Modular interconnects between neutral atom quantum processors

Abstract

A device for modular interconnects between quantum processors is presented. The device includes an optical cavity configured to collect photons simultaneously from two transitions with opposite circular polarization. The optical cavity including a plurality of mirrors in a twisted non-planar ring geometry configured to realize two non-degenerate co-propagating modes with opposite circular polarization.

Description

MODULAR INTERCONNECTS BETWEEN NEUTRAL ATOM QUANTUM PROCESSORS CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims the benefit of, and priority to, U. S. Provisional Patent Application Serial No. 63 / 618,134 filed January 5, 2024, the entire contents of which are hereby incorporated herein by reference.FIELD OF THE DISCLOSURE

[0002] The subject matter of the present disclosure relates generally to the field of quantum computing and, more particularly, to a device for modular interconnects between quantum processors.BACKGROUND

[0003] The development of a large-scale, fault-tolerant quantum computer capable of solving classically intractable problems is expected to require millions of qubits. In many physical computing architectures, it is challenging to imagine scaling a single device to this number of qubits, because of varied constraints including cryogenic cooling power, wiring density, or laser power.

[0004] However, a central challenge to the realization of modular quantum systems is achieving inter-module quantum links with sufficient bandwidth and fidelity. The basic building block of a modular computer is a Bell pair between physical qubits in two modules, this can be used as a resource to perform remote physical or logical gates via teleportation. Spin-photon entanglement in neutral atoms and trapped ions has been used to generate Bell pairs across meter-scale fiber links with a rate of 182 s⁻¹ and a fidelity of 0.94. In superconducting qubits, microwave photons have been used to entangle qubits in the same cryostat and in two cryostats separated by a 30 meter cold link. Entanglement transduction between two qubits across a room-temperature link is an open challenge.

[0005] Accordingly, there remains a need for improvements.SUMMARY

[0006] In accordance with aspects of the disclosure, device for modular interconnects between quantum processors, includes an optical cavity configured to collect photons simultaneously from two transitions with opposite circular polarization. The optical cavityincludes a plurality of mirrors in a twisted non-planar ring geometry configured to realize two non-degenerate co-propagating modes with opposite circular polarization.

[0007] In an aspect of the present disclosure, energy splitting between the two nondegenerate co-propagating modes may be tuned to match spacing between atomic energy levels of opposite spin, so an atom can simultaneously emit photons of both polarizations into the cavity, generating entanglement between spin state and polarization.

[0008] In another aspect of the present disclosure, the atom may be171Yb. The optical cavity is tuned to resonance with transitions from3 / Jo F=l / 2 mF=+ / - / i states to3Zh F=3 / 2 mF=+ / - 3 / 2 states.

[0009] In accordance with aspects of the disclosure, a system, includes a device for modular interconnects between quantum processors. The device includes: an optical cavity configured to collect photons simultaneously from two transitions with opposite circular polarization, the optical cavity including a plurality of mirrors in a twisted non-planar ring geometry configured to realize two non-degenerate co-propagating modes with opposite circular polarization; and an optical tweezer array configured to be transported into the optical cavity using a steerable mirror, the optical tweezer array comprising N > 1 sites.

[0010] In a further aspect of the present disclosure, the system may further include an optical fiber having a first end operably coupled to the optical cavity, such that the first end of the optical fiber is configured to receive a photon emitted by the atom.

[0011] In yet a further aspect of the present disclosure, the system may further include a central router operably coupled to a second end of the optical fiber, configured to receive the photon from the optical fiber.

[0012] In another aspect of the present disclosure, the photon from the optical fiber may be directed towards a beamsplitter in the central router.

[0013] In yet another aspect of the present disclosure, the system may further include a second optical fiber from a second module incident on the beamsplitter, wherein the central router is reconfigured to direct photons from different pairs of modules towards each beamsplitter in a beamsplitter array.

[0014] In accordance with aspects of the disclosure, a method for connecting quantum computing modules based on neutral atom qubits, includes: initializing an optical tweezer array comprising N > 1 sites with a single atom per site, outside of an optical cavity of a first quantum computing module, the optical cavity consisting of a plurality of mirrors in a twisted ring configured to realize two non-degenerate co-propagating modes with opposite circularpolarization, one of the plurality of mirrors being configured as an outcoupler, and energy splitting between the two non-degenerate co-propagating modes is tuned to match spacing between atomic energy levels of opposite spin, so an atom simultaneously emits photons of both polarizations into the optical cavity, generating entanglement between a spin state and each polarization; transporting the optical tweezer array into the optical cavity using a steerable mirror or acousto-optic deflector; optically pumping the optical tweezer array into a single spin state within theJ5o, F=l / 2 ground state; and preparing the optical tweezer array in a superposition of spin states using a single- qubit rotation implemented simultaneously on all the qubits.

[0015] In a further aspect of the present disclosure, the atom may be171Yb. The method may further include allowing a first atom to be excited from the 'Ao F=l / 2 ground state to the3Z>i F=3 / 2 excited state using a two-photon optical transition, to be in a superposition of the3D1F=3 / 2 mF=+ / - 3 / 2 states.

[0016] In yet a further aspect of the present disclosure, the method may further include: allowing the atom to decay by emitting a photon into the optical cavity, the optical cavity being tuned to resonance with the transitions from the3 / Jo F=l / 2 mF=+ / - / i states to the3Zh F=3 / 2 mF=+ / - 3 / 2 states, creating an entangled state between spin of the atom in the3P0state, and polarization of the photon; collecting the photon into an optical fiber and sending the photo to a central router; and interfering on a beamsplitter with a photon from a second quantum computing module, the coincident detection of two photons indicating generation of an entangled state between the atoms in the first and the second quantum computing modules.

[0017] In another aspect of the present disclosure, the method may further include reinitializing at least two atoms with a failed entanglement back into the1S0ground state via optical pumping.

[0018] In yet another aspect of the present disclosure, the method may further include: moving the optical tweezer array out of the optical cavity into a computation zone using an acousto-optic deflector or scannable mirror; and moving another optical tweezer array of atoms into the optical cavity.

[0019] In a further aspect of the present disclosure, information about an arrival time of the detected photons may be used to infer an error probability on the resulting Bell pair, and this information is used in an operation of a quantum error correction code to perform an estimation of the logical qubit state.

[0020] In yet a further aspect of the present disclosure, the method may further include controlling cross-talk and reabsorption of photons within the optical cavity by shifting atoms in the optical cavity that are not undergoing an entanglement attempt at any point in time out of resonance with the optical cavity.

[0021] In another aspect of the present disclosure, shifting atoms out of resonance may utilize an AC Stark shift of a focused array of beams.

[0022] In yet another aspect of the present disclosure, a wavelength of the focused array of beams may be selected to shift the3 / Jo to3Zh transition energy by a large amount compared to the coupling between the atom and optical cavity, to prevent absorption of photons emitted into the optical cavity by other atoms.

[0023] In a further aspect of the present disclosure, a wavelength of the focused array of beams may be selected to shift the3D1state by a large amount compared to a Rabi frequency of the two-photon transition used to excite atoms from ^oto3P1, to control which atom in the 'So state is excited to the3D1state to initiate a spin-photon entanglement attempt.

[0024] In yet a further aspect of the present disclosure, the method may further include applying one or more light shifts to an excited atom while the excited atom is still emitting a photon, to suppress further photon emission into the optical cavity.

[0025] In yet a further aspect of the present disclosure, the applying the one or more light shifts may be before the atom has fully decayed to the3Eo state, at a time when there is no photon excitation in the optical cavity.

[0026] Further details and aspects of exemplary embodiments of the present disclosure are described in more detail below with reference to the appended figures.BRIEF DESCRIPTION OF THE DRAWINGS

[0027] A better understanding of the features and advantages of the present disclosure will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the present disclosure are utilized, and the accompanying drawings of which:

[0028] FIG. l is a block diagram illustrating modular interconnects between neutral atom quantum processors of a quantum computer, in accordance with aspects of the disclosure;

[0029] FIG. 2 is a block diagram illustrating the quantum computer, in accordance with aspects of the disclosure;

[0030] FIG. 3 is a diagram illustrating an optical cavity of the system of FIG. 1, in accordance with aspects of the disclosure;

[0031] FIG. 4 is a diagram illustrating the operation of the system of FIG. 1, in accordance with aspects of the disclosure;

[0032] FIG. 5 is a diagram illustrating the operation of the system of FIG. 1, in accordance with aspects of the disclosure;

[0033] FIG. 6 is an diagram illustrating the entanglement sequence in time of the system of FIG. 1, in accordance with aspects of the disclosure;

[0034] FIG. 7 is a diagram illustrating an atom array inside the cavity of FIG. 3, in accordance with aspects of the disclosure;

[0035] FIG. 8 is a set of graphs illustrating cavity output photon rate, photon extraction efficiency, and Bell pair generation rate, in accordance with aspects of the disclosure; and

[0036] FIG. 9 is a flow diagram illustrating a method for connecting quantum computing modules based on neutral atom qubits, in accordance with aspects of the disclosure.DETAILED DESCRIPTION

[0037] The subject matter of the present disclosure relates generally to the field of quantum computing and, more particularly, to modular interconnects between quantum processors.

[0038] Although the present disclosure will be described in terms of specific examples, it will be readily apparent to those skilled in this art that various modifications, rearrangements, and substitutions may be made without departing from the spirit of the present disclosure.

[0039] For the purpose of promoting an understanding of the principles of the present disclosure, reference will now be made to exemplary embodiments illustrated in the drawings, and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the present disclosure is thereby intended. Any alterations and further modifications of the novel features illustrated herein and any additional applications of the principles of the present disclosure as illustrated herein, which would occur to one skilled in the relevant art and having possession of this disclosure, are to be considered within the scope of the present disclosure.

[0040] The systems and method disclosed herein achieve remote spin entanglement between neutral atom qubits in optical tweezer arrays.171Yb atoms are considered as qubits, which have been used to demonstrate high-fidelity entangling gates, non-destructive and midcircuit readout, and have a pathway to efficient fault-tolerant error correction using erasureconversion. By using an optical tweezer array to place N > 100 atoms inside a single optical cavity (a twisted ring resonator) and controlling their interaction with the cavity using only local light shifts, the present disclosure predicts a remote Bell pair generation rate of 1.12 * 105s⁻¹ with fidelity F> 0.998 for physically reasonable parameters. This rate is orders of magnitude higher than previously demonstrated or proposed remote entanglement approaches for atomic qubits. The entanglement is distributed between modules using 1389 nm photons in a single-mode optical fiber, allowing links over several kilometers without degradation.

[0041] Referring to FIG. 1, a system 100 for connecting quantum computing modules 110, 120 of a neural atom quantum computer 200 (FIG. 2) based on neutral atom qubits is shown. System 100 generally includes quantum computing modules 110, 120 of a quantum computer 200 (FIG. 2) and an optical tweezer array 102 (FIG. 3) comprising N > 1 sites with a single atom per site. Each of the quantum computing modules 110, 120, includes an optical cavity 300 (FIG. 3).

[0042] System 100 solves the problem of slow speed at which entanglement is generated by legacy systems, which require placing one atom at a time in optical cavity to generate spinphoton entanglement. System 100 solves this problem by placing many atoms in a cavity simultaneously, and selectively coupling one atom a time by shifting the transition frequency of the remaining atoms, which can be done quickly.

[0043] The optical tweezer array 102 is located outside of the optical cavity 300. The optical tweezer array 102 is configured to be transported into the optical cavity 300 using a steerable mirror, the optical tweezer array 102 comprising N > 1 sites.

[0044] The optical cavity 300 includes a plurality of mirrors 304 (e.g., four mirrors) in a twisted or non-planar ring configured to realize two non-degenerate co-propagating modes with opposite circular polarization. The optical cavity 300 is configured to collect photons simultaneously from two transitions with opposite circular polarization. One of the plurality of mirrors 304 may be configured as an outcoupler. Energy splitting between the two nondegenerate co-propagating modes is tuned to match the spacing between atomic energy levels of opposite spin so an atom can simultaneously emit photons of both polarizations into the optical cavity, generating entanglement between a spin state and each polarization.

[0045] Referring to FIG. 2, a diagram of the quantum computer 200 is shown. Each module 110, 120 of the quantum computer 200 may be housed in a separate vacuum system 114 and contains an optical cavity used to generate spin-photon entanglement. The resulting photons are entangled with the qubit states in the polarization basis. After the photons leave the opticalcavity, they are coupled into optical fibers and sent to a central, reconfigurable router 112 and detector array. The coincident detection of two photons of different polarization heralds the generation of a Bell state between the qubits in remote modules. The central router 112 is operably coupled to a second end of the optical fiber, configured to receive the photon from the optical fiber. The central router 112 serves to bring together photons from two different modules. The central router 112 is to be able to be reconfigured to bring photons from any pair of modules together on a beamsplitter. The central router 112 may include a second optical fiber from a second module incident on the beamsplitter. The central router 112 is reconfigured to direct photons from different pairs of modules towards each beamsplitter in a beamsplitter array.

[0046] Referring to FIG. 3, an exemplary optical cavity 300 design is shown. The optical cavity 300 includes four mirrors 304 in a twisted ring between two lenses 302 and 306. The large spacing between the mirrors 304 and the atoms eliminates unwanted atom-surface interactions and provides ample optical access for optical tweezers 102 (FIG. 1), imaging, and gate beams. The mirror radius of curvature is chosen to provide a mode waist of w0= w0m at the position of the atoms, resulting in an peak atom-cavity coupling strength of gmax= 2π × 520kHz and providing space for N= 204 atoms with g > 0.9gmax(FIG. 7). The roundtrip length is L = 6.96 cm, corresponding to a free spectral range of 4.3 GHz, and the cavity decay rate K is chosen by selecting the reflectivity of the outcoupler mirror (the other mirrors have R = 1). An outcoupler mirror is typically partially transmissive, allowing a fraction of the light to exit the cavity. This is typically the mirror through which light is output.

[0047] The twist angle is chosen to split the co-propagating < T and o modes by approximately 140 MHz, to match the transitions from |0) and |l)to3Z>i simultaneously in a bias field of 100 Gauss. Other twist angles can be chosen to achieve a different splitting to match the transition frequencies in a different value of the magnetic field.

[0048] The optical cavity 300 within each module 110, 120 is a twisted ring cavity, which enables small beam waists (e.g., about 10 microns) with robust alignment, spatially uniform atom-cavity coupling (z.e., without a standing wave), and non-degenerate modes of opposite circular polarization to couple to two Zeeman-split transitions simultaneously and generate spin-polarization entanglement. Compared to time-bin entanglement when coupling to a single transition, this doubles the entanglement generation rate and avoids storing entanglement in a superposition of electronic levels that can be more sensitive to differential light shifts ormagnetic field fluctuations. In aspects, where the atom is171Yb, the optical cavity may be tuned to resonance with transitions from3Po F=l / 2 mF=+ / - / i states to3Zh F=3 / 2 mF=+ / -3 / 2 states

[0049] The disclosed optical cavity 300 solves a problem of traditional standing wave cavities, by removing fast spatial variation in the atom-cavity coupling strength. The four non-planar mirrors are each at an angle.

[0050] Referring to FIG. 4, a flow diagram illustrating the operation of the system of FIG.1 with a tweezer array 102 is shown. At operation 410, an array of atoms 401 is initialized in a loading zone, then transported into the optical cavity 300. At operation 420, once inside, the entire array 401 is initialized in a superposition state within the1So ground state |i / >0)=( | Op ) + | lg)) / 2. The first atom in the array is excited to a superposition state in the 6s5d3DI manifold, (|0e) + |le)) / 2 which decays to the qubit states in the3Po manifold (FIG. 5), by emitting a 1389 nm photon into the cavity with o or cP polarization. This results in the spinphoton entangled state= (|0, < J — ) + |1, < J +)). By performing the excitation synchronously in two modules 110, 120 (FIG. 1), the emitted photons will arrive simultaneously at the detectors, and an entangled state of two qubits= (|01) ± 110)) / 2 is heralded when two photons of opposite polarization are detected.

[0051] The process is repeated sequentially for each atom in the array 401, with a delay of tent« 1 / zs to ensure that the photon wave packets do not overlap. After exciting all of the atoms once, the procedure can be repeated m times, where m is between 5 and 10, to boost the entanglement fraction. In between repetitions, atoms that were not successfully entangled are re-initialized into the state

[0052] After a sufficient number of Bell pairs are generated, at operation 430, the array is moved out of the cavity (z.e., into a computation zone, where it can be consumed to perform remote gate operations via teleportation), and replaced by a fresh array to continue generating more Bell pairs. By amortizing the temporal cost of moving the atoms (tmoVe ~ 100 / s) over many repetitions of the entanglement sequence (FIG. 6), the average spinphoton entanglement attempt rate approaches the maximum allowed by the cavity, 1 / tent. Saturating this rate requires the number of atoms in the cavity N > tmove / tent« 100.Locally addressed light shifts of the3D state prevent reabsorption of photons by atoms already in3 / Jo, and provide local control of the excitation from1Ao to3D.

[0053] Referring to FIG. 5 an energy diagram of the relevant atomic levels in171Yb is shown. The qubit state used for computation is the3Po manifold.

[0054] The procedure for generating the spin-photon entangled state |ipsp) is shown in FIG.8. After preparing the array in |0^) and via optical pumping, and then in (|0^) + |1^)) / V2 using a single-qubit rotation, a brief optical pulse is used to excite the superposition to3£>i (via the3Pi intermediate state). As g ~ r « K, the photon emission rate out of the cavity is not an exponential decay, but exhibits periodic oscillations at a frequency close to g (FIG. 8). Over 90% of the decay happens within the first cycle of this oscillation, but the residual population in the cavity can cause an error if the next atom is excited right away. Therefore, a strong light shift A > 100$ is applied to the3£>i state suddenly at t ~ n / g, when the cavity photon population is minimized. This traps the residual excitation in the atom, where it decays into free-space modes, and allows the next atom to be excited to3£>i immediately, providing an improvement in speed of over two times. The light shift is kept on for the remainder of the sequence, to prevent the atom from absorbing cavity photons from subsequent excitation rounds (for this, a larger light shift of A « 1000g is preferable). After attempting to excite all N atoms, the atoms that were not entangled can be repumped back to 10g), and the entanglement procedure repeated until the desired number of Bell pairs is generated.

[0055] Referring to FIG. 8, a set of graphs illustrating cavity output photon rate, photon extraction efficiency, and Bell pair generation rate are shown. The photon extraction efficiency is shown as a function of K, reaching a maximum of g = 0.5 when K / I' TI = 1.04MHz (corresponding to a cavity finesse of F = 2070). This does not achieve the maximum possible efficiency g0= C / (l + C), where C = 4g2 / (κΓ) is the cooperativity, because the cavity becomes spectrally narrower than the emitted photon when K is small. Adiabatic preparation of a shaped photon pulse can always achieve g0, at the expense of lower emission rate and significant additional experimental complexity. Each excited atom has a probability Psuc= (1 / 2)T?2« 0.125 of successfully generating a remote Bell pair. Using the sequence in FIG. 6, the average Bell pair rate is:yZ71TV p

[0056] Rbv= -1=1 1"cm- (Eqn. 1)tmove +in' tinit+

[0057] where Nt= — Psuc) is the number of entanglement attempts in round i, and Ai = A. After one round (m = 1) the rate is 83 × 103s⁻¹, increasing to 112 × 103s⁻¹ for m = 5-20 rounds. This is 88% of the maximum rate allowed by the cavity, 1 / tent= 125 × 103s-1, indicating the effectiveness of the multiplexing.

[0058] Next, the present disclosure considers errors affecting the fidelity of the spin-spin entanglement. Previous experimental studies of heralded entanglement based on coincidencedetection have identified errors arising from atomic coherence, the fidelity of single-qubit rotations, polarization mixing, and imperfect mode overlap at the detectors.

[0059] The excellent coherence and high-fidelity single-qubit operations on the nuclear spin qubit in171Yb largely mitigates the first two effects. Coherence times without dynamical decoupling (z.e., T2* ) of several seconds have been demonstrated for the pure nuclear spin qubit inJSo or3Po, because of the low sensitivity to magnetic field noise and absence of differential light shifts. The metastable state lifetime is 3 s in typical optical tweezers, resulting in a decay probability toJ5o of 7x 107per tentor 2 x 104over m = 5 sequence repetitions with N = 204 atoms. Additionally, the metastable state decay errors can be converted into erasure errors, minimizing their impact on logical information. The3£>i state is more sensitive to magnetic fields, but is only populated for ~1 z / s during the entanglement generation. Single qubit gates for bothJ5o and3Po qubits have been demonstrated with fidelities beyond 0.999. The polarization orthogonality of the emitted photons is ensured by the mode structure of the cavity, and an extremely high degree of spatial mode overlap can be achieved by using fiber optic or integrated photonic beamsplitters, which have extremely low loss at telecom-band wavelengths.

[0060] Now, the present disclosure evaluates sources of error that are particular to this implementation. The first is a slight distinguishability of the photon wavepackets from two cavities resulting from variation in the atom-cavity coupling strength or Doppler shift. Given two atoms in two cavities with a fractional difference in coupling strength 8g / g, the resulting distinguishability causes an error= 0.394 X ((J^ / ^)2, such that <5p / ,g < 0.05 is required to reach Eg< 10-3. An R.M.S. variation in g below this level requires matching the cavity waists at the level of 5%, and placing the atoms within 0.4w0≈ 4 μm of the cavity center (compatible with the layout in FIG. 7). This static inhomogeneity can be mitigated by misaligning the atoms in one cavity, or choosing matched pairs of atoms to entangle. Unknown variation in g can arise from alignment drifts between the tweezer array and the cavity or thermal motion of the atoms. To achieve 8g / g < 0.05, the present disclosure requires (Ax, Ay, Az) < (0.87, 2.2, 3.8) gm (assisted by the absence of a standing wave in the cavity), while thermal motion at 10 μK corresponds to δg / g ~ 3 × 10-3.

[0061] Distinguishability errors can also arise from Doppler shifts, given the running-wave mode in the cavity. The error probability is proportional to (k:kBT l )IP where kc= 2zr / Ais the cavity wavevector, fe is Boltzmann’s constant, T is the atomic temperature and mis the mass of the atom. From numerical simulations, the present disclosure finds eT= 7.3 × 10-6μK-1× T. A typical temperature for Yb atoms is 5-10 z / K (without ground-state cooling) corresponding to εT< 10-4

[0062] Next, consider decay back to1S0during the excitation pulse, which collapses the initial spin superposition but can still result in a photon emission into the cavity if the atom is re-excited. The3D1state decays to3P1with a branching ratio of 0.35, and3P1decays to1S0at a rate Γ3= 2TT x 182 kHz. Therefore, the probability to decay toJ5o during an excitation pulse of duration tn« r, T3is ps≈ 0.35tπ2Γ3Γ. The probability of the atom being re-excited and causing an error is εd= p3 / 4. For tn= 20ns, ed= 5.6 x 10-5. There is an additional decay probability of order Γ3 / Δ3, where Δ3is the detuning from3P1of the two-photon excitation lasers. However, this can be suppressed below 104by using a large detuning Δ3> 1 GHz.

[0063] Commercially available superconducting nanowire single-photon detectors (SNSPDs) have a dark count rate Rdc= 10s-1, and >90% quantum efficiency, corresponding to an error probability of edc= 1.5 x 10-3. However, techniques have been demonstrated to achieve Rdc< 10-3s-1, including cold filtering and coupling the detector to a single-mode waveguide, allowing edc< 10-6in principle.

[0064] Cross-talk errors from the presence of multiple atoms inside the cavity take two forms: residual photons in the cavity at the end of one entanglement attempt that leak into the next window, and atoms already in3Po can absorb a photon if they are not sufficiently light-shifted away from the cavity resonance. If the atom-cavity coupling is known exactly, the residual photon errors are suppressed dramatically by the light shift, provided the light shift is turned on instantaneously at the time when the cavity population is zero. However, unknown variation in g makes this precise timing impossible. Using the uncertainty δg / g = 3 × 10-3from thermal atomic motion at 10 z / K, a floor of er= 1.8 X 10-6with light shift of A / g = 2 x 103is found.

[0065] Atoms already in3Po after a successful entanglement attempt can absorb a photon from the cavity during a subsequent round of the protocol. This error is also suppressed with the light shift, as εa(1)= 7.1 × (g / Δ)2. However, because the error is incurred on the atom that was already entangled, the average generated Bell pair experiences N̄r= O(mN) subsequent rounds, amplifying its effect. When N= 204 and m = 5, the present disclosure finds numerically _ _ Zw Xthat Nr« 250. Achieving an average error εa= N̄rεa(1)< 10-3requires Δ / g > 2 × 103. The reabsorption probability through free space is small from geometric considerations but canbe suppressed to much lower levels by adding deliberate disorder to the light shift: a 10% variation in A corresponds to 100 linewidths of the atomic transition.

[0066] Note that only a modest amount of laser power is required for the light-shifting beam when operating close to resonance on the3P0to 6s8p3P1transition, which is possible because the3D1state is not populated on the shifted sites and, therefore, insensitive to scattering errors. With a detuning of 1 GHz, a laser power of < 15 / / W per atom is sufficient to generate a light shift of A / g > 2000.

[0067] In the context of quantum error correction, the details of the error model can significantly affect the overhead required to reach a given logical error rate. For example, a bias towards a single type of Pauli error or information about the location of errors in the form of erasures or soft information has been shown to reduce logical error rates by several orders of magnitude. While many quantum operations are characterized by their average fidelity, the timing of the photon detection events provides shot-to-shot information about the error probability of each Bell pair. Soft information generally includes probabilistic data about quantum states, which includes information that describes the likelihood or confidence of a state being in a particular value rather than a definitive outcome. The disclosed system 100 provides the benefit of providing this soft information, which can be used to determine the type of errors and improve the error rates based on the soft information. For example, the types of errors, e.g., the error rates of a given Bell pair, may be determined based on tuning information. Then, the tuning information can be used to guide fault-tolerant gate design or iteratively refine the error correction process.

[0068] For example, given that a coincident photon detection has occurred at a known time (G, t2), what is the probability that the resulting atomic state is in the correct Bell state or has a Pauli (X Y, Z) or leakage error on one or both qubits? Since the qubit manifold in171Yb has only two levels, leakage error refers to the case that the atom is not in3 / Jo.

[0069] For example, errors can occur due to by photon distinguishability from a variation in the atom-cavity coupling strength of 8glg = 0.031 (correspond to number of atoms N = 204). These errors are purely Pauli Z errors: distinguishability affects the phase of the resulting Bell pair but does not affect the correlation between the photon polarization and spin state (ie., cause an X error) or cause leakage. The error probability is strongly suppressed when the photons are detected at nearly the same time, because there is less which-path information. Using the prior probability distribution for the photon detection times, P(t1; t2), this can be converted into a probability distribution for the error rate, p(εg). The meaning of p(εg) is this:it gives the probability that a generated Bell state has an error rate of eg, using all available information about the photon detection timing. While the mean error rate is 4×10-4, the error rate is less than 6×10-5for over half of Bell pairs. This information can be used to decode logical errors more effectively, as it approximates an erasure error.

[0070] A similar description can be applied to errors from Doppler shifts. The probability of error as a function of photon detection time, εT(t1, t2). As Doppler shifts only affect the distinguishability of the photon wave packets, this only results in Z errors.

[0071] Errors from decay via3Pi during the excitation pulse can be understood as a Z-basis measurement of the spin prior to the spin-photon entanglement and is also purely Z-biased. However, the photon detection timing does not reveal anything about the probability of this error, so it is the same for all Bell pairs.

[0072] Dark counts result in false heralding signals that are uncorrelated with the atomic state and can cause any Pauli error or leakage. The error probability εdc(t1, t2) depends slightly on the detection time and the corresponding cumulative distribution function for Z, X, and leakage errors.

[0073] For example, errors can occur due to the absorption of photons by atoms already in Bell pairs and the decay of atoms out of3P0. Because both errors happen after a successful herald, they do not depend on any photon detection time pattern. However, Bell pairs generated in early rounds have more chances to experience an error than Bell pairs from later rounds. Using the known probability distribution for the number of entanglement rounds Nrthat follow a successful Bell pair generation, the probability distributions for Z, X, and leakage errors are generated. For errors resulting from absorption of photons by atoms already in3P0, because the atom is detuned far from the cavity, the probabilities to excite to all levels of3D1are comparable, and therefore the probability of X, Z, and leakage errors are also roughly comparable. For the decay of atoms out of3o, the error εmis, by definition, purely leakage.

[0074] In summary, these results show that information about the photon detection timing can reveal a significant subset of atoms that have error rates differing from the mean error rate by a factor of about five to ten. Regrouping atoms with different error rates or using this information in the decoding process, can lead to a significant improvement in logical error rates, and a corresponding reduction in overhead.

[0075] System 100 provides the benefit of generating entanglement in parallel with computation using metastable qubits in a nearby zone, without the need to separately control magnetic fields. The local addressing requirement is minimal, consisting of only oneswitchable light shift on each site, and is compatible with recently demonstrated scalable modulators.

[0076] The system 100 enables physical Bell pairs to be converted into logical Bell pairs for distributed fault-tolerant computation. Many previous studies have considered modular quantum computing in the regime where the modules are small, and a single logical qubit spans multiple modules. While a high error threshold of 10% has been demonstrated for the intermodule links, remote Bell pairs are consumed at a high rate just to sustain the logical information against idle errors. In the case of neutral atom quantum computing, the present disclosure envisions modules with 0(104) qubits per module, based on demonstrated arrays of hundreds of qubits and scaling of the underlying optical components to ten thousand sites. With foreseeable error rates below 10-3for all physical operations, achieving logical errors rates of 10-12is possible with an overhead of 103physical qubits per logical qubit using a standard surface code. This can be reduced by another order of magnitude using qubits with engineered noise or efficient block codes. Therefore, NL ^100 logical qubits per module is realistic. In this regime, the remote Bell pairs are not consumed for correcting storage errors and errors from computation within each module, but rather purely for performing logical operations between modules. For a distance d surface code, a gate operation between remote logical qubits can be implemented via lattice surgery, consuming d2physical Bell pairs.

[0077] Alternatively, the same number of Bell pairs can be converted into a logical entangled state by measuring stabilizers locally, and then consumed to apply a logical gate via teleportation using transversal gates within a module. The latter approach has the additional benefit that it can be generalized to any CSS code with a transversal CNOT gate, enabling the use of block codes to achieve a higher coding rate. Therefore, the approach proposed here may enable >103remote logical gates per second between each pair of modules. It is an interesting question for future work to consider how to compile high-level algorithms into such a modular computer.

[0078] The photon based interface between neutral atom quantum processors of system 100 is capable of generating remote entanglement at a rate of 1.12 *105Bell pairs per second, at fidelities that are compatible with fault-tolerant computing. The approach is compatible with existing experimental hardware, and can be operated alongside an atom array performing local computations.

[0079] Referring to FIG. 9 a flow diagram for a method 900 for connecting quantum computing modules based on neutral atom qubits, using system 100 of FIG. 1, is shown.

[0080] At operation 902, the system 100 initializes an optical tweezer array comprising N > 1 sites with a single atom per site, outside of an optical cavity of a first quantum computing module, the optical cavity consisting of a plurality of mirrors in a twisted ring configured to realize two non-degenerate co-propagating modes with opposite circular polarization and energy splitting between the two non-degenerate co-propagating modes is tuned to match spacing between atomic energy levels of opposite spin, so an atom can simultaneously emit photons of both polarizations into the optical cavity, generating entanglement between a spin state and each polarization.

[0081] At operation 904, the system 100 transports the optical tweezer array 102 (FIG. 3) into the optical cavity using a steerable mirror or acousto-optic deflector.

[0082] At operation 906, the system 100 optically pumps the optical tweezer array 102 into a single spin state within the 'So, F=l / 2 ground state.

[0083] At operation 908, the system 100 prepares the optical tweezer array in a superposition of spin states using a single- qubit rotation implemented simultaneously on all the qubits. In a case where the atom is171Yb, the system 100 allows a first atom to be excited from the1S0F=1 / 2 ground state to the3Z>i F=3 / 2 excited state using a two-photon optical transition, to be in a superposition of the3D1F=3 / 2 mF=+ / - 3 / 2 states

[0084] In aspects, the system 100 may allow the atom to decay by emitting a photon into the optical cavity, the optical cavity being tuned to resonance with the transitions from the3P0F=1 / 2 mF=+ / - ½ states to the3D1F=3 / 2 mF=+ / - 3 / 2 states, creating an entangled state between spin of the atom in the3P0state, and polarization of the photon;

[0085] At operation 910, the system 100 collects the photon into an optical fiber and sending the photo to a central router 112 (FIG. 2).

[0086] At operation 912, the system 100 infers on a beamsplitter with a photon from a second quantum computing module, the coincident detection of two photons indicating generation of an entangled state between the atoms in the first and the second quantum computing modules.

[0087] In aspects, the system 100 may re-initialize at least two atoms with a failed entanglement back into the1S0ground state via optical pumping.

[0088] In aspects, the system 100 may move the optical tweezer array out of the optical cavity into a computation zone using an acousto-optic deflector or scannable mirror.

[0089] In aspects, the system 100 may move another optical tweezer array of atoms into the optical cavity.

[0090] In aspects, the system 100 may control cross-talk and reabsorption of photons within the optical cavity by shifting atoms in the optical cavity that are not undergoing an entanglement attempt at any point in time out of resonance with the optical cavity.

[0091] In aspects, the system 100 may shift atoms out of resonance utilizing an AC Stark shift of a focused array of beams.

[0092] In aspects, a wavelength of the focused array of beams is selected to shift the3P0to3D1transition energy by a large amount compared to the coupling between the atom and optical cavity, to prevent absorption of photons emitted into the optical cavity by other atoms. A wavelength of the focused array of beams may be selected to shift the3D1state by a large amount compared to a Rabi frequency of the two-photon transition used to excite atoms from1S0to3P1.

[0093] In aspects, the system 100 may by applying one or more light shifts to an excited atom while it is still emitting a photon, to suppress further photon emission into the optical cavity. In aspects, applying the one or more light shifts after a full period of this oscillation, when there is no excitation in the optical cavity.

[0094] Certain embodiments of the present disclosure may include some, all, or none of the above advantages and / or one or more other advantages readily apparent to those skilled in the art from the drawings, descriptions, and claims included herein. Moreover, while specific advantages have been enumerated above, the various embodiments of the present disclosure may include all, some, or none of the enumerated advantages and / or other advantages not specifically enumerated above.

[0095] The embodiments disclosed herein are examples of the disclosure and may be embodied in various forms. For instance, although certain embodiments herein are described as separate embodiments, each of the embodiments herein may be combined with one or more of the other embodiments herein. Specific structural and functional details disclosed herein are not to be interpreted as limiting, but as a basis for the claims and as a representative basis for teaching one skilled in the art to variously employ the present disclosure in virtually any appropriately detailed structure. Like reference numerals may refer to similar or identical elements throughout the description of the figures.

[0096] The phrases “in an embodiment,” “in embodiments,” “in various embodiments,” “in some embodiments,” or “in other embodiments” may each refer to one or more of the same or different example embodiments provided in the present disclosure. A phrase in the form “Aor B” means “(A), (B), or (A and B).” A phrase in the form “at least one of A, B, or C” means “(A); (B); (C); (A and B); (A and C); (B and C); or (A, B, and C) ”

[0097] It should be understood that the foregoing description is only illustrative of the present disclosure. Various alternatives and modifications can be devised by those skilled in the art without departing from the disclosure. Accordingly, the present disclosure is intended to embrace all such alternatives, modifications, and variances. The embodiments described with reference to the attached drawing figures are presented only to demonstrate certain examples of the disclosure. Other elements, steps, methods, and techniques that are insubstantially different from those described above and / or in the appended claims are also intended to be within the scope of the disclosure.

Claims

What is claimed is:

1. A device for modular interconnects between quantum processors, comprising:an optical cavity configured to collect photons simultaneously from two transitions with opposite circular polarization, the optical cavity including:a plurality of mirrors in a twisted non-planar ring geometry configured to realize two non-degenerate co-propagating modes with opposite circular polarization.

2. The device of claim 1, wherein energy splitting between the two non-degenerate copropagating modes is tuned to match spacing between atomic energy levels of opposite spin, so an atom can simultaneously emit photons of both polarizations into the cavity, generating entanglement between spin state and polarization.

3. The device of claim 2, wherein the atom is171Yb, and wherein the optical cavity is tuned to resonance with transitions from3P0F=1 / 2 mF=+ / - ½ states to3D1F=3 / 2 mF=+ / - 3 / 2 states.

4. A system, comprising:a device for modular interconnects between quantum processors, the device including:an optical cavity configured to collect photons simultaneously from two transitions with opposite circular polarization, the optical cavity including a plurality of mirrors in a twisted non-planar ring geometry configured to realize two nondegenerate co-propagating modes with opposite circular polarization; andan optical tweezer array configured to be transported into the optical cavity using a steerable mirror, the optical tweezer array comprising N > 1 sites.

5. The system of claim 4, further comprising an optical fiber having a first end operably coupled to the optical cavity, such that the first end of the optical fiber is configured to receive a photon emitted by an atom.

6. The system of claim 5, further comprising a central router operably coupled to a second end of the optical fiber, configured to receive the photon from the optical fiber.

7. The system of claim 6, wherein the photon from the optical fiber is directed towards a beamsplitter in the central router.

8. The system of claim 7, further comprising a second optical fiber from a second module incident on the beamsplitter, wherein the central router is reconfigured to direct photons from different pairs of modules towards each beamsplitter in a beamsplitter array.

9. A method for connecting quantum computing modules based on neutral atom qubits, the method comprising:initializing an optical tweezer array comprising N > 1 sites with a single atom per site, outside of an optical cavity of a first quantum computing module, the optical cavity consisting of a plurality of mirrors in a twisted ring configured to realize two nondegenerate co-propagating modes with opposite circular polarization, one of the plurality of mirrors being configured as an outcoupler, and energy splitting between the two nondegenerate co-propagating modes is tuned to match spacing between atomic energy levels of opposite spin, so an atom simultaneously emits photons of both polarizations into the optical cavity, generating entanglement between a spin state and each polarization;transporting the optical tweezer array into the optical cavity using a steerable mirror or acousto-optic deflector;optically pumping the optical tweezer array into a single spin state within aJ5o, F=l / 2 ground state; andpreparing the optical tweezer array in a superposition of spin states using a singlequbit rotation implemented simultaneously on all the qubits.

10. The method of claim 9, wherein the atom is171Yb, and wherein the method further comprises:allowing a first atom to be excited from a1S0F=1 / 2 ground state to a3D1F=3 / 2 excited state using a two-photon optical transition, to be in a superposition of the3D1F=3 / 2 mF=+ / - 3 / 2 states.

11. The method of claim 10, further comprising:allowing the atom to decay by emitting a photon into the optical cavity, the optical cavity being tuned to resonance with the transitions from a3 / Jo F=l / 2 mF=+ / - ’A states to the3Z>i F=3 / 2 mF=+ / - 3 / 2 states, creating an entangled state between spin of the atom in a3P0state, and polarization of the photon;collecting the photon into an optical fiber and sending the photo to a central router; andinterfering on a beamsplitter with a photon from a second quantum computing module, a coincident detection of two photons indicating generation of an entangled state between the atoms in the first and the second quantum computing modules.

12. The method of claim 11, further comprising re-initializing at least two atoms with a failed entanglement back into the1S0ground state via optical pumping.

13. The method of claim 9, further comprising:moving the optical tweezer array out of the optical cavity into a computation zone using an acousto-optic deflector or scannable mirror; andmoving another optical tweezer array of atoms into the optical cavity.

14. The method of claim 11, wherein information about an arrival time of the detected photons is used to infer an error probability on a resulting Bell pair, and this information is used in an operation of a quantum error correction code to perform an estimation of a logical qubit state.

15. The method of claim 9, further comprising controlling cross-talk and reabsorption of photons within the optical cavity by shifting atoms in the optical cavity that are not undergoing an entanglement attempt at any point in time out of resonance with the optical cavity.

16. The method of claim 15, wherein shifting atoms out of resonance utilizes an AC Stark shift of a focused array of beams.

17. The method of claim 16, wherein a wavelength of the focused array of beams is selected to shift a3P0to3D1transition energy by a large amount compared to a coupling between the atom and optical cavity, to prevent absorption of photons emitted into the optical cavity by other atoms.

18. The method of claim 16, wherein a wavelength of the focused array of beams is selected to shift a3D1state by a large amount compared to a Rabi frequency of a two-photon transition used to excite atoms from1S0to3P1, to control which atom in the 'So state is excited to the3D1state to initiate a spin-photon entanglement attempt.

19. The method of claim 9, further comprising: applying one or more light shifts to an excited atom while the excited atom is still emitting a photon, to suppress further photon emission into the optical cavity.

20. The method of claim 19, wherein the applying the one or more light shifts is before the atom has fully decayed to a3P0state, at a time when there is no photon excitation in the optical cavity.

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