IL282705A - Deterministic photonic graph state generator - Google Patents

Description

DETERMINISTIC PHOTONIC GRAPH STATE GENERATOR FIELD id="p-1" id="p-1" id="p-1" id="p-1" id="p-1" id="p-1" id="p-1" id="p-1"

[0001] The present invention relates to the field of quantum computing, and in particular to the generation of photonic graph states.

BACKGROUND id="p-2" id="p-2" id="p-2" id="p-2" id="p-2" id="p-2" id="p-2" id="p-2"

[0002] Currently, quantum computing remains restricted to the proof-of-concept stage, with a relatively small number of qubits sufficient only to demonstrate that quantum computing is feasible in principle. To make quantum computing practical for handling real-world problems, current devices need to be scaled up to handle large numbers of qubits, over 106, including qubits for error correction. id="p-3" id="p-3" id="p-3" id="p-3" id="p-3" id="p-3" id="p-3" id="p-3"

[0003] Qubits for quantum computing are typically hosted in one of three physical regimes: superconducting states, ionic states, and photonic states. id="p-4" id="p-4" id="p-4" id="p-4" id="p-4" id="p-4" id="p-4" id="p-4"

[0004] The photonic state regime offers a number of significant practical advantages over the other regimes. Photons are relatively easy to generate and do not require cryogenic or ultra-high vacuum environments, and construction of micro-miniaturized, reliable photon devices and their communication infrastructure is accomplished utilizing readily available fabrication technologies. Thus, the photonic state regime is currently the best candidate for achieving the high-level scaling necessary for practical quantum computing devices. id="p-5" id="p-5" id="p-5" id="p-5" id="p-5" id="p-5" id="p-5" id="p-5"

[0005] The full potential of the photonic state regime, however, is not presently realized because generating entangled photonic states for use as qubits in quantum computing is currently highly inefficient. Conventional arrangements rely on nonlinear effects in crystals to generate single photons. In order to produce photonic graph states, these photons are entangled in a probabilistic manner using linear optics elements. For this purpose, generated photons should be indistinguishable, generated according to perfectly timed and identically shaped pulses. Unfortunately, this requirement comes at the expense of the generation efficiency. Furthermore, in order to end up with a photonic graph state of a certain number of qubits, the probabilistic entangling process would require a much larger number of initial single photons, and hence a larger number of elements. These points of inefficiency are cumulative and seriously restrict efforts to scale the photonic state regime to meaningful numbers of qubits. id="p-6" id="p-6" id="p-6" id="p-6" id="p-6" id="p-6" id="p-6" id="p-6"

[0006] It is therefore highly desirable to have apparatus and methods for generating photonic graph states which eliminate probabilistic processes and their inherent inefficiencies, and which instead deterministically generate photonic graph states at maximal efficiency for use as qubits. This goal is met by embodiments of the present invention.

SUMMARY id="p-7" id="p-7" id="p-7" id="p-7" id="p-7" id="p-7" id="p-7" id="p-7"

[0007] Embodiments of the present invention provide deterministic apparatus and methods for generating and entanglement of single photons, multiple photons, and photonic graph states usable in quantum computing. By avoiding probabilistic processes, the present invention achieves maximal efficiency, allowing all generated photons to be usable in qubits. id="p-8" id="p-8" id="p-8" id="p-8" id="p-8" id="p-8" id="p-8" id="p-8"

[0008] Deterministic single photon generation is combined with deterministic cavity- enhanced photon-atom entanglement to produce time-sequenced entangled photons, and in related embodiments, generating and entanglement units are incorporated into integrated arrays which emit multi-dimensional clusters of entangled photons having one temporal dimension and one or two additional dimensions. id="p-9" id="p-9" id="p-9" id="p-9" id="p-9" id="p-9" id="p-9" id="p-9"

[0009] Single photon generation, atom-photon entanglement, and photon-photon entanglement are accomplished by a four-state atomic system within an optical cavity, whose transitions are independently addressable according to energy and polarization of incoming photons. Types of operation include single-photon sourcing, atom-photon entanglement, multiple photon entanglement, and preparation and measurement of the atomic qubit. id="p-10" id="p-10" id="p-10" id="p-10" id="p-10" id="p-10" id="p-10" id="p-10"

[0010] According a first aspect of the presently disclosed subject matter, there is provided a method for sourcing a graph state of quantum-entangled photons, the method comprising: providing a photon source unit for sourcing single photons, the photon source unit comprising a source unit atom disposed within an intra-cavity field of a source- optical cavity; providing a photon entanglement unit for quantum entanglement of photonic states, the photon entanglement unit atom disposed within an intra-cavity field of an entanglement-optical cavity; sending a pulse to the photon entanglement unit to set the entanglement unit atom to 1 an atomic quantum superposition state (|0) + |1)); sending a pulse to the photon source unit to initialize the source unit atom to a quantum state |1); sending a pulse of photons in a first photonic mode into the photon source unit to cause the source unit atom to output a single photon in a second photonic mode, wherein the first photonic mode couples to a first transition of the source unit atom, and wherein the second photonic mode couples to a second transition of the source unit atom; routing the single photon in the second photonic mode to the photon entanglement unit to a superposition of a third photonic mode and a fourth photonic mode; wherein the third photonic mode couples to a third transition of the entanglement unit atom; wherein the fourth photonic mode does not couple to any transition of the source unit atom; wherein the fourth photonic mode does not couple to the entanglement-optical cavity; and wherein the output photon in a superposition of a third photonic mode and a fourth photonic mode is quantum-entangled with the entanglement unit atom; repeating the routing at least once to route at least one additional single photon in the second photonic mode to the photon entanglement unit in a superposition of the third photonic mode and the fourth photonic mode in quantum entanglement with the entanglement unit atom; performing a measurement on the entanglement unit atom, thereby disentangling it from the photons in the third photonic mode and the fourth photonic mode; wherein the at least two photons in the superposition state of the third photonic mode and the fourth photonic mode are quantum entangled; and outputting the at least two photons in the superposition state of the third photonic mode and the fourth photonic mode as time-sequenced mutually entangled photons. id="p-11" id="p-11" id="p-11" id="p-11" id="p-11" id="p-11" id="p-11" id="p-11"

[0011] Performing a measurement on the entanglement unit atom may include performing a measurement in an x-y plane of a Bloch sphere. id="p-12" id="p-12" id="p-12" id="p-12" id="p-12" id="p-12" id="p-12" id="p-12"

[0012] According to a second aspect of the presently disclosed subject matter, there is provided a device for sourcing a graph state of quantum-entangled photons, the device comprising: a plurality of single photon source units; a first stage of linear optics elements; and a first plurality of entanglement units; wherein the plurality of single photon source units, the first stage of linear optics elements, and the first plurality of entanglement units are correspondingly displaced along a predetermined spatial axis; wherein each single photon source unit of the plurality of photon source units outputs single photons to the first stage of linear optics elements, and therefrom into a respective entanglement unit of the first plurality of entanglement units; and wherein the first plurality of entanglement unit outputs a one-dimensional spatial array of entangled photons in a time-dimensional sequence. id="p-13" id="p-13" id="p-13" id="p-13" id="p-13" id="p-13" id="p-13" id="p-13"

[0013] The single photon source units and/or the entanglement units may each comprise an atom being in a first ground state, a first excited state, a second ground state, a second excited state, or a superposition thereof, the atom being further configured to selectively undergo: a first transition between the first ground state and the first excited state; a second transition between the first excited state and the second ground state; and a third transition between the second ground state and the second excited state; the device comprising an optical cavity defining an intra-cavity field for disposing therewithin the atom, a photonic waveguide coupled to the optical cavity, a magnet configured to produce a magnetic field on the atom, and a laser source configured to produce pulses of photons in coherent states, the device being configured such that each of the transitions are within the resonance of the optical cavity. id="p-14" id="p-14" id="p-14" id="p-14" id="p-14" id="p-14" id="p-14" id="p-14"

[0014] The first and second transitions may be selected such that they are orthogonally polarized with respect to each other. id="p-15" id="p-15" id="p-15" id="p-15" id="p-15" id="p-15" id="p-15" id="p-15"

[0015] The first and second excited states may be at the same energy level. id="p-16" id="p-16" id="p-16" id="p-16" id="p-16" id="p-16" id="p-16" id="p-16"

[0016] The first and second ground states may be at different energy levels from one another. id="p-17" id="p-17" id="p-17" id="p-17" id="p-17" id="p-17" id="p-17" id="p-17"

[0017] The laser source may be configured for selectively generating: a pulse of initializing photons configured to initialize the atom by inducing it to undergo the first and second transitions from the first ground state to the second ground state via the first excited state; and a pulse of sourcing photons configured to source a single photon from the atom by inducing it to undergo the second and first transitions from the second ground state to the first ground state via the first excited state. id="p-18" id="p-18" id="p-18" id="p-18" id="p-18" id="p-18" id="p-18" id="p-18"

[0018] The laser source may be configured to set the state of the atom to a quantum superposition state and to generate a preparation photon being in state of superposition of first and second preparation modes, wherein interaction of the preparation photon with the atom results in its first and second ground states being in a state of superposition corresponding to the state of superposition of the first and second preparation modes, i.e., the interaction results in the first and second ground states of the atom being in a superposition with probability amplitudes equal to the probability amplitudes of the first and second preparation modes of the incoming preparation photon. id="p-19" id="p-19" id="p-19" id="p-19" id="p-19" id="p-19" id="p-19" id="p-19"

[0019] The atom may be a Rubidium atom. id="p-20" id="p-20" id="p-20" id="p-20" id="p-20" id="p-20" id="p-20" id="p-20"

[0020] The magnet may be a solenoid. id="p-21" id="p-21" id="p-21" id="p-21" id="p-21" id="p-21" id="p-21" id="p-21"

[0021] The first stage of linear optics elements may include phase control. id="p-22" id="p-22" id="p-22" id="p-22" id="p-22" id="p-22" id="p-22" id="p-22"

[0022] The device may further comprise: a second stage of linear optics elements; and a second plurality of entanglement units; wherein the second stage of linear optics elements, and the second plurality of entanglement units are correspondingly displaced with the plurality of single photon source units, the first stage of linear optics elements, and the first plurality of entanglement units along the predetermined spatial axis; and wherein the single photons in an entangled state output from each respective entanglement unit of the first plurality of entanglement units are input to the second stage of linear optics elements and therefrom into a respective entanglement unit of the second plurality of entanglement units. id="p-23" id="p-23" id="p-23" id="p-23" id="p-23" id="p-23" id="p-23" id="p-23"

[0023] The second plurality of entanglement unit may be configured to output a two­ dimensional spatial array of entangled photons in a time-dimensional sequence. id="p-24" id="p-24" id="p-24" id="p-24" id="p-24" id="p-24" id="p-24" id="p-24"

[0024] The device may be configured to produce entangled qubits for use with a quantum computer. id="p-25" id="p-25" id="p-25" id="p-25" id="p-25" id="p-25" id="p-25" id="p-25"

[0025] The device may be configured for carrying out the method of the first aspect of the presently disclosed subject matter.

BRIEF DESCRIPTION OF THE DRAWINGS id="p-26" id="p-26" id="p-26" id="p-26" id="p-26" id="p-26" id="p-26" id="p-26"

[0026] The subject matter disclosed may best be understood by reference to the following detailed description when read with the accompanying drawings in which: id="p-27" id="p-27" id="p-27" id="p-27" id="p-27" id="p-27" id="p-27" id="p-27"

[0027] Fig. 1 schematically illustrates a device for use in quantum computing according to an embodiment of the present invention. id="p-28" id="p-28" id="p-28" id="p-28" id="p-28" id="p-28" id="p-28" id="p-28"

[0028] Fig. 2A is a state diagram for a process of the device shown in Fig. 1. id="p-29" id="p-29" id="p-29" id="p-29" id="p-29" id="p-29" id="p-29" id="p-29"

[0029] Fig. 2B is a state diagram for another process of the device shown in Fig. 1. id="p-30" id="p-30" id="p-30" id="p-30" id="p-30" id="p-30" id="p-30" id="p-30"

[0030] Fig. 2C is a state diagram showing a no interaction condition of the device shown in Fig. 1. id="p-31" id="p-31" id="p-31" id="p-31" id="p-31" id="p-31" id="p-31" id="p-31"

[0031] Fig. 2D is a state diagram showing another no interaction condition of the device shown in Fig. 1. id="p-32" id="p-32" id="p-32" id="p-32" id="p-32" id="p-32" id="p-32" id="p-32"

[0032] Fig. 2E schematically illustrates making a measurement on an atom of the device shown in Fig. 1, according to an embodiment of the present invention. id="p-33" id="p-33" id="p-33" id="p-33" id="p-33" id="p-33" id="p-33" id="p-33"

[0033] Fig. 3 schematically illustrates entanglement of an atom of the device shown in Fig. 1 with a photon. id="p-34" id="p-34" id="p-34" id="p-34" id="p-34" id="p-34" id="p-34" id="p-34"

[0034] Fig. 4A schematically shows a single-photon source unit according to an embodiment of the present invention. id="p-35" id="p-35" id="p-35" id="p-35" id="p-35" id="p-35" id="p-35" id="p-35"

[0035] Fig. 4B schematically shows producing a sequential series of single photons from the photon source unit of Fig. 4A. id="p-36" id="p-36" id="p-36" id="p-36" id="p-36" id="p-36" id="p-36" id="p-36"

[0036] Fig. 5A schematically shows an entanglement unit for quantum entanglement of a photonic state with an atomic state according to an embodiment of the present invention. id="p-37" id="p-37" id="p-37" id="p-37" id="p-37" id="p-37" id="p-37" id="p-37"

[0037] Fig. 5B schematically illustrates quantum entanglement of a sequential series of single photonic states with an atomic state according to an embodiment of the present invention. id="p-38" id="p-38" id="p-38" id="p-38" id="p-38" id="p-38" id="p-38" id="p-38"

[0038] Fig. 6 is a flowchart of a method for sourcing photonic graph states according to an embodiment of the present invention. id="p-39" id="p-39" id="p-39" id="p-39" id="p-39" id="p-39" id="p-39" id="p-39"

[0039] Fig. 7 schematically illustrates an apparatus for sourcing a multi-dimensional cluster of quantum-entangled photonic states according to an embodiment of the present invention. id="p-40" id="p-40" id="p-40" id="p-40" id="p-40" id="p-40" id="p-40" id="p-40"

[0040] For simplicity and clarity of illustration, elements shown in the figures are not necessarily drawn to scale, and the dimensions of some elements may be exaggerated relative to other elements. In addition, reference numerals may be repeated among the figures to indicate corresponding or analogous elements.

DETAILED DESCRIPTION id="p-41" id="p-41" id="p-41" id="p-41" id="p-41" id="p-41" id="p-41" id="p-41"

[0041] Fig. 1 schematically illustrates a device 100 for use in quantum computing according to an embodiment of the present invention. Device 100 includes a four-state system 101 of an atom 102 contained within an optical cavity 103 having input/output photon waveguides 104 and 105. A laser source 151 provides pulses for altering the state of atom 102 and to induce emission of photons therefrom. Four-state system 101 includes the following states of atom 102: a first ground state 111, a first excited state 112, a second ground state 113, and a second excited state 114. A transition 121 between first ground state 111 and first excited state 112 has an energy E1, and is associated with an interacting photonic mode 1. A transition 122 between first excited state 112 and second ground state 113 has an energy E2, and is associated with an interacting photonic mode 2. A transition 123 between second ground state 113 and second excited state 114 has an energy E4, and is associated with an interacting photonic mode 3. The transitions 122 and 123 may be selected such that they are orthogonally polarized with respect to each other. A photon 180 is in a non-interacting photonic mode 4, which is not associated with any transitions of atom 102 in optical cavity 103. Photon 180 in photonic mode 4 does not pass through the waveguide associated with optical cavity 103 and atom 102, and therefore does not interact therewith. The modes are indicated in the text by their mode numbers in underlined bold, and in drawings by bold mode numbers in square boxes. id="p-42" id="p-42" id="p-42" id="p-42" id="p-42" id="p-42" id="p-42" id="p-42"

[0042] The device 100 further comprises a magnet 141 generating a magnetic field. The magnetic field may be configured to ensure that the transitions are within the bandwidth of the optical cavity 103. It may be further configured to ensure that the first and second excited states 112, 114 are at the same energy level, i.e., that E2 and E4 are equal.

Accordingly, a photon emitted in in transition 122 (photonic mode 2) have the same energy as one emitted in transition 123 (photonic mode 3). The first and second ground states 111, 113 may be maintained at different energy levels (i.e., E1 ≠ E4), facilitating addressing transition 121 and transition 123 independently of each other. id="p-43" id="p-43" id="p-43" id="p-43" id="p-43" id="p-43" id="p-43" id="p-43"

[0043] The term "mode" (or "photonic mode") herein denotes a solution of the electromagnetic wave equation under some boundary conditions. As a non-limiting example, a given mode might apply to a pulse of photons having a particular pulse shape centered at a wavelength of 780 nm, propagating left in a (single mode) fiber and having a vertical polarization. A change of any parameter (direction, polarization, size, divergence, etc.) renders the originally assigned mode no longer applicable, and changes the mode of the photons to a different, perhaps undefined mode. In embodiments of the present invention, atomic transitions are coupled to mode 1, mode 2, or mode 3 of the incoming/outgoing photons. As noted and illustrated in Fig. 1, however, there is no coupling between atomic transitions of this embodiment and a photon in mode 4. id="p-44" id="p-44" id="p-44" id="p-44" id="p-44" id="p-44" id="p-44" id="p-44"

[0044] There is no direct transition between first ground state 111 and second ground state 113. The energy difference E3 between them arises on account of an energy splitting of the ground states due to the magnetic field of a magnet 141 located proximate to optical cavity 103. According to this embodiment, the energy differences of the transitions – notably on account of the magnetic field – are one factor that provides the ability to individually address the different transitions. Another factor for individually addressing the transitions involves the polarization of photons used to excite the transitions, as is discussed in more detail below. Consequently, a control/selection capability 152 uses individual addressing of the transitions for control and selection of the various functions enabled by the individual addressing of the different transitions. id="p-45" id="p-45" id="p-45" id="p-45" id="p-45" id="p-45" id="p-45" id="p-45"

[0045] In a related embodiment, magnet 141 is a solenoid. In another related embodiment, the magnetic field in the region of atom 102 is substantially 50 gauss or greater. In a further related embodiment, laser source 151 is located within device 101 or external to device 101; and in yet another related embodiment, multiple dedicated laser sources are provided. id="p-46" id="p-46" id="p-46" id="p-46" id="p-46" id="p-46" id="p-46" id="p-46"

[0046] In another embodiment, device 100 is incorporated into a miniaturized component along with additional functional units (indicated by ellipsis 161) for specialized purposes. id="p-47" id="p-47" id="p-47" id="p-47" id="p-47" id="p-47" id="p-47" id="p-47"

[0047] In another related embodiment, atom 102 is a Rubidium atom, such as an atom of the isotope 87Rb. id="p-48" id="p-48" id="p-48" id="p-48" id="p-48" id="p-48" id="p-48" id="p-48"

[0048] Fig. 2A is a state diagram for a transition of atom 102 of device 100 (Fig. 1), which is initially in first ground state 111, designated as a state |1)a (shown in dotted lines). An incoming photon 171 via waveguide 104 (Fig. 1) excites a transition 121A in atom 102, from first ground state 111 to first excited state 112. Transition 121A followed by a transition 122A from first excited state 112 to second ground state 113, is a transition sequence which results in an emission of an outgoing photon 172 via waveguide 104 in a direction opposite to that of incoming photon 171. Photon 171 is designated as being in a state |0)p with a direction-polarity denoted as a+. In contrast, photon 172 is designated as being in a state |1)p with a direction-polarity denoted as a–. After transition 122A, atom 102 is designated as being in a state |0)a. id="p-49" id="p-49" id="p-49" id="p-49" id="p-49" id="p-49" id="p-49" id="p-49"

[0049] The transition described above and illustrated in Fig. 2A is used in a single-photon source unit according to an embodiment of the present invention, as described and illustrated below. The verb "source" and its inflected forms herein denote the providing of photons according to embodiments of the present invention, including the providing of single photons, the providing of photon pulses, and the providing of clusters of single photons. The term "single photon source" herein denotes the case where only a single photon is sourced at a time. id="p-50" id="p-50" id="p-50" id="p-50" id="p-50" id="p-50" id="p-50" id="p-50"

[0050] Fig. 2B is a state diagram for a transition of atom 102 of device 100 (Fig. 1), which is initially in second ground state 113, state |0)a (shown in dotted lines). An incoming photon 173 via waveguide 105 (Fig. 1) excites a transition 122B in atom 102, from second ground state 113 to first excited state 112. Transition 122B followed by a transition 122B from first excited state 112 to first ground state 111, is a transition sequence which results in an emission of an outgoing photon 174 via waveguide 105 in a direction opposite to that of incoming photon 173. Photon 173 is in a state |1)p with a direction-polarity a–. In contrast, photon 174 is in state |0)p with a direction-polarity a+. After transition 121B, atom 102 is in state |1)a. id="p-51" id="p-51" id="p-51" id="p-51" id="p-51" id="p-51" id="p-51" id="p-51"

[0051] The transition described above and illustrated in Fig. 2B is also used in the source unit according to an embodiment, as described and illustrated below. id="p-52" id="p-52" id="p-52" id="p-52" id="p-52" id="p-52" id="p-52" id="p-52"

[0052] Fig. 2C is a state diagram showing no transitions of atom 102 in second ground state 113 (in state |0)a) for an incoming a+ photon 175 in state |0)p. Incoming a+ photon 175 continues on its way unchanged. id="p-53" id="p-53" id="p-53" id="p-53" id="p-53" id="p-53" id="p-53" id="p-53"

[0053] Likewise, Fig. 2D is a state diagram showing no transitions of atom 102 in first ground state 111 (in state |1)a) for an incoming a– photon 176 in state |1)p. Incoming a photon 176 continues on its way unchanged. id="p-54" id="p-54" id="p-54" id="p-54" id="p-54" id="p-54" id="p-54" id="p-54"

[0054] Fig. 2E illustrates a swap gate 201 performing "read" and "write" operations of a qubit on the atom 102, enabling, inter alia, a measurement 200 of the atom of the device 100, according to an embodiment of the present invention. This figure combines the results of the transitions previously discussed and illustrated in Fig. 2A through Fig. 2D.

In Fig. 2E, the atom 102 is initially in a superposition state of the first and second ground states 111, 113 with probability amplitudes y and 5, respectively. The incoming photon 202 is in a superposition of photonic modes 1 and 2 with probability amplitudes a and p, respectively (in Fig. 2E, a single photon, e.g., 202, in a superposition of photonic modes is illustrated as two photons; it will be appreciated that this is not meant to imply the presence of two separate photons). Since the processes described in Fig. 2A through 2D are coherent, the state of the incoming photon is swapped with the state of the atom; the outgoing photon 204 is in a superposition state of modes 1 and 2 with probability amplitudes 5 and y, respectively, and the atom 102 is left in a superposition state of the first and second ground states 111, 113 with probability amplitudes P and a, respectively.

This interaction allows measuring and setting the state of atom 102 in a single step, by appropriately choosing the state of the incoming photon and by measuring the direction­ polarization of the outgoing photon 204. In a related embodiment, this is utilized in an entanglement method, as discussed below. id="p-55" id="p-55" id="p-55" id="p-55" id="p-55" id="p-55" id="p-55" id="p-55"

[0055] As illustrated in Fig. 3, the atom 102 is initially in a superposition of ground states 111 and 113, and incoming photon 301 is in a superposition of mode 3 and (non­ interacting) mode 4, and has energy E4. (In order to distinguish from the description above of the photon in modes 1 and 2, the photon in modes 3 and 4 will be indicated as |1)p* and |0)p*, respectively.) As the atom 102 and the incoming photon 301 may initially be described by their respective superpositions, the atom and the emitted photon 302 are entangled. In particular, the atom 102 and the emitted photon 302 are in a size-2 cluster state, in which a first mode corresponds to a superposition of modes 3 and 4 of the 1 outgoing photon 302 ( [|^⟩p* - |1⟩p* ]) with the atom in its first ground state 111 of the atom 102, and the second mode corresponds to a complementary superposition of 1 modes 3 and 4 of the outgoing photon 302 ( [|^⟩p* + |1⟩p* ]) with the atom in its second ground state 113 of the atom 102. (One having skill in the art will recognize that this is one implementation of controlled-Z gate with the Duan-Kimble protocol.) The different input states may be summarized as follows: • the incoming photon 301 is in mode 4 and the atom 102 is in its first ground state 111: no interaction therebetween; • the incoming photon 301 is in mode 4 and the atom 102 is in its second ground state 113: no interaction therebetween. • the incoming photon 301 is in mode 3 and the atom 102 is in its first ground state 111: atom is unaffected, but the waveform of the photon is phase-flipped (i.e., the atom is in a non-interacting state with the intra-cavity field, implying that the photon interacts with an empty cavity; accordingly, a photon on resonance with the empty cavity induces an intra-cavity field buildup which in turn results in a phase flip of the outgoing photon 302 relative to a the photon in non-interacting mode 4); and • the incoming photon 301 is in mode 3 and the atom 102 is in its second ground state 113: the atom transitions from the second ground state to the second excited state 114 (shown as transition 123A), then transitions back to the second ground state (shown as transition 123B), and in the process emits a photon 302, also with energy E4 (i.e., the atom is in an interacting state with the intra-cavity field, implying that the transition 123 is addressed by the incoming photon in mode 3; accordingly, the atom eliminates the intra-cavity field build up, and no phase flip of the outgoing photon 302 occurs). id="p-56" id="p-56" id="p-56" id="p-56" id="p-56" id="p-56" id="p-56" id="p-56"

[0056] The quantum entanglement is graphically represented in the drawings by a double line 310 connecting atom 102 with photon 302. The double-line graphical convention also indicates quantum entanglement among photons, where applicable. id="p-57" id="p-57" id="p-57" id="p-57" id="p-57" id="p-57" id="p-57" id="p-57"

[0057] Fig. 4A schematically shows a single-photon source unit 401 according to an embodiment of the present invention. Source unit 401 includes a device corresponding to device 100 of Fig. 1. In particular, a source unit atom 402 corresponds to atom 102 in Fig. 1, but for clarity the other elements corresponding to those of device 100, such as optical cavity 103, are omitted from Fig. 4A. id="p-58" id="p-58" id="p-58" id="p-58" id="p-58" id="p-58" id="p-58" id="p-58"

[0058] To initialize source unit 401 into an initial |1)a state, an initialization pulse 403 of multiple a– photons in state |1)p is introduced. If atom 402 is already in first ground state 111 (in state |1)a), then as shown in Fig. 2D and described above, initialization pulse 403 will have no effect on atom 402, which will remain in state |1)a. However, if atom 402 is in second ground state 113 (in state |0)a), the first photon of initialization pulse 403 to enter source unit 401 will cause atom 402 to transition to first ground state 111 (in state |1)a), as shown in Fig. 2B and described above, thereby initializing source unit 401 into the desired initial state. id="p-59" id="p-59" id="p-59" id="p-59" id="p-59" id="p-59" id="p-59" id="p-59"

[0059] Returning to Fig. 4A, after introducing initialization pulse 403, a generating pulse 404 of multiple a+ photons in state |0)p is introduced into source unit 401. A time axis 405 shows the sequence of initialization pulse 403 followed by generating pulse 404.

Having first initialized source unit 401 such that atom 402 is in the |1)a state, the first a+ photon in state |0)p of generating pulse 404 will cause the transition of Fig. 2A, as previously described, resulting in the output of a single a– photon 406 in state |1)p. Photon 406 is output in the opposite direction from the photons of generating pulse 404 and therefore is easily separated from the other photons of generating pulse 404, which are discarded. id="p-60" id="p-60" id="p-60" id="p-60" id="p-60" id="p-60" id="p-60" id="p-60"

[0060] Fig. 4B schematically shows producing a time-sequenced series 412 of a specific number of single photons from single-photon source unit 401 according to an embodiment of the present invention. A time-sequenced series 410 of initialization pulse­ generating pulse pairs is input into source unit 401, resulting in a time-sequenced series 412 having a single photon output for each pair of initialization pulse – generating pulse input. The output photons are individually output and are not yet entangled as of this operation. id="p-61" id="p-61" id="p-61" id="p-61" id="p-61" id="p-61" id="p-61" id="p-61"

[0061] It is emphasized that the single photons which emanate from single-photon source unit 401 according to embodiments of the present invention are all usable in this architecture; entangling photons through the cavity-enhanced atom-photon interaction does not require the use of indistinguishable photons, as is the case for the probabilistic entanglement with linear optics. In particular, input photon pulses (e.g., pulse 404) do not have to be precisely timed and shaped. Single photons produced according to embodiments of the present invention are perfectly suitable for qubit entanglement even when they exhibit irregularities that make them readily distinguishable. id="p-62" id="p-62" id="p-62" id="p-62" id="p-62" id="p-62" id="p-62" id="p-62"

[0062] Fig. 5A schematically shows an entanglement unit 501 for quantum entanglement of a photonic state with an atomic state of an entanglement unit atom 502 according to an embodiment of the present invention. Entanglement unit 501 includes a device corresponding to device 100 of Fig. 1. In particular, atom 502 corresponds to atom 102 in Fig. 1, but for clarity the other elements corresponding to those of device 100 are omitted from Fig. 5A. id="p-63" id="p-63" id="p-63" id="p-63" id="p-63" id="p-63" id="p-63" id="p-63"

[0063] Entanglement unit 501 must first be prepared by setting atom 502 into the 1 quantum superposition state (|0) a+|1)a). This is done by introducing a pulse 503 in the appropriate superposition of modes 1 and 2, in order to swap in the desired state.

Thereafter, the entanglement mechanism relating to atom 502 corresponds to the process shown in Fig. 3 and described previously. By making a measurement 200 of the state of atom 502, the entanglement between atom 502 and any photon(s) previously entangled therewith is broken. Measurement 200 according to an embodiment of the present invention is illustrated in Fig. 2E as previously described. It is noted that device 100 as described above with reference to and as illustrated in Fig. 1 is thus capable of both entanglement of a photon with atom 102 as well as breaking the entanglement (via measurement 200). id="p-64" id="p-64" id="p-64" id="p-64" id="p-64" id="p-64" id="p-64" id="p-64"

[0064] Fig. 5B schematically illustrates quantum entanglement of time-sequential series 412 of single photonic states with the prepared superposition state of atom 502 according to an embodiment of the present invention. The entanglement operation results in a time- sequential series 512 of entangled photons. After measurement 200 is performed, atom 502 itself is no longer entangled with the photons of series 512, but the photons remain entangled with each other. The photons of series 512 are represented mutually connected by double lines to a single atom, indicating that they are mutually entangled therewith. id="p-65" id="p-65" id="p-65" id="p-65" id="p-65" id="p-65" id="p-65" id="p-65"

[0065] Fig. 6 is a flowchart of a method for sourcing a photonic graph states according to an embodiment of the present invention. In a related embodiment, this method is performed by a control/select unit 152 of device 100 as detailed in Fig. 1 and described previously. In a preparation step 601, an entanglement unit atom (such as entanglement 1 unit 501 atom 502) is set to state (|0 ) a+|1)a) by utilizing a pulse 503 in the appropriate superposition of modes 1 and 2, in order to swap in the desired state as previously described. id="p-66" id="p-66" id="p-66" id="p-66" id="p-66" id="p-66" id="p-66" id="p-66"

[0066] After preparation, a loop begins point 602 starts a loop of steps to repeat n times through a loop end point 608. id="p-67" id="p-67" id="p-67" id="p-67" id="p-67" id="p-67" id="p-67" id="p-67"

[0067] Inside loop 602 – 608 a step 603 initializes a source unit atom (such as source unit 401 atom 402) to a state |1)a by injecting a pulse 403 of a– photons in state |1)p, as previously illustrated and described. id="p-68" id="p-68" id="p-68" id="p-68" id="p-68" id="p-68" id="p-68" id="p-68"

[0068] Next, in a step 604, a single photon is generated by injecting a classical laser pulse 404 of mode 1 photons into the source unit, as previously illustrated and detailed, and illuminated in a caption 605. id="p-69" id="p-69" id="p-69" id="p-69" id="p-69" id="p-69" id="p-69" id="p-69"

[0069] Following, in a step 606, the single mode 2 photon from step 604 is routed into an entanglement unit (such as entanglement unit 501 with atom 502) in a superposition of mode 3 and mode 4: |1 )2→ 1(|1 )4 + |0 )3|1 )3 |0 )4 ), and which is subsequently quantum-entangled with the entanglement unit atom. id="p-70" id="p-70" id="p-70" id="p-70" id="p-70" id="p-70" id="p-70" id="p-70"

[0070] A caption 607 details how photonic mode 3 interacts with cyclic transition 123 (Fig. 1) of entanglement unit 501 atom 502, whereas photonic mode 4 has no interaction.

This particular configuration implements a controlled-Z quantum gate. id="p-71" id="p-71" id="p-71" id="p-71" id="p-71" id="p-71" id="p-71" id="p-71"

[0071] At loop end 608, after n repetitions the state of entanglement unit atom (such as atom 502) will be entangled with the states of n photons, as illuminated in a caption 609. id="p-72" id="p-72" id="p-72" id="p-72" id="p-72" id="p-72" id="p-72" id="p-72"

[0072] In a step 610, a measurement is performed on the entanglement unit atom (such as atom 502) in the x-y plane of the Bloch sphere, such as measurement 200, which is illustrated schematically in Fig. 2E and as detailed previously. Carrying out measurement 200 disentangles the entanglement unit atom from being quantum entangled with the photons, leaving a time-sequenced cluster state of n photonic states in an entangled state.

It is again noted that device 100 as provided by an embodiment of the present invention is capable both of operation as an entanglement unit (such as entanglement unit 501) and of carrying out measurement 200 without the need for additional measurement apparatus.

This step is illuminated in a caption 611. id="p-73" id="p-73" id="p-73" id="p-73" id="p-73" id="p-73" id="p-73" id="p-73"

[0073] Finally, in a step 612, the time-sequenced cluster state of n entangled photons is output for qubit use in quantum computing. id="p-74" id="p-74" id="p-74" id="p-74" id="p-74" id="p-74" id="p-74" id="p-74"

[0074] Fig. 7 schematically illustrates an apparatus according to an embodiment of the present invention, which employs an arrangement of multiple devices based on device 100 for sourcing a multi-dimensional graph state or cluster of quantum-entangled photonic states. In this embodiment, a one-dimensional spatial array combined with a time-dimensional sequence of entangled photons is output; and in a related embodiment, a two-dimensional spatial array combined with a time-dimensional sequence of entangled photons is output. In these embodiments, linear optics elements are used judiciously in a limited capacity to perform specific adjunct functions, rather than as basic components, thereby avoiding the difficulties and shortcomings of linear optics as previously discussed. id="p-75" id="p-75" id="p-75" id="p-75" id="p-75" id="p-75" id="p-75" id="p-75"

[0075] In the embodiment illustrated, a series of pulses 701 is fed to a single-photon source unit 702 whose single photon output passes through first stage linear optics and phase control elements 703 to a first stage entanglement unit 704, and from then to second stage linear optics and phase control elements 705, to a second stage entanglement unit 706, and from thence to an output channel 707, which outputs a time-sequence 405 of entangled photons in photonic clusters and/or graph states. Arranged along a spatial axis 710 is an array 708 of similar components fed by similar series of pulses, as shown in Fig. 7. In related embodiments, spatial axis 710 is an x-axis, a y-axis, or a combination thereof in an x-y plane. For a one-dimensional spatial array, only the first stage linear optics, phase control elements, and entanglement units may be needed, for output of a one-dimensional spatial array of entangled photons in a time-dimensional sequence. With both x-axis and y-axis for a two-dimensional spatial array, the second stage linear optics, phase control elements, and entanglement units are also used, for output of a two­ dimensional spatial array of entangled photons in a time-dimensional sequence. In all cases, each single-photon source, the linear optics and phase control elements, and respective entanglement unit (or respective entanglement units, in the case of two-stage operation) are correspondingly displaced along the appropriate spatial axis 710.

Claims (16)

1. A method for sourcing a graph state of quantum-entangled photons, the method comprising: providing a photon source unit for sourcing single photons, said photon source unit comprising a source unit atom disposed within an intra-cavity field of a source- optical cavity; providing a photon entanglement unit for quantum entanglement of photonic states, said photon entanglement unit atom disposed within an intra-cavity field of an entanglement-optical cavity; sending a pulse to the photon entanglement unit to set the entanglement unit atom to 1 an atomic quantum superposition state (|0) + |1)); sending a pulse to the photon source unit to initialize the source unit atom to a quantum state |1); sending a pulse of photons in a first photonic mode into the photon source unit to cause the source unit atom to output a single photon in a second photonic mode, wherein the first photonic mode couples to a first transition of the source unit atom, and wherein the second photonic mode couples to a second transition of the source unit atom; routing the single photon in the second photonic mode to the photon entanglement unit to a superposition of a third photonic mode and a fourth photonic mode; wherein the third photonic mode couples to a third transition of the entanglement unit atom; wherein the fourth photonic mode does not couple to any transition of the source unit atom; wherein the fourth photonic mode does not couple to the entanglement-optical cavity; and wherein the output photon in a superposition of a third photonic mode and a fourth photonic mode is quantum-entangled with the entanglement unit atom; repeating the routing at least once to route at least one additional single photon in the second photonic mode to the photon entanglement unit in a superposition of the - 16 - P-592799-IL third photonic mode and the fourth photonic mode in quantum entanglement with the entanglement unit atom; performing a measurement on the entanglement unit atom, thereby disentangling it from the photons in the third photonic mode and the fourth photonic mode; wherein the at least two photons in the superposition state of the third photonic mode and the fourth photonic mode are quantum entangled; and outputting the at least two photons in the superposition state of the third photonic mode and the fourth photonic mode as time-sequenced mutually entangled photons.

2. The method according to claim 2, wherein performing a measurement on the entanglement unit atom includes performing a measurement in an x-y plane of a Bloch sphere.

3. A device for sourcing a graph state of quantum-entangled photons, the device comprising: a plurality of single photon source units; a first stage of linear optics elements; and a first plurality of entanglement units; wherein the plurality of single photon source units, the first stage of linear optics elements, and the first plurality of entanglement units are correspondingly displaced along a predetermined spatial axis; wherein each single photon source unit of the plurality of photon source units outputs single photons to the first stage of linear optics elements, and therefrom into a respective entanglement unit of the first plurality of entanglement units; and wherein the first plurality of entanglement unit outputs a one-dimensional spatial array of entangled photons in a time-dimensional sequence.

4. The device according to claim 3, wherein the single photon source units and/or the entanglement units each comprise: an atom in a first ground state, a first excited state, a second ground state, a second excited state, or a superposition thereof; the atom being further configured to selectively undergo: a first transition between the first ground state and the first excited state; a second transition between the first excited state and the second ground state; and - 17 - P-592799-IL a third transition between the second ground state and the second excited state; the device comprising an optical cavity defining an intra-cavity field for disposing therewithin the atom, a photonic waveguide coupled to the optical cavity, a magnet configured to produce a magnetic field on the atom, and a laser source configured to produce pulses of photons in coherent states, the device being configured such that each of said transitions are within the resonance of the optical cavity.

5. The device according to claim 4, wherein the first and second transitions are selected such that they are orthogonally polarized with respect to each other.

6. The device according to any one of claims 4 and 5, wherein the first and second excited states are at the same energy level.

7. The device according to any one of claims 4 through 6, wherein the first and second ground states are at different energy levels from one another.

8. The device according to any one of claims 4 through 7, wherein said laser source is configured for selectively generating: a pulse configured to initialize the atom by inducing it to undergo the first and second transitions from the first ground state to the second ground state via the first excited state; and a pulse configured to source a single photon from the atom by inducing it to undergo the second and first transitions from the second ground state to the first ground state via the first excited state.

9. The device according to any one of claims 4 through 8, said laser source being configured to set the state of the atom to a quantum superposition state and for generating a preparation photon being in state of superposition of first and second preparation modes, wherein interaction of the preparation photon with the atom results in its first and second ground states being in a state of superposition corresponding to the state of superposition of the first and second preparation modes.

10. The device according to any one of claims 4 through 9, wherein the atom is a Rubidium atom.

11. The device according to any one of claims 4 through 10, wherein the magnet is a solenoid. - 18 - P-592799-IL

12. The device according to any one of claims 3 through 11, wherein the first stage of linear optics elements includes phase control.

13. The device according to any one of claims 3 through 12, further comprising: a second stage of linear optics elements; and a second plurality of entanglement units; wherein the second stage of linear optics elements, and the second plurality of entanglement units are correspondingly displaced with the plurality of single photon source units, the first stage of linear optics elements, and the first plurality of entanglement units along the predetermined spatial axis; and wherein the single photons in an entangled state output from each respective entanglement unit of the first plurality of entanglement units are input to the second stage of linear optics elements and therefrom into a respective entanglement unit of the second plurality of entanglement units.

14. The device according to claim 13, wherein the second plurality of entanglement unit is configured to output a two-dimensional spatial array of entangled photons in a time-dimensional sequence.

15. The device according to any one of claims 3 through 14, configured to produce entangled qubits for use with a quantum computer.

16. The device according to any one of claims 3 through 15, configured to carry out the method according to any one of claims 1 and 2. - 19 -