Generating photonic quantum states for quantum computation

Abstract

Photonic quantum computation comprises generating n-qubit photonic states, the generating comprising: emitting from a two-dimensional (2D) array of photon emitters, photons that propagate in a direction substantially perpendicular to a first plane over which the 2D array of photon emitters are arranged, and generating the n-qubit photonic states based at least in part on the 2D array of photon emitters; modulating the n-qubit photonic states in a volumetric spatial light modulator (VSLM), the modulating comprising receiving at least a portion of the n-qubit photonic quantum states and generating a distribution of photonic quantum states; generating detection event signals from respective photon detectors distributed over a region that receives a portion of the distribution of photonic quantum states; and controlling at least some modulation applied by the VSLM based at least in part on detection event signals from two or more of the photon detectors.

Description

GENERATING PHOTONIC QUANTUM STATES FOR QUANTUM COMPUTATIONCROSS-REFERENCE TO RELATED APPLICATION(S)

[0001] This application claims priority to and the benefit of U.S. Provisional Application Serial No. 63 / 521,123, entitled “GENERATING PHOTONIC QUANTUM STATES FOR QUANTUM COMPUTATION,” filed June 15, 2023, the entire disclosure of which is incorporated herein by reference.STATEMENT AS TO FEDERALLY SPONSORED RESEARCH

[0002] This invention was made with government support under Grant No. W911NF2110325, awarded by the Army Research Office. The government has certain rights in the invention.TECHNICAL FIELD

[0003] This disclosure relates to generating photonic quantum states for quantum computation.BACKGROUND

[0004] While the properties of particles and fields cannot be fully explained by classical mechanics, quantum mechanics has emerged as a toolbox to capture and explain their rich behaviors. Properties of the quantum world can be utilized in applications that are not fundamentally possible using classical systems. Quantum computing, for example, harnesses the ability of quantum objects to exist in superpositions of multiple states. Whereas classical computers rely on bytes that can exist in states of one or zero, quantum computers rely on qubits that can exist in a “superposition” of multiple possible states: one, zero, or the linear combination thereof. On the basis of the exponential scaling of computational power, quantum computers can, in theory, quickly outpace the processing power of current state-of-the-art supercomputers. Quantum computing’s advantage (over classical computing) is sometimes stated in terms of scaling laws. These potential advantages should also be assessed in view of potentially importantconstant factors or other overhead costs, which can in some cases impact the utility of quantum computing. For example, it could be cheaper (in terms of the overall costs) to use classical supercomputing to solve a problem compared to using a quantum computer. This might be true, despite there being a scaling-law advantage for quantum computing.

[0005] Some quantum computers utilize optical or photonic fields and a measurement-based quantum computer (MBQC) architecture to perform computations. In a measurement-based quantum computer, an entangled resource state, such as a cluster state, is prepared by entangling many qubits. A portion of these qubits are then “read-out” or measured, which collapses the entanglement of the cluster states. This measurement step provides the basis for logical gates in the quantum computer. A potential advantage of MBQC is the ability to use the results of the read-out phase to correct for any errors in the operational step. Photonic fields can be desirable in quantum computers to their high generation rates and efficient manipulation, which could provide a path toward scaling quantum computational power with lower rates of error. In addition, optical / photonic fields can be generated and manipulated with devices with low physical footprints and power requirements. These considerations have motivated the further development of photonic quantum computing architectures.SUMMARY

[0006] In one aspect, in general, an apparatus for photonic quantum computation comprises: a source module configured to generate a plurality of n-qubit photonic states, the source module comprising: a two-dimensional (2D) array of photon emitters configured to emit photons that propagate in a direction substantially perpendicular to a first plane over which the 2D array of photon emitters are arranged, and a modulation unit configured to generate the plurality of n- qubit photonic states based at least in part on the 2D array of photon emitters; a volumetric spatial light modulator configured to receive at least a portion of the plurality of n-qubit photonic quantum states and generate a distribution of photonic quantum states; a plurality of photon detectors, each configured to generate a corresponding detection event signal, distributed over a region that receives a portion of the distribution of photonic quantum states; and a control module configured to control at least some modulation applied by the volumetric spatial light modulator based at least in part on detection event signals from two or more of the plurality of photon detectors.

[0007] Aspects can include one or more of the following features.

[0008] Each n-qubit photonic quantum state comprises an entangled state generated from n of the photons emitted from the 2D array of photon emitters.

[0009] The control module is configured to identify at least some of the plurality of n-qubit photonic quantum states based at least in part on processing detection event signals from a first set of photon detectors of the plurality of photon detectors.

[0010] The volumetric spatial light modulator is configured to generate the distribution of photonic quantum states based on linear combinations of photons in the n-qubit photonic quantum states.

[0011] The control module is configured to identify at least some photonic quantum states in the distribution based at least in pail on processing detection event signals from a second set of photon detectors of the plurality of photon detectors that is different from the first set of photon detectors.

[0012] The 2D array of photon emitters in the source module comprises an array of colorcenter spin emitters.

[0013] The plurality of photon detectors comprises a plurality of single-photon detectors, each single-photon detector configured to detect single photons with a probability of at least around 90%.

[0014] The volumetric spatial light modulator comprises plurality of transmissive 2D spatial light modulators (SLMs), and each of the transmissive 2D SLMs includes phase modulation pixels arranged over a plane that is substantially parallel to the first plane.

[0015] The volumetric spatial light modulator comprises a plurality of transmissive 2D spatial light modulators (SLMs), and each of the transmissive 2D SLMs includes phase modulation pixels arranged over a plane that is substantially perpendicular to a direction of propagation of the photons emitted from the 2D array of photon emitters at a time of phase modulation by the transmissive 2D SLMs.

[0016] The apparatus further comprises a quantum computation module configured to receive the distribution of photonic quantum states and process detection event signals from a set of photon detectors of the plurality of photon detectors based at least in part on a quantum circuit that comprises one or more quantum gates.

[0017] Each of a plurality of propagation paths from a photon emitter of the 2D array ofphoton emitters to a corresponding photon detector of the set of photon detectors is a propagation path that is free from any waveguide propagation.

[0018] The modulation unit of the source module comprises a volumetric spatial light modulator.

[0019] The volumetric spatial light modulator of the source module comprises a plurality of transmissive 2D spatial light modulators (SLMs), and each of the transmissive 2D SLMs includes phase modulation pixels arranged over a plane that is substantially perpendicular to a direction of propagation of the photons emitted from the 2D array of photon emitters at a time of phase modulation by the transmissive 2D SLMs.

[0020] The modulation unit of the source module comprises a microwave source configured to modulate the 2D array of photon emitters to generate the plurality of n-qubit photonic states.

[0021] The plurality of n-qubit photonic states comprises a plurality of 3-qubit Greenberger- Home-Zeilinger (GHZ) photonic states.

[0022] The plurality of n-qubit photonic states comprises a plurality of 5-qubit Greenberger- Home-Zeilinger (GHZ) photonic states.

[0023] The plurality of n-qubit photonic states comprises a plurality of n-qubit star-shaped cluster states.

[0024] The photonic quantum states comprise a long-range connected sub-lattice of a Rausendorf-Harrington-Goyal (RHG) lattice.

[0025] The photonic quantum states comprise a three-dimensional (3D) photonic cluster state.

[0026] The 2D array of photon emitters comprises an array of quantum dots.

[0027] The 2D array of photon emitters comprises an array of quantum dots and color-center spin emitters.

[0028] The volumetric spatial light modulator comprises a 3D refractive index distribution.

[0029] The plurality of photon detectors comprises a plurality of single photon detecting pixels of a camera.

[0030] In another aspect, in general, a method for photonic quantum computation comprises: generating a plurality of n-qubit photonic states, the generating comprising: emitting from a two- dimensional (2D) array of photon emitters, photons that propagate in a direction substantially perpendicular to a first plane over which the 2D array of photon emitters are arranged, andgenerating the plurality of n-qubit photonic states based at least in part on the 2D array of photon emitters; modulating the n-qubit photonic states in a volumetric spatial light modulator, the modulating comprising receiving at least a portion of the plurality of n-qubit photonic quantum states and generating a distribution of photonic quantum states; generating detection event signals from respective photon detectors distributed over a region that receives a portion of the distribution of photonic quantum states; and controlling at least some modulation applied by the volumetric spatial light modulator based at least in part on detection event signals from two or more of the photon detectors.

[0031] Aspects can include one or more of the following features.

[0032] Each n-qubit photonic quantum state comprises an entangled state generated from n of the photons emitted from the 2D array of photon emitters.

[0033] The controlling comprises identifying at least some of the plurality of n-qubit photonic quantum states based at least in part on processing detection event signals from a first set of photon detectors of the plurality of photon detectors.

[0034] The volumetric spatial light modulator generates the distribution of photonic quantum states based on linear combinations of photons in the n-qubit photonic quantum states.

[0035] The controlling comprises identifying at least some photonic quantum states in the distribution based at least in part on processing detection event signals from a second set of photon detectors of the plurality of photon detectors that is different from the first set of photon detectors.

[0036] The 2D array of photon emitters comprises an array of color-center spin emitters.

[0037] The plurality of photon detectors comprises a plurality of single-photon detectors, each single-photon detector configured to detect single photons with a probability of at least around 90%.

[0038] The volumetric spatial light modulator comprises plurality of transmissive 2D spatial light modulators (SLMs), and each of the transmissive 2D SLMs includes phase modulation pixels arranged over a plane that is substantially parallel to the first plane.

[0039] The volumetric spatial light modulator comprises a plurality of transmissive 2D spatial light modulators (SLMs), and each of the transmissive 2D SLMs includes phase modulation pixels arranged over a plane that is substantially perpendicular to a direction of propagation of the photons emitted from the 2D array of photon emitters at a time of phasemodulation by the transmissive SLMs.

[0040] The method further comprises performing a quantum computation by receiving the distribution of photonic quantum states and processing detection event signals from a set of photon detectors of the plurality of photon detectors based at least in part on a quantum circuit that comprises one or more quantum gates.

[0041] Each of a plurality of propagation paths from a photon emitter of the 2D array of photon emitters to a corresponding photon detector of the set of photon detectors is a propagation path that is free from any waveguide propagation.

[0042] Aspects can have one or more of the following advantages: compact form factor, high quality deterministic photonic qubits, ultra-low loss, and / or ultra-compact gate realization.

[0043] Other features and advantages will become apparent from the following description, and from the figures and claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The disclosure is best understood from the following detailed description when read in conjunction with the accompanying drawing. It is emphasized that, according to common practice, the various features of the drawing are not to-scale. On the contrary, the dimensions of the various features are arbitrarily expanded or reduced for clarity.

[0045] FIG. 1A is a schematic diagram of an example photonic quantum computing system.

[0046] FIG. IB is a schematic diagram of an example source module of a photonic quantum computing system.

[0047] FIG. 1C is a schematic diagram of an example volumetric spatial light modulator of a photonic quantum computing system.

[0048] FIG. ID is a schematic diagram of an example detector module of a photonic quantum computing system.

[0049] FIG. 2 is a schematic diagram of an example circuit to generate photonic qubits.DETAILED DESCRIPTION

[0050] Broadly, quantum computing includes steps such as generating and preparing a system of qubits, subjecting the qubit system to a series of logical gates to perform calculations, and then reading out or detecting the final qubit states. A consideration in quantum computing ismaintaining qubit states throughout the process of their preparation and manipulation. At each step of this process, a qubit can lose its quantum state, or decohere, which translates directly to a loss of computational power. Optimizing a quantum system’s fidelity, or the quality and reliability of the qubits as well as the logic gates, to preserve the “indistinguishability” of the superposition of qubit states can be useful. Schemes for quantum error correction and / or mitigation can be used, and in some systems techniques can be used with a goal of making quantum computing architectures that are fundamentally stable against errors, or “fault-tolerant.”

[0051] Some fault-tolerant architectures for quantum computing include all-photonic approaches where photons encode the qubit, as well as matter-qubit approaches such as superconducting, trapped-ion and color-center spin-based qubits. Detailed quantification of the hardware resource requirements to achieve fault-tolerant operation are also relevant to these architectures. At a broad level, “resource requirements” can be classified into the following two categories: (1) construction cost, e.g., device fabrication, cryostats, labor, etc. - the full cost of production, and (2) operational cost, e.g., wall-plug power, physical space requirement, programming, etc.). Balancing these resource requirements with the capabilities of a quantum computing system represents a challenge within the field of quantum computing.

[0052] Meeting the fault-tolerance threshold is a helpful goal for certain quantum computer architecture to be useful. When a quantum computer’s device specifications collectively barely meet the fault-tolerance threshold, the device overhead, e.g., logical-to-physical qubit ratio, may be impractically large. The further inside the fault-tolerance threshold one gets by building better devices and better codes, the overhead decreases. It remains a challenge to quantify a quantum computer’s cost (sum of both categories of casts stated above) rigorously and determine an operational scenario where that total cost is significantly smaller than the computational value provided by the quantum computer.

[0053] Some of the techniques described herein provide examples of approaches to fault- tolerant utility-scale quantum computing, which could break the aforesaid cost-to-value barrier more effectively compared to other approaches.

[0054] FIG. 1A shows an example of a photonic quantum computing system 100A comprising a source module 102 that can output a 2D array of n-qubit photonic states 104. A volumetric spatial light modulator 106 can modulate the n-qubit photonic states to generate a distribution of photonic quantum states 108 before a detector module 110 comprising a pluralityof detectors resolves the signals. A control module 112 can be configured to control the modulation applied by the volumetric spatial light modulator 106 based at least in part on detection event signals from the detector module 110.

[0055] FIG. IB depicts an example implementation of the source module 102. In this example, a plurality of photon emitters 122 is arranged on a two-dimensional (2D) array 126 such that the emitters produce single photons 124 that propagate in a direction substantially perpendicular to the first plane over which the 2D array of photon emitters are arranged. The photon emitters can consist of a densely packed 2D array of silicon vacancy (SiV) color-center spin emitters comprising an atomic silicon defect embedded in a carbon crystalline lattice. The qubits can be encoded by the emitted photons. In this example, the qubits comprise dual-rail time-bin discrete variable single-photon qubits wherein each qubit comprises a single photon in a superposition of two distinct temporal and / or spatial modes. In this example, a modulation unit 126 generates a plurality of n-qubit photonic quantum states 128, for instance, Greenberger- Home-Zeilinger or GHZ states, from n-photons emitted from the 2D array of photon emitters. N- qubit GHZ cluster states comprise a system of n qubits that are maximally entangled with each other such that the state of one qubit in the cluster depends on the states of the other qubits in the cluster. In this example, fault-tolerant 3-qubit GHZ cluster states 127 are generated from single photons.

[0056] FIG. 1C depicts an example implementation of the volumetric spatial light modulator 106. A volumetric spatial light modulator can comprise a series of linear optical elements that can modulate an input 2D array of optical fields as they propagate the length of the sorter. In this example, the volumetric spatial light modulator 106 comprises a plurality of one or more transmissive phase spatial light modulators (SLMs) 132 separated by gaps through which the optical fields can propagate in free space. Each transmissive phase SLM in this example comprises a plurality of elements 134 that can apply some phase modulation to a portion of an optical wave. The volumetric spatial light modulator 106 can be used to generate a distribution of photonic quantum states 138 from the plurality of n-qubit photonic quantum states 128. In this example, a long-range-connected sub-lattice of the cluster state lattice referred to as a Rausendorf-Harrington-Goyal (RHG) lattice is generated from 3-qubit GHZ cluster states 127. The RHG lattice comprises repeating unit cells of a cubic lattice with qubits arranged at the center of each face and at the center of each edge. Other implementations of the volumetricspatial light modulator 106 are also possible. For example, instead of, or in combination with, a series of 2D SLMs, there may be a material or device capable of continuously modulating the optical wave as it propagates through a defined 3D volume.

[0057] FIG. ID depicts an example implementation of the detector module 110. In this example, the detector module 110 comprises a plurality of photon detectors 146, each configured to generate a corresponding detection event signal in time and space, that can resolve the optical signals from the photonic quantum state 138. The output signal from the photon detectors 148 is directed to a control module 112 that can directly modulate the volumetric spatial light modulator 106 by means of a connection 144. The control module 112 is configured to modulate the volumetric spatial light modulator based in part on signals collected from a portion of the plurality of photon detectors 142, e.g., using electro-optic feedback. In this way, a quantum algorithm can be executed by an adaptive set of single photon measurements. In some implementations of a photonic quantum computer, the plurality of photon detectors can comprise a plurality of superconducting nanowire single-photon detectors or avalanche photodiodes. In some implementations, an electron-multiplying intensified charge coupled device can be used as the plurality of photon detectors.

[0058] In some implementations of a photonic quantum computing architecture, the single photon emitter array can consist of a 2D array of vacancy centers of other atoms doped into a carbon crystalline lattice, including tin and nitrogen. With this configuration, an optical source such as a laser is utilized to excite the vacancy center, which causes the emission of single photons. Alternatively, other implementations of the emitter array can consist of a 2D array of quantum dots, or some combination of vacancy centers and quantum dots. Further, some examples can utilize an on-chip sFWM or SPDC array of photon emitters. In some implementations, the system described herein may be designed to operate over a predetermined range of optical wavelengths such as, for example, the A = 400 nm to 1600 nm. In some implementations, the system described herein may be designed to operate at a single optical wavelength such as, for example, the zero-phonon line emission of a SiV center, A = 738 nm.

[0059] A volumetric spatial light modulator can be used as the modulator of the source unit to prepare resource states for MBQC. Resource states arc small n-qubit entangled cluster states, for instance 3- or 5-qubit states, that are used to create a cluster state large enough to support MBQC. In some implementations, resource states can be n-qubit GHZ states, in otherimplementations, resource states can be n-qubit star-shaped cluster states. An n-qubit star-shaped cluster state is local-Clifford equivalent to the n-qubit GHZ state, such that applying Hadamard gates to the n-1 arm qubits of the star converts it into a GHZ state and vice versa.

[0060] In some implementations of a photonic quantum computer, deterministic 3-qubit GHZ states can be utilized as resource states. FIG. 2 shows an example circuit 200 that can generate photonic 3-qubit GHZ states by interfering 6 photons produced from photon sources 202 in a 12-mode linear-optical circuit 208 comprising several linear-optical elements 204. These linear-optical elements can comprise optical beam-splitters or spatial spatial light modulators, such that each linear-optical element has two possible output states. A photon impinging on an input state of a linear-optical element can thus be directed to one output state or the other, for instance one spatial mode or another. By using a succession of these linear optical elements connected to each other, superpositions of the input 6 photons can be prepared among the 12 output modes and utilized as qubits. Following the linear-optical circuit, 6 detectors 206 resolve the signals, leaving 6 undetected modes carrying the photonic 3-qubit GHZ states. In such an example, each qubit is encoded in two modes of the linear-optical circuit. In this example, the fidelity of the linear-optical circuit measures its ability to successfully prepare the superposition of the two modes during the sorting step. The probability of success for generating the 3 photonic 3-qubit GHZ states in such a circuit is (77 / (2 — 77)A2 / 32, where r| is the overall unheralded loss in the 12- mode circuit. In principle, the circuit can be scaled produce any desired number of 3-qubit GHZ states by varying the number of input photons and linear-optical elements.

[0061] The second volumetric spatial light modulator in a photonic quantum computing architecture can perform fusion operations on the resource states to create a larger lattice of entangled qubits. In a fusion operation, two qubits are projected on one of the rotated Bell states and the resource states are grown into a fault-tolerant lattice or “cluster state” on which the computation is performed. The geometry of the cluster state formed after two cluster states have undergone fusion operations is determined by a graph theoretic rule, which depends upon the “rotation” of the Bell state measurement being performed.

[0062] Single photons can be strung together using fusion circuits, or Bell basis measurements on two photonic qubits using linear-optical circuits which succeed with probability 1, into a long-range-connected entangled photonic cluster state. As long as exceedsa percolation threshold, this cluster state could be used for measurement-based quantum computing. The quantum algorithm instructions can then be encoded in a succession of adaptive single photon measurements performed on the photonic cluster state. To date, the best-known linear-optical Bell Measurement (BM) circuit can achieve a success probability A > 0.78. In theory, however, the BM success probability can be relaxed when other photonic states are fused to generate the cluster state, or when the long-range-connected cluster state comprises other types of lattices. For instance, a cluster state for quantum computing can be generated by fusing 3-photon clusters into a 4D extension of the (10,3)-b lattice with a BM success probability k > 0.6. This decreased success requirement leaves room for meeting the percolation threshold even with detector and spatial light modulator losses.

[0063] Some implementations of a photonic quantum computing system can include a 2D array of photon emitters, such as SiV color-centers, tin-vacancy color centers, or quantum dots, that is configured to directly produce n-qubit photonic quantum states, for instance n-photon cluster states. In such an implementation, the atomic spin centers can be repeatedly modulated with microwave pulses to prepare superpositions of spin states prior to their emission such that n-qubit GHZ states are directly produced from the 2D array. In this configuration, optimization of the number of qubits in the n-qubit GHZ state might be necessary to prevent decoherence of the qubit, which in turn would decrease the fidelity of the quantum computer. In such an implementation, a single volumetric spatial light modulator can receive the n-qubit photonic quantum states and generate distributions of photonic quantum states. A plurality of photon detectors, each configured to generate a corresponding detection event signal in space and time, can be used to measure these photonic quantum states. A control module can be configured to control at least some of the phase modulation applied by the volumetric transmission phase shifter based at least in part on detection event signals from two or more of the plurality of photon detectors (e.g., using electro-optic feedback). This configuration could be beneficial due to reduced resource overheads.

[0064] In some implementations of a photonic quantum computing system, the volumetric spatial light modulator can comprise a series of phase SLM elements programmed to sort arbitrary spatial mode sets. In some implementations, the series of phase SLM elements can comprise one or more photonic crystal cavity arrays. A photonic crystal cavity array comprises a plurality of wavelength-scale optical antennas that are arranged in a 2D pattern on asemiconductor slab to form cavities with a resonant frequency. The detuning of these cavities can be modulated by free-carrier dispersion in the semiconductor using an out-of-plane high-speed pLED. In turn, this detuning varies the amplitude and phase of the optical emission from photonic crystal cavity device. By optimizing the design of the underlying unit cells of the photonic crystal cavity array, high-quality beamforming performance can be achieved with nearunity vertical coupling to high-finesse microcavities and femtoJ-order switching energies. Such a design can simultaneously modulate wavelength-scale modes at the space- and time-bandwidth- limit, approaching fundamental limits of multimode optical control. In addition, a photonic crystal cavity array can be produced through optimized, 300 mm full-wafer processing, offering scalable fabrication of compact devices.

[0065] Some implementations of a volumetric spatial light modulator can incorporate SLMs that utilize other materials, for example liquid crystals, to apply a phase modulation to an optical beam. Other implementations can include a device with a volumetric 3D refractive-index distribution that could be implemented using optical metamaterials or holographic techniques. An important consideration in implementing a volumetric spatial light modulator is the balance between the physical footprint of the quantum computer and the gate fidelity. In the quantum computing architecture described herein, the gate fidelity depends on the distance between spatial pixel-basis modes of neighboring photonic qubits, as this distance determines the distinguishability of the spatial modes into which the incoming qubits are sorted. Similarly, crosstalk between pixels of a spatial light modulator could also affect this indistinguishability and output quantum state.

[0066] Unlike the optimized BM configuration described above, the generation of a long- range-connected cluster state for MBQC described herein can, in theory, tolerate sub-unity success probability for the cluster creation process. Starting with the linear-optical creation of 3- qubit GHZ states, a fault-tolerant sub-lattice of the MQBC lattice proposed by Rausendorf- Harrington-Goyal (RHG) can be directly generated, while ensuring that the erasure errors, e.g., missing sites, and logical errors, e.g., caused by imperfections in the fusion gates, are arranged to be within the fault-tolerance threshold of the RHG code. The RHG code is the MQBC version of a topological surface code, such as described in R. Raussendorf, J. Harrington, and K. Goyal, Topological Fault-Tolerance in Cluster State Quantum Computation, New J. Phys. 9, incorporated herein by reference. It is possible to evaluate accurate estimates of the number offault-tolerant photonic qubits we can encode in the diffraction-limited form-factor allowed for using implementations of a photonic computing system as described herein that include, for example, a spin array, and a volumetric spatial light modulator configured by feedback as described herein, also referred to as a volumetric mode sorter.

[0067] Some implementations of a photonic quantum computing system can include optical elements to precisely tailor the properties of the photonic fields from the 2D array of photon emitters prior to a volumetric mode sorter. Such optical elements can be transmissive or reflective and can be placed parallel to the plane of the 2D photon emitters, or at varying angles relative to the plane. In some implementations, the optical elements can be used to separate the photonic fields desired for quantum computing from spurious photonic fields, which can interfere and lower the fidelity of the photonic quantum computing device. Optical elements that can be used to separate photonic fields include, but are not limited to, filtering elements such as: wavelength filters (i.e. edgepass, bandpass) to separate photons with wavelengths outside the desired operating range, polarizing filters to separate photons with polarizations outside the desired operating range, and spatial filters to remove fields from undesired spatial modes.Additionally, optical elements that can modify the photonic properties of the fields impinging on the volumetric phase shifter unit can be utilized to improve the fidelity of the photonic quantum computer, including but not limited to: frequency shifters and half-wave or quarter-wave plates to rotate the polarization state of the optical fields. These optical elements could be particularly helpful in the case of a SiV atomic emitter, as the photons emitted from each individual spin can be of ever-so-slightly different frequencies. If left unaddressed, the slightly different frequencies can result in imperfect visibilities of the interferometric gates, thus increasing coding overheads and reducing the logical qubit counts.

[0068] Advantageous features of the example system compared to traditional photonic MBQC architectures can include one or more of the following:

[0069] (a) Compact form factor: The combination of the high-density array of spin-based emitters and the adaptive-mode sorter enables a super-resolution imaging technique that can be 10-lOOx more efficient in resolving highly sub-diffraction spots, leading to denser qubit counts. A spin-based emitter array that incorporates -128 SiV emitters can be coupled to a low-loss photonic integrated circuit. Given that the described MBQC configuration couples emitters into a free-space SLM-based mode sorter, a much larger and denser array of bulk-spin emitters can bemade. Densities close to 10-100 resolvable spin-dependent emitters per micrometer2can be achieved. Additionally, an SLM -based mode sorter that implements various photonic gates can be used backwards in a test and evaluation (T&E) mode before initializing the quantum computer. This configuration can be used to locate a large number of diffraction-limited photon emitters, an approach that may not be possible with a confocal microscope as utilized in spin qubit-based configurations.

[0070] (b) High quality deterministic photonic qubits: The described architecture is not affected by the probabilistic two-photon emissions associated with spontaneous four-wave mixing (sFWM) or spontaneous parametric down-conversion (SPDC) based sources, which could result in better fault-tolerance overheads. Further, this quantum computing architecture does not require complicated spin-specific microwave control. Instead the spins, together at a clock edge, emit photons entangled with the electron spin qubit of the Zeeman-split levels of the ground state of the atom. Therefore, this system is able to use a spatially-uniform optical-laser and microwave initializing pulses, but no further microwave control is required. Further, the interaction time per emitter can be about 2 ns, which results in a fast clock rate, commensurate with the typical detector bandwidths achievable with superconducting nanowire single photon detectors.

[0071] (c) Ultra-low loss: the described architecture does not need to couple the photons into waveguides. In some approaches to photonic quantum computing, the largest contributor to the fault-tolerance overhead (the logical-to-physical qubit ratio) is photon loss. In these other approaches, loss accrues during the coupling of a photonic qubit into and out of a waveguide, as well as during its waveguide propagation. In the described MBQC architecture, a photon generated from the emission of an atomic emitter transverses the succession of SLMs in the volumetric mode sorter and then is detected with a free-space-coupled single-photon detector’s active surface. The entire module containing 100s of fault- tolerant logical qubits can be packaged into a compact module situated inside a ~1K capable cryostat. The losses can be limited to be extremely low in a well-engineered system, thus allowing the entire system to remain within the percolation threshold limits.

[0072] (d) Ultra-compact gate realization using an adaptive mode sorter: The photonic gates can be realized in a compact form factor using a universal-linear-optical multi-spatial-mode unitary transformation capable mode sorter. This mode sorter passes millions of photons througha succession of SLMs, each imparting a spatial phase distribution. The number of SLM stages does not increase with the size of the computation. The qubits are encoded in “spatial pixel basis” dual-rail time-bin photonic qubits. This encoding results in very low loss and compact gate realization, as many complex beamsplitter interactions acting on spatial-pixel-basis dual-rail qubits can be efficiently and non-trivially “packed” into the mode sorter. The number of orthogonal spatial modes (which roughly translates to the number of qubits up to a small constant factor) that a 1 cm3size system ( 1 cm by 1 cm spin array, followed by 1 cm propagation through SLM stages) act upon together is given by the diffraction limited Fresnel number product AtAr / L)2, which roughly equals 200 million for = 737 nm, the wavelength of photons emitted by SiV color centers in diamond. This form factor, in principle, might suffice to realize fault-tolerant quantum computing on ~50 logical qubits, modulo system design constraints. With a slightly larger system size that is still able to be fabricated in a small-form- factor package that can fit in a single cryostat and best-available codes, fault-tolerant quantum computing on 1000s of logical qubits could be realized at very low (manufacturing and operational) costs, meeting a useful-scale goal.

[0073] Some implementations of a photonic quantum computing system can utilize other system configurations or architectures. For instance, some system configurations can omit the feedback loop between the volumetric transmission shifter and the plurality of photon detectors, and / or the volumetric transmission shifter could be replaced with a boson sampling apparatus.

[0074] While the disclosure has been described in connection with certain embodiments, it is to be understood that the disclosure is not to be limited to the disclosed embodiments but, on the contrary, is intended to cover various modifications and equivalent arrangements included within the scope of the appended claims, which scope is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures as is permitted under the law.

Claims

What is claimed is:

1. An apparatus for photonic quantum computation, comprising; a source module configured to generate a plurality of n-qubit photonic states, the source module comprising: a two-dimensional (2D) array of photon emitters configured to emit photons that propagate in a direction substantially perpendicular to a first plane over which the 2D array of photon emitters are arranged, and a modulation unit configured to generate the plurality of n-qubit photonic states based at least in part on the 2D array of photon emitters; a volumetric spatial light modulator configured to receive at least a portion of the plurality of n-qubit photonic quantum states and generate a distribution of photonic quantum states; a plurality of photon detectors, each configured to generate a corresponding detection event signal, distributed over a region that receives a portion of the distribution of photonic quantum states; and a control module configured to control at least some modulation applied by the volumetric spatial light modulator based at least in part on detection event signals from two or more of the plurality of photon detectors.

2. The apparatus of claim 1, wherein each n-qubit photonic quantum state comprises an entangled state generated from n of the photons emitted from the 2D array of photon emitters.

3. The apparatus of claim 2, wherein the control module is configured to identify at least some of the plurality of n-qubit photonic quantum states based at least in part on processing detection event signals from a first set of photon detectors of the plurality of photon detectors.

4. The apparatus of claim 3, wherein the volumetric spatial light modulator is configured to generate the distribution of photonic quantum states based on linear combinations of photons in the n-qubit photonic quantum states.

5. The apparatus of claim 4, wherein the control module is configured to identify at leastsome photonic quantum states in the distribution based at least in part on processing detection event signals from a second set of photon detectors of the plurality of photon detectors that is different from the first set of photon detectors.

6. The apparatus of claim 1, wherein the 2D array of photon emitters in the source module comprises an array of color-center spin emitters.

7. The apparatus of claim 1, wherein the plurality of photon detectors comprises a plurality of single-photon detectors, each single-photon detector configured to detect single photons with a probability of at least around 90%.

8. The apparatus of claim 1, wherein the volumetric spatial light modulator comprises plurality of transmissive 2D spatial light modulators (SLMs), and each of the transmissive 2D SLMs includes phase modulation pixels arranged over a plane that is substantially parallel to the first plane.

9. The apparatus of claim 1, wherein the volumetric spatial light modulator comprises a plurality of transmissive 2D spatial light modulators (SLMs), and each of the transmissive 2D SLMs includes phase modulation pixels arranged over a plane that is substantially perpendicular to a direction of propagation of the photons emitted from the 2D array of photon emitters at a time of phase modulation by the transmissive 2D SLMs.

10. The apparatus of claim 1, further comprising a quantum computation module configured to receive the distribution of photonic quantum states and process detection event signals from a set of photon detectors of the plurality of photon detectors based at least in part on a quantum circuit that comprises one or more quantum gates.

11. The apparatus of claim 10, wherein each of a plurality of propagation paths from a photon emitter of the 2D array of photon emitters to a corresponding photon detector of the set of photon detectors is a propagation path that is free from any waveguide propagation.

12. The apparatus of claim 1, wherein the modulation unit of the source module comprises a volumetric spatial light modulator.

13. The apparatus of claim 12, wherein the volumetric spatial light modulator of the source module comprises a plurality of transmissive 2D spatial light modulators (SLMs), and each of the transmissive 2D SLMs includes phase modulation pixels arranged over a plane that is substantially perpendicular to a direction of propagation of the photonsemitted from the 2D array of photon emitters at a time of phase modulation by the transmissive 2D SLMs.

14. The apparatus of claim 1, wherein the modulation unit of the source module comprises a microwave source configured to modulate the 2D array of photon emitters to generate the plurality of n-qubit photonic states.

15. The apparatus of claim 1, wherein the plurality of n-qubit photonic states comprises a plurality of 3-qubit Greenberger-Home-Zeilinger (GHZ) photonic states.

16. The apparatus of claim 1, wherein the plurality of n-qubit photonic states comprises a plurality of 5-qubit Greenberger-Home-Zeilinger (GHZ) photonic states.

17. The apparatus of claim 1, wherein the plurality of n-qubit photonic states comprises a plurality of n-qubit star-shaped cluster states.

18. The apparatus of claim 1, wherein the photonic quantum states comprise a long-range connected sub-lattice of a Rausendorf-Harrington-Goyal (RHG) lattice.

19. The apparatus of claim 1, wherein the photonic quantum states comprise a three- dimensional (3D) photonic cluster state.

20. The apparatus of claim 1, wherein the 2D array of photon emitters comprises an array of quantum dots.

21. The apparatus of claim 1, wherein the 2D array of photon emitters comprises an array of quantum dots and color-center spin emitters.

22. The apparatus of claim 1, wherein the volumetric spatial light modulator comprises a 3D refractive index distribution.

23. The apparatus of claim 1, wherein the plurality of photon detectors comprises a plurality of single photon detecting pixels of a camera.

24. A method for photonic quantum computation, comprising: generating a plurality of n-qubit photonic states, the generating comprising: emitting from a two-dimensional (2D) array of photon emitters, photons that propagate in a direction substantially perpendicular’ to a first plane over which the 2D array of photon emitters are arranged, and generating the plurality of n-qubit photonic states based at least in part on the 2D array of photon emitters;modulating the n-qubit photonic states in a volumetric spatial light modulator, the modulating comprising receiving at least a portion of the plurality of n-qubit photonic quantum states and generating a distribution of photonic quantum states; generating detection event signals from respective photon detectors distributed over a region that receives a portion of the distribution of photonic quantum states; and controlling at least some modulation applied by the volumetric spatial light modulator based at least in part on detection event signals from two or more of the photon detectors.

25. The method of claim 24, wherein each n-qubit photonic quantum state comprises an entangled state generated from n of the photons emitted from the 2D array of photon emitters.

26. The method of claim 25, wherein the controlling comprises identifying at least some of the plurality of n-qubit photonic quantum states based at least in part on processing detection event signals from a first set of photon detectors of the plurality of photon detectors.

27. The method of claim 26, wherein the volumetric spatial light modulator generates the distribution of photonic quantum states based on linear combinations of photons in the n- qubit photonic quantum states.

28. The method of claim 27, wherein the controlling comprises identifying at least some photonic quantum states in the distribution based at least in part on processing detection event signals from a second set of photon detectors of the plurality of photon detectors that is different from the first set of photon detectors.

29. The method of claim 24, wherein the 2D array of photon emitters comprises an array of color-center spin emitters.

30. The method of claim 24, wherein the plurality of photon detectors comprises a plurality of single-photon detectors, each single-photon detector configured to detect single photons with a probability of at least around 90%.

31. The method of claim 24, wherein the volumetric spatial light modulator comprises plurality of transmissive 2D spatial light modulators (SLMs), and each of the transmissive 2D SLMs includes phase modulation pixels arranged over a plane that is substantially parallel to the first plane.

32. The method of claim 24, wherein the volumetric spatial light modulator comprises a plurality of transmissive 2D spatial light modulators (SLMs), and each of the transmissive 2D SLMs includes phase modulation pixels arranged over a plane that is substantially perpendicular to a direction of propagation of the photons emitted from the 2D array of photon emitters at a time of phase modulation by the transmissive SLMs.

33. The method of claim 24, further comprising performing a quantum computation by receiving the distribution of photonic quantum states and processing detection event signals from a set of photon detectors of the plurality of photon detectors based at least in part on a quantum circuit that comprises one or more quantum gates.

34. The method of claim 33, wherein each of a plurality of propagation paths from a photon emitter of the 2D array of photon emitters to a corresponding photon detector of the set of photon detectors is a propagation path that is free from any waveguide propagation.

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