there is provided a non-transitory computer-readable medium comprising instructions operable by a processor to perform the method of the third aspect.

[0062] According to a sixth aspect, there is provided a method of performing a quantum gate operation using a quantum system including two or more neutral atoms, wherein each atom in the two or more neutral atoms is configured to transition between atomic states including a first hyperfine ground state of the atom, a second hyperfine ground state of the atom, a Rydberg state, and at least one intermediate excited state, and the quantum system further includes an interaction between the Rydberg states in the two or more neutral atoms. The quantum gate operation may correspond to a desired evolution of the quantum system transition between the atomic states. The method further includes acquiring pulse sequence data representative of a pulse sequence, the pulse sequence data being based on a calculation using a model of the quantum system, the model including at least one portion representing the behavior and / or effect of at least one hyperfine component of the at least one intermediate state on the dynamics of the quantum system, and the pulse sequence data including values ​​of an effective Rabi frequency and a two-photon detuning frequency that results in a desired evolution of the quantum system. The method may further include generating a pulse sequence according to the acquired pulse sequence data, and supplying the generated pulse sequence to the two or more neutral atoms.

[0063] Features in one embodiment may be provided as features in any other embodiment, if desired. For example, method features may be provided as apparatus features, and vice versa. Any feature in one embodiment may be provided in combination with one or more of any suitable features in any other embodiment.

[0064] Various aspects of the present invention will now be described, by way of example only, with reference to the accompanying drawings, in which: [Brief description of the drawings]

[0065] [Figure 1] FIG. 1 is a schematic diagram of a quantum computing device. [Figure 2a] A three-level energy level scheme is shown. [Figure 2b]The hyperfine components of intermediate states in a three-level energy level scheme are shown. [Diagram 3] 3a-3d show a first pulse sequence of a two-photon excitation protocol, according to one embodiment. [Figure 4] 4a-d show a second pulse sequence of a two-photon excitation protocol according to a further embodiment. [Diagram 5] 1 illustrates a further quantum computing device; [Figure 6a] 1 illustrates an exemplary qubit configuration. [Figure 6b] 1 illustrates an exemplary qubit configuration. [Figure 6c] 1 illustrates an exemplary qubit configuration. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0066] The embodiments described below describe adiabatic rapid passage (ARP) based gates for implementing two or more qubit quantum gates for the two-photon transition regime in neutral atoms. A neutral atom is any atom that is uncharged. Suitable neutral atoms include alkali atoms, such as sodium (Na), rubidium (Rb), cesium (Cs), and potassium (K) atoms. For the purposes of the following description, suitable neutral atoms are neutral atoms that can be excited to a Rydberg atomic state (one or more electrons have a high quantum number n, e.g., a quantum number n greater than 50). Below, a scheme is described for generating entanglement between two or more alkali atomic qubits excited to a Rydberg level through a two-photon process using ARP pulses.

[0067] By way of background, in its original form, ARP was designed to coherently transition populations between states of a two-level system by adiabatically sweeping the Rabi frequency (denoted by Ω(t)) and detuning (denoted by δ(t)) following the eigenstates of a two-level Hamiltonian. The method described below uses a multi-level ladder system in which the detuning of the intermediate states is large enough to allow an efficient two-level description by adiabatic removal of the intermediate states.

[0068] In the described embodiment, the method below incorporates precise values ​​of the atomic parameters of the neutral atoms (cesium atoms are used in the described embodiment) and also takes into account the complete hyperfine structure of the intermediate states. The method described below is presented for comparison with the best currently available two-qubit gates. The method described below achieves Bell state fidelity F of

number

[0069] In the following, methods of performing quantum gate operations are described, it being understood that such methods may include preparing a quantum state, for example an entangled quantum state.

[0070] FIG. 1 shows a quantum computing device 10 having an excitation source 12, a quantum gate 14, a controller 16 and a readout module 18. The quantum computing device 10 is configured to perform a quantum gate operation on the quantum gate 14. The quantum gate 14 may also be referred to as a quantum system or a part of a quantum system. In this embodiment, the quantum gate is a controlled phase gate, but it will be understood that other gates may be implemented, for example, a CNOT gate. The following method is described with reference to a controlled phase gate, but it will be understood that it may be possible to implement other types of gates by adding a single qubit rotation. For example, a controlled phase gate is considered as a basic quantum gate, but a CNOT gate is provided by applying a half phase pulse before and a half phase pulse after the described pulse to the target qubit. These additional qubit rotations may be imparted by another source, for example, an additional laser.

[0071] It will be appreciated that Figure 1 is presented as a schematic diagram of a portion of a quantum computing device 10 for purposes of illustrating quantum gate operations. It will be appreciated that the concepts described below can be scaled up and implemented as a quantum computer in a number of different ways. An exemplary implementation of a quantum computer based on the quantum gate operations described below is provided with reference to Figure 5.

[0072] Quantum gate 14 comprises neutral atoms which correspond to or represent qubits. In this embodiment, quantum gate 14 has two qubits as described below, such that quantum gate 14 has two neutral atoms which correspond to first and second quantum qubits. Although this embodiment relates to a quantum gate 14 having two neutral atoms providing two qubits, it will be understood that quantum gate 14 may have more than two neutral atoms.

[0073] The apparatus 10 includes a controller 16. The controller 16 controls the excitation source 12. Thus, the controller 16 provides control of the quantum gate 14. More specifically, the excitation source is controlled to generate a pulse sequence according to a two-photon excitation scheme. Implementing the two-photon excitation scheme includes controlling the excitation source 12 to generate a pulse sequence such that one or more pulses have desired pulse characteristics. The pulse characteristics include, for example, pulse shape, size, amplitude, and intensity. The controller 16 may be any suitable circuitry or processing resources. The readout module 18 is configured to read out the quantum state of the qubit array. The control of the excitation source 16 may be performed by selecting and / or modifying one or more operating parameters of the excitation source.

[0074] The excitation source 12 is a laser system configured to generate two-photon pulses. In this embodiment, the excitation source 12 comprises a first laser and a second laser configured to generate excitation pulses for exciting the neutral atoms. The first and second lasers are positioned and configured to simultaneously apply excitation pulses to the neutral atoms of the quantum gate 14.

[0075] In this embodiment, the excitation source is a laser system with a corresponding optical modulation device. More specifically, this embodiment includes a first laser and a second laser, each having an electro-optic modulator (or an acousto-optic modulator in other embodiments). The electro-optic (or acousto-optic) modulator receives an RF control signal generated by the pulse generator to modulate the laser light generated by each laser, thereby changing / selecting the characteristics (e.g., frequency, amplitude and phase) of the laser pulses.

[0076] Although electro-optical and acousto-optical control are described above, it will be understood that in other embodiments, other types of modulators and methods of shaping the laser pulses may be used. In the following, a laser is described as being controlled to generate laser pulses having a desired shape, but it will be understood that the pulse shaping and pulse characteristics may be controlled by an optical modulator, as described above. It will be understood that in this embodiment, the excitation source is controlled by retrieving predetermined pulse sequence data, for example from a storage resource. The predetermined pulse sequence data represents the desired pulse sequence and is determined by performing a calculation that uses a dynamical model of the quantum system that is the subject of the pulse sequence. The model used has at least one part (e.g., a matrix element or term) that allows modeling the effect of the hyperfine structure of the intermediate state of the neutral atom on the dynamics of the quantum system. This model allows the effect of these hyperfine components to be included in the calculation. In other embodiments, the pulse sequence data may be determined and used in real time.

[0077] In this embodiment, the first and second lasers are arranged and configured to simultaneously provide excitation pulses to the first and second neutral atoms according to a two-photon protocol. Furthermore, the first and second lasers provide excitation pulses symmetrically to the first and second neutral atoms such that an identical pulse is applied to each neutral atom. In an embodiment with more than two neutral atoms, the first and second lasers are arranged and configured to simultaneously and symmetrically provide excitation pulses to all neutral atoms according to a two-photon protocol.

[0078] In this embodiment, where the cesium atom is the neutral atom, the first laser (which non-resonantly couples the intermediate state with the Rydberg state) has a wavelength of 1039 nm and the second laser (which non-resonantly couples the second hyperfine ground state with the intermediate state) has a wavelength of 459 nm. It will be understood that the laser wavelengths used are determined by atomic physics and also depend, for example, on the atom being excited. For example, for rubidium, the wavelength of the first laser is 1004 nm and the wavelength of the second laser is 422 nm. The lasers used typically have wavelengths in the range of 300 nm to 1500 nm.

[0079] With respect to the power of the lasers, exemplary maximum powers are provided below. For example, in one example, the maximum output of the first laser is 108.00 mW and the maximum output of the second laser is 20.23 mW, and in another example, the maximum output of the first laser is 108.00 mW and the maximum output of the second laser is 17.70 mW. It will be understood that the power of each laser must be sufficient to allow for a change in power (of one or both of the lasers) to produce the desired change in the effective Rabi frequency, and thus these values ​​can be changed. Lasers having a maximum output in the range of 5 mW to 500 mW may be used, although it will be understood that other values ​​of power outside this range may be appropriate depending on the experiment and system settings. For example, lasers having a maximum output of more than 500 mW may be used.

[0080] In operation, controller 16 controls excitation source 11 to generate excitation pulses to neutral atoms in quantum gate 14 according to a two-photon excitation protocol. Quantum gate operations are performed by providing excitation pulses to quantum gate 14 according to the two-photon excitation protocol. The excitation protocol is described in further detail with reference to Figures 2, 3 and 4.

[0081] Referring to Figure 2, two neutral atoms and their respective energy levels are shown. As shown in Figure 2, the first neutral atom corresponds to the first qubit of quantum gate 14, and the control qubit and the second neutral atom correspond to the second qubit, or target qubit, of quantum gate 14. In Figure 2, the atomic state of the first neutral atom is therefore assigned the subscript "c" (for control) and the state of the second neutral atom is assigned the subscript "t" (for target).

[0082] The neutral atoms forming the quantum gate 14 (in this embodiment, the first and second neutral atoms) can each be characterized by a set of atomic states between which each neutral atom can transition. Each neutral atom can move between these atomic states in response to receiving or releasing an amount of energy (e.g., via a photon). For example, a neutral atom can be moved to a higher energy atomic state in response to interaction with an excitation pulse from the excitation source 12, or moved to a lower energy atomic state in response to interaction with a de-excitation pulse from the excitation source 12 or as a result of spontaneous emission.

[0083] More specifically, the first neutral atom is movable between an unbonded state 102a, a first ground state 104a, a second ground state 106a, an intermediate state 108a, and an excited Rydberg state 110a. Although only the states of the first neutral atom are described below, it will be understood that the second neutral atom has a set of corresponding states, namely, an unbonded state 102b, a first ground state 104b, a second ground state 106b, an intermediate state 108b, and an excited Rydberg state 110b. Furthermore, in embodiments in which the quantum system has more than two neutral atoms (i.e., three or more), it will be understood that each neutral atom is movable between a set of corresponding atomic states.

[0084] Although only a single intermediate state per neutral atom is depicted in FIG. 2, it will be understood that these intermediate states are decomposed into hyperfine components of the intermediate atomic states. The hyperfine components of the intermediate atomic states are shown in FIG. 2(b), which illustrates the fine and hyperfine splitting in the intermediate states of a three-level system. Thus, the intermediate states of each neutral atom can be considered as two or more separate quantum states (i.e., multiple quantum states with different hyperfine quantum numbers).

[0085] As depicted in Figure 2(b), the intermediate state |e> can be described by two or more hyperfine splittings due to the interaction between the nucleus and the electron. e and each intermediate state with fixed angular momentum quantum number I has quantum number f e The complete hyperfine structure of the intermediate state is e Set of

number

[0086] Each ultrafine component f e is degenerate, as depicted in FIG. 2(b). The embodiment described below uses the component f e We use a model that takes into account the hyperfine division into

[0087] For the first neutral atom (corresponding to the target qubit), the unbound state 102a is c and occupy all other hyperfine ground states of the first neutral atom. The first ground state 104a and the second ground state 106a of the first neutral atom correspond to the computational state |0> of the first control qubit, respectively. c and |1> c Similarly, for the second neutral atom, the non-bonded state 102b corresponds to |d> tand occupy all other hyperfine ground states of the second neutral atom. The first ground state 104b and the second ground state 106b of the second neutral atom are respectively represented by the computational state |0> of the second target qubit. t and |1> t Corresponds to.

[0088] In this embodiment, the first and second neutral atoms are cesium atoms and are maintained at a temperature approaching T=0 Kelvin. In practice, the temperature is the product of the Boltzmann constant and the temperature (K B It will be appreciated that the energy scale T is kept low enough so that the energy scale T is lower than any relevant energy scale. In this embodiment, the following states are selected: the first ground states 104a, 104b are each an atomic state |0>=|6S 1 / 2 ,f=3,m f The second ground states 106a, 108a are selected to be the atomic states |1>=|6S 1 / 2 ,f=4,m f = 0>. The intermediate states 108a and 108b are selected so that the atomic state |e>=|7P 1 / 2 >. As mentioned above, the intermediate state |e> is chosen to be the hyperfine component (hyperfine splitting) of the quantum state |f e , m fe The excited Rydberg states 110a and 110b are decomposed into the atomic states |r>=|82S 1 / 2 >. In embodiments having more than two neutral atoms, it will be understood that the atomic state of the third (or more) neutral atom is selected to correspond to the above states for the other neutral atoms. The above states are presented only as exemplary states. Atomic states suitable for the Rydberg state have any n (e.g., n greater than 50) that result in a sufficiently strong interaction.

[0089] For each neutral atom, the calculated states |0> and |1> are qThe unbound state |d> accounts for all other hyperfine ground states other than the computational basis. As described in more detail below, the second ground state |1> of each neutral atom is coupled to each excited Rydberg state via a two-photon transition with intermediate state detuning Δ and two-photon detuning δ. The pulse sequence of the two-photon protocol described according to the embodiment couples the computational states (hyperfine ground states) to each other via both the intermediate states and the Rydberg states, thus enabling electronic population transfer between the states.

[0090] As shown in Figure 2, there is a potential V between the Rydberg states of the neutral atom. rr There is an interaction 112 characterized by: Rydberg-Rydberg = Rydberg+R ...

[0091] Also depicted in Figure 2 are frequency levels and frequency differences between the above-mentioned atomic states. In the following description, the quantity frequency is used to define the characteristic difference between the atomic states, but it will be understood that due to the relationship between photon energy and photon frequency, energy quantities may also be used. In the following, the Rabi frequency and detuning of quantum systems are described, and it will be understood that the desired values ​​of these quantities can be provided by the laser.

[0092] In this embodiment, as shown in FIG. 2, the hyperfine component |e> of the intermediate state and the Rydberg state are at the Rabi frequency Ω e r and detuning δ. The hyperfine components of the second hyperfine ground state |1> and the intermediate state |e> in each atom are non-resonantly coupled (e.g., by a second laser) to the Rabi frequency Ω 1 e and the laser detuning Δe is given.

[0093] The center of mass of the hyperfine component is detuned by Δ from the resonant transition frequency to |1>. The non-bonded level |d> represents all hyperfine ground states different from |0> and |1>, and the population lost by spontaneous emission from |e> and |r> is denoted by γ e and γ r Accumulate using.

[0094] Parameter Ω e r and Ω 1 e are the intermediate hyperfine component states corresponding to the intermediate states (each component is |f e , m fe >), for the Rabi frequencies to drive the excitation from |1> to |e> and from |e> to |r>. These frequencies Ω e r and Ω 1 e are the Rabi frequencies of the individual lasers used, and fully parameterize the Hamiltonian.

[0095] As will be explained below, to implement the two-photon protocol and control the quantum gate 14, an effective Rabi frequency Ω R and effective detuning δ R The intermediate state detuning Δ is chosen so that the two-photon excitation process can be effectively described by . The parameter Δ is chosen to be large compared to the hyperfine splitting of the intermediate state in order to reduce the risk of having near-resonant transitions with hyperfine levels. Such resonant transitions can lead to large errors.

[0096] Thus, by appropriate choice of laser parameters, a three-level system can be modeled as a two-level system. In particular, if the intermediate state is a far-away resonant tone (i.e. has a value much larger than the Rabi frequency), it can be eliminated by adiabatic elimination. A superposition of all allowed transitions from the ground state to the Rydberg state via all hyperfine components of the intermediate state is included in the calculation. In this working approximation, the two-photon Rabi frequency is

number

number

[0097] Different values ​​of Ω e r and Ω 1 e , we may obtain the same effective parameters for |r>, but the complete dynamics may not be equivalent. The effective detuning from |1> to |r> is δ R = δ + Δ AC and is tuned to zero for resonant excitation, where Δ AC is the combined AC Stark shift

number

[0098] As mentioned above, a three-level quantum system has an effective Rabi frequency Ω Rand two-photon detuning. The laser is then controlled over time to give the desired variation in these quantities. The effective Rabi frequency Ω R is controlled by controlling the laser power of the first and / or second laser, and the two-photon detuning δ is controlled by varying the frequency of the first and / or second laser and / or by controlling the detuning of these lasers. In the embodiment described below, the variation of the effective Rabi frequency is achieved by holding the first laser at a constant power and varying the power of the second laser over time. Similarly, the variation of the two-photon detuning is achieved by chirping the frequency of one of the two lasers (the first laser in this example). In the described embodiment, the second laser detuning Δ is kept constant, so any change in the first laser detuning corresponds to a change in the two-photon detuning δ. The second laser detuning is kept constant and is large enough to allow an effective two-level description with adiabatic removal of the intermediate state.

[0099] As mentioned above, the excitation source 12 comprises two lasers, a first laser and a second laser. In this embodiment, the first laser has sufficient power to non-resonantly couple the intermediate state with the excited Rydberg state, and the second laser has sufficient power to non-resonantly couple the intermediate state with the second ground state. The two-photon excitation scheme is described below with reference to Figures 3 and 4. It will be appreciated that the two-photon excitation scheme may be implemented by controlling one or more operating parameters of the excitation source.

[0100] In this embodiment, the two-photon excitation scheme involves generating a first excitation pulse from a first laser excitation to non-resonantly couple the intermediate state to the excited Rydberg state. The power of the first laser is locked such that the power of the laser remains constant during the first pulse duration. The power of the second laser (which non-resonantly couples the second ground state |1> and the intermediate state) is varied over time during the first pulse duration. This combination of power changes results in the desired change in the effective Rabi frequency. The second laser detuning is kept constant, but the first laser detuning, high enough, is varied over time such that the intermediate state is far away from the resonance between the second ground state and the intermediate state, resulting in a fluctuation in the two-photon resonance.

[0101] FIG. 3 shows the Bell state, starting from the |00> state and using pulses produced according to the first two-photon excitation scheme.

number

[0102] The two-photon protocol described implements a gate operation. The effect of the protocol is:

number

[0103] This operation is represented mathematically as a diagonal matrix where the first entry is 1 and all other diagonals are -1.

[0104] Whether this gate generates entanglement or not depends on the input applied. Any input state can be applied, and the expansion to the output state is given by the gate matrix U C k Z It is described by |0> kThe components remain unchanged and all other elements get a factor of -1 in their complex amplitudes. Following a ramp pulse, described below, the protocol C k Z requires an additional global single-qubit pulse Z(φ) to obtain

[0105] Two-qubit controlled phase gate U C k Z is implemented using pulses delivered according to the first two-photon excitation scheme, which can be considered as an adiabatic fast-passage protocol. An example is shown in Figures 3 and 4. By combining ARP pulses with single-qubit global rotations, a maximally entangled two-qubit state can be prepared.

[0106] Figures 3 and 4 show the Bell states starting from the |00> state.

number

[0107] In the following two-photon excitation scheme, the first and second lasers are controlled to emit a pulse sequence: For all plots, the intermediate state detuning is Δ / 2π=30 GHz, the Rydberg-Rydberg interaction strength is Vrr / 2π=578 MHz, the Gaussian beam waist is w=3.5 μm, the maximum power of the second laser coupling the transition between |1>⇔|e> is 20.23 mW, and the maximum power of the first laser coupling the transition between |e>⇔|r> is 108.00 mW.

[0108] 3(a)-3(d) show plots of the time dependence of the laser characteristics and the population of states of a neutral atom. Each plot has time as the x-axis (202a, 202b, 202c, 202d) shown in microseconds. In FIG. 3, pulses from a first laser and a second laser are incident on the neutral atom for a time period hereafter referred to as the pulse duration. In particular, FIGS. 3(a) and 3(b) depict the variation of the laser pulse over the pulse duration, and FIGS. 3(c) and 3(d) depict the resulting states and changes in the state population of the quantum gate 14 as a result of the laser pulse being incident on the quantum gate 14. An excitation pulse is provided to the quantum gate as part of the pulse sequence. FIGS. 3(a) and 3(b) show the shape of the analysis pulse for the two-photon protocol.

[0109] Laser chirp is directly related to the shape of line 208 (the two-photon detuning) in Figure 3(a). Line 208 represents the total cumulative detuning between the two lasers. Although only one laser is described above as being chirped, it will be understood that both lasers may be chirped to provide the desired variation in the effective detuning (line 208).

[0110] FIG. 3(a) illustrates the effective single-photon Rabi frequency Ω (depicted by line 206). R 3(a) and 3(b) are plots showing the time dependence of the two-photon detuning δ (depicted by line 208). The two-photon detuning line 208 may also be referred to as the detuning curve. The y-axis 204 of FIG. 3(a) is frequency. As shown in FIG. 3(a), the Rabi frequency has a time-dependent profile 206 with two repeating parts, each part having a first rising section, a second plateau section, and a third falling section. The detuning frequency similarly has a profile 208 with two repeating parts, each part having three sections: a first section that quickly reduces the detuning frequency to a minimum value, a rising section that increases the frequency from the minimum value to a maximum value, and a falling section that reduces the frequency from the maximum value to an intermediate value. Thus, this profile can be characterized by a peak at a maximum value followed by an immediate drop.

[0111] In contrast to the known pulse shapes described in [1], the change in shape from the smooth pulse of [1] to the pulse depicted in Fig. 3(a) is mainly due to the change in the effective detuning δ of the atoms when varying δ. R = δ + Δ AC AC shifts are perturbative effects on the hyperfine components. These shifts are defined in terms of the individual Rabi frequencies involved in the process. The individual Rabi frequencies are two-photon transitions, and the combined AC Stark shift

number

[0112] Thus, at least part of the shape of the line 208 results from the consideration of the hyperfine structure of the intermediate states. In particular, the detuning curve 208 has at least one feature that compensates for perturbation effects on the intermediate order, such as the AC Stark shift. In particular, between a first and a second part, there is a first compensation feature in the form of an abrupt drop 209a, such that the shape is not a smooth function. For example, an abrupt drop 209a exists between the first and second parts of the line 208. A second compensation feature is the presence of a drop section 209b. By including the complete hyperfine structure in the calculation of the time-dependent Stark shift, these shifts are compensated for by these compensation features.

[0113] The two-photon protocol described herein takes into account the multilevel hyperfine structure of the intermediate states. If the hyperfine structure is neglected, the model will underestimate both the AC Stark shift and the further contribution to the spontaneous emission fraction. In such cases, the calculated pulse shape may not yield high-fidelity operation when implemented in the laboratory.

[0114] The shape of the two-photon detuning curve δ follows a smooth cosine profile similar to that shown in Fig. 2 of [1], with the effective detuning δ Ris chosen to ensure a smooth evolution. The model used allows the calculation of the exact detuning curve required in a lab frame to achieve the targeted fidelity. The detuning curve therefore includes compensation features that allow a smooth effective detuning (the effective detuning is the sum of the two-photon detuning curve and the AC Stark shift). In general, without considering the full hyperfine structure of the intermediate states, the errors will be underestimated and shorter pulses will be optimized in terms of the reduced AC shift.

[0115] The allowable ARP pulse shape is limited by the adiabatic condition, which can be expressed as:

number

[0116] FIG. 3(b) depicts the power profiles of the two lasers assuming Gaussian beams, showing the time dependence of the power of the first and second lasers. The Y-axis 204b of FIG. 3(b) is the power (as a fraction of the maximum laser power) such that the value corresponds to a value of 1 when the laser operates at its maximum. As mentioned above, the power of the first laser, which non-resonantly couples the intermediate state with the Rydberg state, remains constant for the pulse duration. The output of the first laser has a rectangular shaped profile 212. The power of the second laser (which non-resonantly couples the second ground state with the intermediate state) then varies continuously over the pulse duration and has a sine shaped power profile 210. The power of the second laser has a symmetric shape around the midpoint (corresponding to half the pulse duration). This shape may be considered as sine, but more precisely, this shape is mathematically expressed as the function exp{-(tT)^4}.

[0117] The combination of varying the power of the second laser to produce variations in the effective Rabi frequency and varying the detuning of the first laser (to produce variations in the two-photon detuning) provides an adiabatic sweep over a range of frequencies that includes the resonance frequency between the second hyperfine ground state and the Rydberg atomic state. The detuning shown in Figure 3(a) refers to the two-photon detuning. The intermediate excited state is not resonant with the second hyperfine ground state, and a population transition occurs between the ground state and the Rydberg state.

[0118] FIG. 3(c) is a plot of the time evolution of the population of the intermediate state 216 and the dark ground state 214 of the neutral atom. The Y-axis 204c of FIG. 3(c) is the population. Because the intermediate state detuning is finite, the intermediate state is populated every time the laser is turned on. Since the intermediate state decays quickly via spontaneous emission of light, this creates an error, and this graph represents the leakage through the intermediate state from the calculated basis, which is the dominant error in implementing controlled gates. The intermediate state is populated as a result of turning on the power of the laser. Towards the end of the process, the intermediate state is depopulated as a result of turning off the laser as well as due to the effects of natural decay.

[0119] Figure 3(d) shows the time evolution and fluctuation of the population of the computational state and the Rydberg state. The Y axis in Figure 3(d) is the population. Figure 3(d) shows the Bell state

number

[0120] To take into account the dissipative effects, we determine the dynamics of the two-qubit density matrix by the Lindblad master equation and the following equation:

number

[0121] FIG. 4 shows a further pulse sequence according to a two-photon excitation scheme. FIG. 4 is a modified version of the pulse sequence described with reference to FIG. 3. More specifically, the pulses are modulated using standard optimal control, which in this embodiment is based on Fourier series expansion. Applying the known optimal control pulse shaping to the ARP gate protocol, the fidelity can be further improved by reducing the power of the second laser (which couples the |1> and |e> states). The pulse sequence of FIG. 4 can be considered as an optimized version of the pulse sequence of FIG. 3. The reference numbers of FIG. 4 are therefore numbered to correspond to the reference numbers mentioned above for FIG. 3. Examples of optimal quantum control can be found, for example, in the non-patent document "Phys Rev. A 84, 022326 (2011)".

[0122] The further modulation includes varying at least one of the shape, amplitude, and intensity duration of the pulse. The further modulation may comprise varying the time-dependent variation of a single effective Rabi frequency and a single detuning parameter. In this embodiment, the optimal quantum control process is performed by numerically optimizing the parameters of an envelope function expanded as a sum of orthogonal functions. The numerical optimization process may comprise applying a numerical solver to find the relevant values ​​of the pulse parameters. In this embodiment, the calculations and optimization (before performing any gating operations) are performed offline, while in other embodiments the optimization may be performed in situ. For example, the optimization may be performed in response to performing a calibration measurement. Such an approach requires a computation time comparable to the readout speed.

[0123] In all plots in Fig. 4, the intermediate state detuning is Δ / 2π = 30 GHz and the Rydberg-Rydberg interaction strength is V rr4, the maximum power of the second laser coupling the transition between |1>⇔|e> is 17.70 mW, and the maximum power of the first laser coupling the transition between |e>⇔|r> is 108.00 mW. In FIG. 4, in the region where the effective Rabi frequency is negative, a phase factor π must be incorporated into either the Rabi frequency of the excitations |1>⇔|e> or |e>⇔|r>. In the example shown in FIG. 4, the fidelity of the Bell state is F=0.9983. Although the above laser parameters are presented, they are presented as non-limiting examples, and the above method can be implemented with a number of different parameters (e.g., power / w 2 It will be appreciated that this will work for lasers of comparable strength by keeping the ratio of

[0124] In FIG. 4(a) the time dependence of the effective single-photon Rabi frequency 306 and the two-photon detuning 308 is shown. In contrast to FIG. 3(a), an additional modulation to the shape of these profiles can be observed. More specifically, the Rabi frequency has a profile 306 with two repetitive parts. In contrast to FIG. 3(a), each part has four sections, namely a first falling section (taking the frequency from an initial value of zero to the first negative value), a second rising section (taking the frequency from the first negative value to its maximum value), a third falling section (taking the frequency from the maximum value to the minimum value), and a fourth rising section taking the frequency from the minimum value to its initial value. In contrast to FIG. 3(a), the Rabi frequency takes negative values ​​and does not have a plateau. The first to fourth sections form a continuous smooth function for each repetitive part, but between the first and second parts there is a discontinuity. Each part may be characterized by a peak and a (smaller) minimum value (nadir).

[0125] In Fig. 4(b) the time dependence of the two-photon detuning 308 is shown. As explained with reference to Fig. 3(a), the profile 308 has two repeating parts, but its shape is modified in contrast to Fig. 3(a). In particular, in contrast to the profile 208, which drops immediately and then rises to a maximum peak, the profile 308 also has an additional secondary peak following the maximum peak, which is lower than the maximum peak. In total, the profile 308 has two repeating parts, each of which has five sections: a first section that drops the detuning frequency immediately to a minimum value, a first rising section that raises the detuning frequency to a maximum value, a first falling section that drops the detuning frequency to an intermediate value, a second rising section that raises the detuning frequency to a second intermediate value, and a second falling section that drops the detuning frequency to a third intermediate value.

[0126] FIG. 4(b) shows the power profiles of the first laser (312) and the second laser (line 310) assuming a Gaussian beam. By comparison with FIG. 3(b), an additional modulation to the power profile of the second laser can be observed. The power profile of the first laser 312 corresponds to the power profile 212 of the first laser as explained with reference to FIG. 3(b), whereas the power profile of the second laser 310 has been altered compared to the power profile 210. In particular, the power has been altered such that the measure of the total power applied (in this case the integral of the power profile) is lower than that of FIG. 3(b). The power profile 310 is a modulated version of the symmetric sinusoidal shaped profile 210. More precisely, each part of the power profile 310 is modulated by a symmetric exponential function (exp{(T 0 -t)^ -4}) It will be appreciated that in other embodiments the pulses have various non-trivial shapes.

[0127] The power profile has two repeating parts, each part having three sections: a first section with a low peak, a second section with a high peak (reaching the maximum available power), and a third section with an intermediate peak. Thus, the power profile 310 can be characterized by a first peak and a second, lower peak.

[0128] Figure 4(c) shows the time evolution of the populations of the intermediate state 314 and the dark ground state 316. In contrast to Figure 3(c), the variation of the populations due to the additional modulation can be observed. In Figure 4(d), the time evolution and variation of the populations of the computational state and the Rydberg state are shown. In contrast to Figure 3(d), an improvement of the population of the Bell state can be observed.

[0129] As a benchmark for the above ARP protocol, we determined the Bell state fidelity corresponding to the known protocol, obtaining F = 0.9983. Compared to known single-photon protocols, the found fidelity indicates that the above method can provide a competitive alternative for high-speed two-qubit gates.

[0130] The above-described embodiments may offer many advantages over known methods and systems, such as taking into account multi-level hyperfine shifts, which may otherwise limit the fidelity of gating, as compared to known methods.

[0131] Although the above embodiments relate primarily to two-atom quantum gates, it will be appreciated that the methods are applicable to multi- (i.e., more than two) qubit gate protocols. Such multi-qubit gates may be implemented using exactly the same modality (global addressing of multiple qubits) with the same architecture as considered for two-qubit gates. The advantage of implementing multi-qubit gates natively is that it avoids the requirement to separate higher order gates into lots of one- and two-qubit gates (e.g., the three-qubit gate we optimize is equivalent to six separate two-qubit operations), thus allowing for increased parallelism and improved fidelity.

[0132] It will be appreciated that, although the above description relates to performing quantum gate operations on a single gate, according to further embodiments, a quantum computing device having a plurality of such quantum gates can be provided. Furthermore, it will be appreciated that a quantum computing device based on the above method of controlling a quantum gate can be implemented in a number of different ways. FIG. 5 shows a non-limiting example of how such a quantum computing device can be embedded. It will be appreciated that the quantum gates defined above can be applied to any other subset of qubits in a qubit array by simply changing which atoms are processed by the laser. An exemplary configuration of qubits is described with reference to FIG. 6.

[0133] The system shown in Figure 5 has some components that correspond to the system described with reference to Figure 1. For example, Figure 5 has a controller 516 that corresponds to controller 16 for performing gating operations, an excitation source 512 that corresponds to excitation source 12, and a readout module 518 that corresponds to readout module 18.

[0134] The excitation source may be referred to as a Rydberg laser, as described with reference to Figure 1. The system includes a qubit array 520 (also referred to as a neutral atom array) prepared in a vacuum chamber 21. The qubit array provides one or more quantum gates that correspond approximately to quantum gates 14.

[0135] The quantum computer further comprises a neutral atom controller for controlling the neutral atom array apart from the controller 516 and the excitation source 512. In particular, the neutral atom controller further comprises a laser for initializing / loading and maintaining the neutral atom array (e.g., by cooling, transporting and trapping neutral atoms). In particular, as shown in FIG. 5, the system comprises a cooling laser 522 for initializing the qubits and a trapping laser 524 for trapping the neutral atoms. The neutral atom array may be an optical or magnetic neutral atom array. The neutral atom array 520 comprises a plurality of neutral atoms that provide a quantum register for the qubits. The qubits may include both computational qubits and auxiliary qubits.

[0136] 1 and is configured to read out the state of one or more quantum gates of the neutral atom array 520. The readout module 518 may be any suitable device for capturing the state of the neutral atoms. In the embodiment of FIG. 5, the readout module comprises a camera 526 and associated circuitry for performing fluorescence imaging.

[0137] 6 shows non-limiting examples of neutral atom configurations for multiple qubits. It will be understood that these neutral atom configurations may form part of a larger neutral atom array (e.g., neutral atom array 520). As shown in FIG. 6, FIG. 6(a) shows an example of a two-atom configuration having a control atom 602 and a labeled target atom 604. The separation between the two atoms is labeled as R.

[0138] Figure 6(b) shows examples of 3, 4 and 5 atom configurations. Figure 6(b)(i) shows an exemplary 3 atom configuration with a central control atom 606 and two target atoms 608a, 608b. The three atoms are arranged in a right angle triangle.

[0139] FIG. 6(b)(ii) shows an exemplary four-atom configuration with a central control atom 610 and three target atoms 612a, 612b, 614c. The three target atoms are arranged in a triangle shape with the control atom located in the middle. FIG. 6(c)(iii) shows an exemplary five-atom configuration with a central control atom 614 and four target atoms 616a, 616b, 616c, 616d. The four target atoms are arranged in a diamond shape with the control atom 614 located in the middle of the diamond. FIG. 6(d) shows the five-atom configuration of FIG. 6(c)(iii) provided in a qubit array. This five-atom configuration is shown surrounded by additional atoms 618. FIG. 6(d) is an example of how quantum gates can be applied to different subsets of qubits in the array by changing which atoms are addressed by the laser.

[0140] It will be understood that configurations with more than two neutral atoms will have corresponding pairs of Rydberg interactions, for example a three atom configuration will have three Rydberg interactions.

[0141] Using similar parameters and global excitation schemes as described above, optimal pulse sequences enabling 3-qubit UCCZ were found to yield fidelity F>0.995 (2-qubit gates require fidelity F>0.999 to compete in performance), and pulse sequences enabling 4-qubit UCCCZ with F>0.99 were found.

[0142] Those skilled in the art will appreciate that variations in the enclosed configuration are possible without departing from the invention.

[0143] For example, while in the above embodiments the first and second lasers are described as being controlled by a controller controlling suitable optical modulation devices, it will be appreciated that in alternative embodiments the lasers may be supplied with further pulse shaping devices (e.g. optical devices) that are also or alternatively controlled by the controller to generate the excitation pulses. Alternatively, the lasers themselves may be configured to be controlled to generate the desired pulse sequence.

[0144] Thus, the above description of specific embodiments is by way of example only and not by way of limitation, as will be apparent to those skilled in the art, minor modifications can be made without significantly altering the operation of the described embodiments.

Claims

1. 1. A method of performing quantum gate operations using a quantum system including two or more neutral atoms, each atom of the two or more neutral atoms configured to transition between atomic states including a first hyperfine ground state of the atom, a second hyperfine ground state of the atom, a Rydberg state, and at least one intermediate excited state, the quantum system further including interactions between the Rydberg states in the two or more neutral atoms, the method comprising: generating a pulse sequence; and providing the generated pulse sequence to two or more neutral atoms to transition the atoms between the atomic states, the pulse sequence taking into account at least a portion of the hyperfine structure of at least one intermediate atomic state.

2. 2. The method of claim 1, wherein the quantum gate operations correspond to evolution of the at least two neutral atoms between the atomic states, and the pulse sequence includes at least one property based on a calculation or application of a model of the quantum system that includes an effect of at least one hyperfine component of the at least one intermediate state on the evolution.

3. The method of claim 2 , wherein the at least one characteristic includes at least one of a shape, a size, an amplitude, a frequency, or a duration of the pulse.

4. 4. The method of claim 2 or 3, further comprising the step of selecting and / or modifying operational parameters of a pulse generator, said selecting and / or modifying said operational parameters resulting in the pulse sequence having said at least one characteristic.

5. 5. The method according to claim 2, wherein the at least one characteristic of the pulse sequence is represented by one or more pulse parameters, the method comprising the step of obtaining values ​​of the one or more pulse parameters based on the calculation or applying the model.

6. 6. The method of claim 1, wherein at least one pulse of the pulse sequence is characterized by a frequency detuning curve, the frequency detuning curve including at least one compensation feature for compensating for a perturbation effect on at least one hyperfine component of the intermediate state.

7. The method of claim 6 , wherein the compensation features include discontinuities, rates of change, adjustments in rates of change, maximums, minimums or turning points, peaks and / or minimums.

8. In the method according to any one of claims 1 to 7, the step of generating the pulse sequence comprises:

11. A method comprising: controlling at least one laser to generate at least one chirped excitation pulse, the chirped excitation pulse comprising a sweep over a range of frequencies that includes at least a two-photon resonance frequency between the second hyperfine ground state and the Rydberg state.

9. In the method according to any one of claims 1 to 8, the step of generating the pulse sequence comprises: generating a first pulse that includes a range of frequencies sufficient to non-resonantly couple the at least one intermediate atomic state and the Rydberg state; and generating a second pulse comprising a sweep over a range of frequencies including a resonance frequency between the first hyperfine ground state and the Rydberg state; A method comprising:

10. The method of any one of claims 1 to 9, wherein the pulse sequence comprises a two-photon adiabatic rapid passage (ARP) protocol.

11. 11. The method of claim 1, wherein the quantum system is represented by a first model having a first number of dimensions, and the pulse sequence is generated as part of a time-dependent detuning process over a sufficiently large frequency range such that the quantum system can be effectively represented by a second model having a second, lower number of dimensions.

12. 12. The method of claim 11, wherein the detuning process is such that the quantum system can be characterized by a single effective Rabi frequency and a single detuning parameter.

13. The method according to any one of claims 1 to 12, wherein the pulse sequence is characterized by a time-dependent change in at least an effective Rabi frequency and a two-photon detuning parameter.

14. The method according to any one of claims 1 to 13, further comprising the step of performing a further modulation on the generated pulse sequence.

15. 15. The method of claim 14, wherein the further modulation is based on an optimal quantum control process.

16. 16. The method of claim 1, wherein the transitions between atomic states comprise Rabi oscillations.

17. The method according to any one of claims 1 to 16, comprising the step of symmetrically supplying the generated pulse sequences to the two or more neutral atoms.

18. The method of any one of claims 1 to 17, wherein the two or more neutral atoms comprise alkali atoms.

19. 19. The method of any one of claims 1 to 18, wherein the two or more neutral atoms comprise one of sodium (Na), rubidium (Rb), cesium (Cs), and potassium (K) atoms.

20. 20. The method of claim 1, wherein the generated pulse sequence has energies based on an energy separation of the hyperfine ground level, the intermediate state and the Rydberg state, with a selected detuning value imposed.

21. The method of any one of claims 1 to 20, wherein the pulse sequence includes applying a single qubit rotation.

22. 22. The method of any one of claims 1 to 21, wherein Rydberg interactions between the Rydberg states of the two or more neutral atoms prevent the two or more neutral atoms from being excited simultaneously into their respective Rydberg states.

23. The method of any one of claims 1 to 22, wherein preparing the entangled quantum state is effected as part of a quantum gate protocol.

24. 1. A quantum computer device, comprising: a quantum system including two or more neutral atoms, each atom of the two or more neutral atoms configured to transition between atomic states including a first hyperfine ground state of the atom, a second hyperfine ground state of the atom, a Rydberg state, and at least one intermediate atomic state, the quantum system further including an interaction between the Rydberg states in the two or more neutral atoms; a pulse generator configured to generate a pulse sequence and to supply the generated pulse sequence to two or more neutral atoms to transition the atoms between the atomic states, the pulse sequence including at least one pulse having properties that take into account at least a portion of the hyperfine structure of at least one intermediate atomic state; An apparatus comprising:

25. 1. A method comprising: performing a calculation to determine a pulse sequence for a quantum system, the determined pulse sequence being such that a desired quantum gate operation is obtained, the quantum system including two or more neutral atoms configured to transition between atomic states including a first hyperfine ground state of the atoms, a second hyperfine ground state of the atoms, a Rydberg state, and at least one intermediate excited state, the quantum system further including interactions between the Rydberg states in the two or more neutral atoms, the calculation taking into account at least a portion of the hyperfine structure of the at least one intermediate state; storing pulse sequence data representative of the determined pulse sequence; A method comprising:

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