System and method for machine learning for universal photonic quantum computing resources

Abstract

The present disclosure presents systems and methods for implementing a quantum error correction code with quantum light. One such method comprises iteratively training, by a computing system using reinforcement learning, at least one neural network that is interacting with a model of a measurement-based quantum optical circuit to generate circuit parameters for the measurement-based quantum optical circuit, wherein the generated circuit parameters produce a target optical quantum state of the measurement-based quantum optical circuit; applying the generated circuit parameters to the measurement-based quantum optical circuit; and / or outputting a quantum state of the measurement-based quantum optical circuit.

Description

Docket: 02962-02 (222117-2390) SYSTEM AND METHOD FOR MACHINE LEARNING FOR UNIVERSAL PHOTONIC QUANTUM COMPUTING RESOURCES CROSS-REFERENCE TO RELATED APPLICATION

[0001] This application claims priority to co-pending U.S. provisional application entitled, “System and Method for Machine Learning for Universal Hybrid Quantum Information Precursors,” having application number 63 / 537,350, filed September 8, 2023, which is entirely incorporated herein by reference. STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

[0002] This invention was made with government support under Grant Nos.2112867 and 2219760, awarded by the National Science Foundation. The government has certain rights in the invention. TECHNICAL FIELD

[0003] The present disclosure is generally related to measurement-based quantum computing. BACKGROUND

[0004] Quantum technology, e.g. for quantum sensing, quantum communication, and quantum computing, is the anticipated and necessary outcome of the second quantum revolution. The key challenge standing in the way of the realization of field-deployable, practical quantum technology is quantum decoherence, that is, the randomization of quantum information due to the untraceable interactions of a quantum optical circuit (e.g. sensor / emitter / receiver / computer) with the physical environment.Docket: 02962-02 (222117-2390) Decoherence leads to critical errors in quantum computing and negates any quantum advantage to be had over classical technology.

[0005] Circumventing decoherence can be achieved, in principle, in three major ways. A first approach is to totally decouple the quantum system of interest from the environment, as can be achieved for atoms vis-á-vis the radiation vacuum in cavity quantum electrodynamics. A second approach is to define and employ decoherence-free subspaces in the space of quantum states of the system, which can be achieved using, for example, metastable stables in trapped earth-alkali ions or topologically protected systems. Barring the availability of the first two approaches, which are not always available, one can finally use measurement-based quantum computing to circumvent critical errors and reach genuine fault tolerance. Implementing quantum error correction requires resource quantum states that can provide a redundant encoding able to protect against any possible type of error. A wide variety of error encodings have been proposed, both for discrete-variable qubits and for continuous-variable qumodes whose experimental implementation has just begun in trapped-ion and superconducting qubits. No implementation of quantum error correction has yet been achieved with quantum light. SUMMARY

[0006] Embodiments of the present disclosure include systems and methods for implementing a quantum error correction code with quantum light. One such method comprises iteratively training, by a computing system using reinforcement learning, at least one neural network that is interacting with a model of a measurement-based quantum optical circuit to generate circuit parameters for the measurement-basedDocket: 02962-02 (222117-2390) quantum optical circuit, wherein the generated circuit parameters produce a target optical quantum state of the measurement-based quantum optical circuit; applying the generated circuit parameters to the measurement-based quantum optical circuit; and / or outputting a quantum state of the measurement-based quantum optical circuit.

[0007] The present disclosure can also be viewed as a system for implementing a quantum error correction code with quantum light comprising a processor of a computing device; and a memory in communication with the processor with the memory storing program instructions. Accordingly, the processor is operative with the program instructions to perform operations of: iteratively training, by a computing system using reinforcement learning, at least one neural network that is interacting with a model of a measurement-based quantum optical circuit to generate circuit parameters for the measurement-based quantum optical circuit, wherein the generated circuit parameters produce a target optical quantum state of the measurement-based quantum optical circuit; and / or outputting the generated circuit parameters to the measurement-based quantum optical circuit. The system can further include the measurement-based quantum optical circuit having the generated circuit parameters applied to the measurement-based quantum optical circuit, wherein the measurement-based quantum optical circuit is configured to output a quantum state of the measurement-based quantum optical circuit.

[0008] The present disclosure can also be viewed as a non-transitory, tangible computer readable storage medium having instructions stored thereon that, in response to execution by a computer-based system, cause the computer-based system to perform operations comprising: iteratively training, by a computing system using reinforcementDocket: 02962-02 (222117-2390) learning, at least one neural network that is interacting with a model of a measurement- based quantum optical circuit to generate circuit parameters for the measurement-based quantum optical circuit, wherein the generated circuit parameters produce a target optical quantum state of the measurement-based quantum optical circuit; and / or outputting the generated circuit parameters to the measurement-based quantum optical circuit.

[0009] In one or more aspects for such systems, methods, and / or devices, the quantum state is encoded as discrete qubit variables; the quantum state is encoded as continuous qumode variables; the quantum state comprises a GKP state; the quantum state comprises a squeezed cat state; the circuit parameters comprise at least one of a field amplitude parameter, a phase displacement parameter, or a beam splitter reflectivity parameter; and / or the measurement-based quantum optical circuit comprises an optical parametric oscillator, one or more variable beam splitters, and a photon-number resolving detector.

[0010] Other systems, methods, features, and advantages of the present disclosure will be or become apparent to one with skill in the art upon examination of the following drawings and detailed description. It is intended that all such additional systems, methods, features, and advantages be included within this description, be within the scope of the present disclosure, and be protected by the accompanying claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] Many aspects of the present disclosure can be better understood with reference to the following drawings. The components in the drawings are not necessarily to scale, emphasis instead being placed upon clearly illustrating the principles of theDocket: 02962-02 (222117-2390) present disclosure. Moreover, in the drawings, like reference numerals designate corresponding parts throughout the several views.

[0012] FIG. 1 is an exemplary reinforcement learning paradigm involving a neural network and a quantum optical circuit in accordance with various embodiments of the present disclosure.

[0013] FIG. 2 is an exemplary quantum optical circuit for resource quantum state generation driven by deep reinforcement learning in accordance with various embodiments of the present disclosure.

[0014] FIG.3 shows Wigner functions of 4 target squeezed cat states (r=1.38,α=3) used in a reward function calculation of FIG.1 in accordance with various embodiments of the present disclosure.

[0015] FIGS.4A-4C show histograms for training results of the neural network(s) of FIG.1 in accordance with various embodiments of the present disclosure.

[0016] FIG.5 is a block diagram illustrating an exemplary computing system or device 500 that can be utilized for systems and methods of the present disclosure. DETAILED DESCRIPTION

[0017] The present disclosure relates to systems and methods for implementing a quantum error correction code with quantum light that is driven by machine learning. Implementing quantum error correction requires resource quantum states that can provide a redundant encoding able to protect against any possible type of error. Accordingly, in various embodiments, an exemplary system or method can generate, using machine learning techniques, universal quantum resources, encoded over either discrete (qubit) or continuous (qumode) variables.Docket: 02962-02 (222117-2390)

[0018] In various embodiments, the quantum resources comprise a stable optical beam in a controllable quantum state, which can be a squeezed state, Fock state, or any other state of light, including a statistical mixture such as thermal light. For example, in certain embodiments, deep reinforcement learning is used to control a measurement- based quantum processor (e.g., a time-multiplexed quantum optical circuit sampled by a photon-number-resolving (PNR) detector in FIG. 2). In this example, the exemplary measurement-based quantum processor that is driven by reinforcement learning is able to generate squeezed cat states quasi-deterministically with an average success rate of 98% for 50-step episodes. Such quantum resources guarantee both sensitivity and resilience to physical noise, yielding quantum advantage for sensor acuity, entanglement channel distribution, and fault tolerant quantum computing and are usable for quantum sensing, quantum communication, and quantum computing.

[0019] The paradigm of machine learning used here is reinforcement learning. Reinforcement learning, particularly deep reinforcement learning (DRL) which utilizes deep neural networks, has proven to be a powerful approach for solving both deterministic and stochastic control tasks. As represented in FIG. 1, an exemplary reinforcement learning paradigm contains an agent 110 modeled by neural network(s) 120, interacting with an environment (the quantum optical circuit 130) by selecting actions 140 on the environment (quantum optical circuit 130) that produce a reward 150. Given the density matrix of the output state 160 of the circuit at a given time as input, the goal of the agent 110 is to learn which circuit parameters to select such that the cumulative reward 150 (fidelity of the generated state 160 to a squeezed cat state) is maximized. Prior work on using machine learning (ML) methods for circuit optimization has focused on circuits thatDocket: 02962-02 (222117-2390) utilize non-Gaussian unitaries such as Kerr interactions. In this case, due to the deterministic nature of the circuits, gradient-descent-based approaches could be used to optimize the individual parameters of gates in the quantum optical circuit 130 directly. However, the requirement of higher-order nonlinearities like Kerr interactions adds significant complexity to an optical experiment thereby reducing the appeal of this deterministic approach.

[0020] In the case of Tzitrin et al. (2020), a simpler Gaussian boson sampler (GBS) was used whose photon-number-resolving (PNR) measurements constituted the non- Gaussian resource, and a global optimization algorithm was used to determine the GBS parameters for a given subset of all possible photon counting patterns. See I. Tzitrin, J. E. Bourassa, N. C. Menicucci, et al., “Progress Towards Practical Qubit Computation Using Approximate Gottesman-Kitaev-Preskill Codes,” Phys. Rev. A 101, 032315 (2020). The disadvantage with this approach is that it is based on the post-selection of the particular photon counting pattern that the GBS was optimized for, thereby resulting in very low success probabilities. An exemplary approach of the present disclosure, however, is not based on post-selection and therefore does not suffer from the low, probabilistic success rates thereof. Lastly, the traditional forms of the gradient-based optimization methods used in prior works must perform function evaluations sequentially as each gradient update depends on the previous one. In contrast, an exemplary approach of the present disclosure takes advantage of parallelization to compute many function evaluations at once. Thus, by recasting the measurement-based circuit optimization problem as a sequential and stochastic control task, the present disclosureDocket: 02962-02 (222117-2390) uses DRL techniques that can learn state preparation strategies that are adaptive, thereby removing the need for photon number post-selection.

[0021] Referring now to FIG. 2, a quantum optical circuit 130 is presented for squeezed cat state generation driven by deep reinforcement learning in accordance with various embodiments of the present disclosure. The circuit 130 utilizes variable beam splitters (t) that can be implemented with Mach-Zehnder interferometry devices based, for example, on optical path or on polarization and using the electro-optic effect.

[0022] Therefore, in accordance with the present disclosure, the quantum optical circuit 130 of FIG. 2 can be controlled by a machine learning process, for example a reinforcement learning process implemented by one or more neural networks 120, where the neural network will be trained by inputting photon-number resolving measurements from the PNR detector and outputting in-loop circuit parameters | ^^^^, such as, but not limited to, field-amplitude & phase displacements and beamsplitter reflectivity changes. In accordance with the paradigm of reinforcement learning, an agent 110 interacts with an environment (quantum optical circuit 130) at step j, (j = 0, ...,m), an input state | ^^^^ is split by VBS1, of field transmission coefficient ^^^^, and sent back to VBS1 via a phase- stable loop. VBS2 is a switchable mirror of ^^ଶ^= 0 for j<m and ^^ଶ^= 1 at final step m. The other output of VBS1 undergoes a photon-number-resolving (PNR) measurement yielding result ^^^, while the loop’s input to VBS1 will interfere with state | ^^^ା^^. All input states are squeezed vacuum states |0, ^^^ , ^^^^ of adjustable squeezing parameter ^^^. Note that the phase inside the loop and the squeezing angle ^^^are both set to 0 for these simulations but can be controlled by the agent 110 as well, if desired.Docket: 02962-02 (222117-2390)

[0023] The experimental implementation of this circuit 130 will require the standard care associated with squeezed modes of light, in terms of mode-matching, losses, and optical phase control. The input state | ^^^^ = |0, ^^^ , ^^^^ can be produced by an optical parametric oscillator (OPO) 170Simply controlling the amplitude parameter of a pump beam of the OPO 170 will yield control of ^^^ and controlling the optical phase parameter between the OPO and VBS1 will control ^^^. This can be done in a precise way with electro-optic modulators. The VBS (e.g., VBS1 or VBS2) can be implemented by using, as a variable beam splitter, a Mach–Zehnder interferometer whose relative arm phase is controlled by an electro-optic modulator.

[0024] In various embodiments, the neural network(s) 120 are trained by extracting the output quantum state | ^^^ and evaluating it against a target type of quantum resource. Further, the neural network(s) 120 can be trained to be able to perform adaptive control of the quantum optical circuit 130 (by selecting circuit parameters) that has stochastic outcomes at each step (PNR) so that it can steer the evolution of the quantum state to a desired or target state via the optical circuit 130. The agent 110 (e.g., neural network(s) 120) thus becomes able to steer the evolution in the desired direction even if it receives a photon number detection pattern it had never seen during training.

[0025] The quantum resources generated by this exemplary scheme are generated quasi-deterministically once the neural network(s) 120 have been trained, unlike current proposals that are probabilistic (i.e., fail a significant fraction of the time). In accordance with the present disclosure, quantum resources can comprise Gaussian and non- Gaussian quantum resources (in terms of their Wigner function) as well as iterative feedback. Because the disclosed scheme employs both Gaussian and non-GaussianDocket: 02962-02 (222117-2390) resources, universal quantum information resources, such as Gottesman-Kitaev-Preskill (GKP) grid states, cubic-phase states, other types of CV magic states, bosonic rotational codes, etc. can be produced.

[0026] In various embodiment, the agent 110 of FIG. 1 is modeled using two deep neural networks 120 with three hidden layers of size 256, 128 and 64 respectively with tanh as the activation function. The state of the environment ^^^at step j is represented using the density matrix of the input state ^^^ൌ | ^^^^ ^ ^^^|. In particular, a vector ^^^= [Re( ^^^௨), Im( ^^^௨), diag( ^^^)] is defined, where ^^^௨of ^^^that are above its diagonal. is represented as a vector ^^^= ^ ^^^ , ^^ଶ^^. A reward function R( ^^^) is given by the fidelity of the current state ^^^with one of 4 target states: whereFourier transform (FT) and the fidelity is given by ^^( ^^^, ^^ଶ)= ^^ ^^ଶ^^ ^^^⁄ ଶ^ ^^ଶ^^^⁄ ଶ^^⁄ ଶ^. The target states ^^േ=| ^^േ^ ^ ^^േ| are squeezed cat states of ± parity: with aWigner functions of these 4 states are plotted in FIG.3.

[0027] Here, each of the 4 target states can be distinguished by the detection sequence of their generation episode: even-parity states (positive Wigner function at the origin) are generated when the total detected photon number ^^ ൌ∑^^ୀ^^^^is even. Odd- parity states (negative Wigner function at the origin) have odd N. Moreover, FT’d statesDocket: 02962-02 (222117-2390) can be distinguished by checking the agent’s action in the last step of the episode: FT’d states have ^^^<0, the other have ^^^>0. Exponent P in Equation (1) is used to penalize low-fidelity states and is taken to be 50 in the simulations. The initial state |0, ^^^^has ^^^=1.38.

[0028] For evaluation purposes, in one embodiment, an exemplary reinforcement learning algorithm comprises proximal policy optimization (PPO), implemented by Python library StableBaselines3, and where the quantum optical circuit 130 is simulated using Python library Strawberry Fields. For this simulation, an actor-critic version of PPO was used, which selects an action given a particular state sjand a critic network which approximates the value of a state. The agent (modeled using two deep neural networks) was trained over 7×106steps with 10-step episodes. The results were evaluated by examining 5 sets of 25050-step episodes, each set having a different random-number seed to simulate PNR results. Each episode was composed of at most 50 steps, i.e., loop iterations, and the agent invariably concluded each and every episode by setting ^^^^, denoted as ^^^from here on, to 0 and not changing it in all steps thereafter. FIGS.4A-4C capture the results.

[0029] Accordingly, FIG.4A clearly demonstrates high fidelity and further scrutiny of each individual episode revealed that the outcome is a squeezed cat state 98% of the time on average, be it different from the target state at times. In assessing success, all obtained squeezed cat states were included, even those with parameters different from ( ^^ = 1.38, ^^ = 3) and therefore suffering from lower fidelities, for the following two reasons: (i) it is well known that small cat states can be deterministically “bred” to larger sizes so they are still useful and, (ii) all generation sequences {( ^^^, ^^^, ^^^)}juniquely label eachDocket: 02962-02 (222117-2390) output which allows generation of accurate lookup tables to drive an experimental setup with full knowledge of the generated state based on the generation sequence. These considerations validate the observed average success rate of 98% for 50-step episodes.

[0030] FIG.4B gives a sense of the average detected photon number per episode, which includes large detected photon numbers at times as the number of steps per episode was often much less than 50, as FIG.4C shows.

[0031] The simulation was also run with a 1% loss channel placed before the PNR detector, yielding 75% success rate with little degradation of the state quality, for 4.5×106training steps. It should be emphasized here that the 75% success rate at 1% loss per PNR detection is quite a remarkable result and already a record in and of itself if one ignored the 98% success rate of the lossless case. The reason is the following: the loss of an odd number of photons changes the state’s parity and therefore tends to make cat states orthogonal in the process, resulting in a sudden and marked decrease of the reward function, which is based on the fidelity. One may expect this to bring confusion to the neural network’s training but, as it turned out, the training can still proceed and converge.

[0032] FIG.5 is a block diagram illustrating an exemplary computing system or device 500 that can be utilized for systems and methods of the present disclosure. Computing system 500 includes at least one processor 510, e.g., a quantum processing unit (QPU), coupled to memory elements 520 through a data bus 530 or other suitable circuitry. Computing system 500 stores program code within memory elements 520, 522. Processor 510 executes the program code or instructions 524 accessed from memory elements 520, 522 via the data bus 530. The program code or instructions 524 can includeDocket: 02962-02 (222117-2390) neural network(s) 120, optical circuit models, and neural network training data, as disclosed herein.

[0033] In one aspect, computing system 500 may be implemented as a computer or other data processing system, including server computers that are accessed using browsers at client computers. It should be appreciated, however, that computing system 500 can be implemented in the form of any system including a processor (e.g., a GPU simulating a quantum processor) and memory that is capable of performing the functions described within this disclosure.

[0034] An aspect of an embodiment of the present disclosure includes, but not limited thereto, a system, method, and computer readable medium that provides one or more of the following operations: a) performing machine learning for universal quantum computing resources (e.g., universal hybrid quantum information precursors); b) performing machine learning for efficient generation of universal quantum computing resources (e.g., universal hybrid quantum computing precursors); c) generating any quantum error correcting code, applicable to qubits or qumodes, by employing an iterative quantum optical procedure informed by machine learning; and d) driving the quantum optical circuit used for generation with machine learning. As such, the exemplary computing system 500 of FIG. 5 can implement one or more the foregoing embodiments.

[0035] Referring back to FIG.5, an example computing system 500 can include the processor 510 (e.g., a quantum processing unit (QPU), a central processing unit (CPU), a graphics processing unit (GPU) or a combination of two or more processing units), a main memory 520 and a static memory 522, some or all of which can communicate with each other via the bus 530. The computing system 500 can further include a display unitDocket: 02962-02 (222117-2390) 540, an alphanumeric input device 542 (e.g., a keyboard), and a user interface (UI) navigation device 544 (e.g., a mouse). In an example, the display unit 540, input device 542 and UI navigation device 544 can be a touch screen display. The computing system 500 can additionally include a storage device (e.g., drive unit) 550, a signal generation device 554 (e.g., a speaker), a network interface device 560, and / or one or more quantum optical circuit elements 130.

[0036] The storage device 550 can include a machine readable medium 552 on which is stored one or more sets of data structures or instructions 524 (e.g., software) embodying or utilized by any one or more of the methodologies or functions described herein. The instructions 524 can also reside, completely or at least partially, within the main memory 520, within static memory 522, or within the processor 510 during execution thereof by the computing system 500. In an example, one or any combination of the processor 510, the main memory 520, the static memory 522, or the storage device 550 can constitute machine readable media.

[0037] While the machine readable medium 552 is illustrated as a single medium, the term "machine readable medium" can include a single medium or multiple media (e.g., a centralized or distributed database, and / or associated caches and servers) that configured to store the one or more instructions 524. The term “machine readable medium” can also be taken to include any tangible medium that is capable of storing, encoding, or carrying instructions for execution by the machine and that cause the machine to perform any one or more of the methodologies of the present disclosure or that is capable of storing, encoding or carrying data structures utilized by or associated with such instructions. The term “machine readable medium” can accordingly be taken toDocket: 02962-02 (222117-2390) include, but not be limited to, solid-state memories, and optical and magnetic media. Specific examples of machine readable media can include non-volatile memory, including, by way of example, semiconductor memory devices (e.g., Electrically Programmable Read-Only Memory (EPROM), Electrically Erasable Programmable Read-Only Memory (EEPROM)) and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM and DVD- ROM disks.

[0038] The instructions 524 can further be transmitted or received over a communications network 562 using a transmission medium via the network interface device 560 utilizing any one of a number of transfer protocols (e.g., frame relay, IP, TCP, UDP, HTTP, etc.). Example communication networks can include a local area network (LAN), a wide area network (WAN), a packet data network (e.g., the Internet), mobile telephone networks (e.g., cellular networks), Plain Old Telephone (POTS) networks, and wireless data networks (e.g., IEEE 802.11 standards family known as Wi-Fi®, IEEE 802.16 standards family known as WiMax®), peer-to-peer (P2P) networks, among others. The term “transmission medium” shall be taken to include any intangible medium that is capable of storing, encoding or carrying instructions for execution by the machine, and includes digital or analog communications signals or other intangible medium to facilitate communication of such software.

[0039] Examples of computing system 500 can include logic, one or more components, circuits (e.g., modules), or mechanisms. Circuits are tangible entities configured to perform certain operations, which can include electrical and optical circuitry. In an example, circuits can be arranged (e.g., internally or with respect to external entitiesDocket: 02962-02 (222117-2390) such as other circuits) in a specified manner. In an example, one or more computer systems (e.g., a standalone, client or server computer system) or one or more hardware processors (e.g., quantum processors, computing processors, graphical processors, etc.) can be configured by software (e.g., instructions, an application portion, or an application) as a circuit that operates to perform certain operations as described herein. In an example, the software can reside (1) on a non-transitory machine readable medium or (2) in a transmission signal. In an example, the software, when executed by the underlying hardware of the circuit, causes the circuit to perform the certain operations.

[0040] In an example, a circuit can be implemented mechanically, optically, quantumly, and / or electronically. For example, a circuit can comprise dedicated circuitry or logic that is specifically configured to perform one or more techniques such as discussed above, such as including a special-purpose processor, a quantum optical circuit, a field programmable gate array (FPGA) or an application-specific integrated circuit (ASIC). In an example, a circuit can comprise programmable logic (e.g., circuitry, as encompassed within a general-purpose processor or other programmable processor) that can be temporarily configured (e.g., by software) to perform the certain operations. It will be appreciated that the decision to implement a circuit mechanically (e.g., in dedicated and permanently configured circuitry), or in temporarily configured circuitry (e.g., configured by software) can be driven by cost and time considerations.

[0041] Accordingly, the term “circuit” is understood to encompass a tangible entity, be that an entity that is physically constructed, permanently configured (e.g., hardwired), or temporarily (e.g., transitorily) configured (e.g., programmed) to operate in a specified manner or to perform specified operations. In an example, given a plurality of temporarilyDocket: 02962-02 (222117-2390) configured circuits, each of the circuits need not be configured or instantiated at any one instance in time. For example, where the circuits comprise a processor configured via software, the processor can be configured as respective different circuits at different times. Software can accordingly configure a processor, for example, to constitute a particular circuit at one instance of time and to constitute a different circuit at a different instance of time.

[0042] In an example, circuits can provide information to, and receive information from, other circuits. In this example, the circuits can be regarded as being communicatively coupled to one or more other circuits. Where multiple of such circuits exist contemporaneously, communications can be achieved through signal transmission (e.g., over appropriate circuits and buses) that connect the circuits. In embodiments in which multiple circuits are configured or instantiated at different times, communications between such circuits can be achieved, for example, through the storage and retrieval of information in memory structures to which the multiple circuits have access. For example, one circuit can perform an operation and store the output of that operation in a memory device to which it is communicatively coupled. A further circuit can then, at a later time, access the memory device to retrieve and process the stored output. In an example, circuits can be configured to initiate or receive communications with input or output devices and can operate on a precursor (e.g., a collection of information).

[0043] The various operations of method examples described herein can be performed, at least partially, by one or more processors that are temporarily configured (e.g., by software) or permanently configured to perform the relevant operations. Whether temporarily or permanently configured, such processors can constitute processor-Docket: 02962-02 (222117-2390) implemented circuits that operate to perform one or more operations or functions. In an example, the circuits referred to herein can comprise processor-implemented circuits.

[0044] Similarly, the methods described herein can be at least partially processor- implemented. For example, at least some of the operations of a method can be performed by one or processors or processor-implemented circuits. The performance of certain of the operations can be distributed among the one or more processors, not only residing within a single machine, but deployed across a number of machines. In an example, the processor or processors can be located in a single location (e.g., within a home environment, an office environment or as a server farm), while in other examples the processors can be distributed across a number of locations.

[0045] The one or more processors can also operate to support performance of the relevant operations in a "cloud computing" environment or as a "software as a service” (SaaS). For example, at least some of the operations can be performed by a group of computers (as examples of machines including processors), with these operations being accessible via a network (e.g., the Internet) and via one or more appropriate interfaces (e.g., Application Program Interfaces (APIs).)

[0046] Example embodiments (e.g., apparatus, systems, or methods) can be implemented in digital electronic circuitry, quantum computing circuitry, in computer hardware, in firmware, in software, or in any combination thereof. Example embodiments can be implemented using a computer program product (e.g., a computer program, tangibly embodied in an information carrier or in a machine readable medium, for execution by, or to control the operation of, data processing apparatus such as a programmable processor, a computer, or multiple computers).Docket: 02962-02 (222117-2390)

[0047] A computer program can be written in any form of programming language, including compiled or interpreted languages, and it can be deployed in any form, including as a stand-alone program or as a software module, subroutine, or other unit suitable for use in a computing environment. A computer program can be deployed to be executed on one computer or on multiple computers at one site or distributed across multiple sites and interconnected by a communication network.

[0048] In the context of this document, a "computer-readable medium" can be any means that can contain, store, communicate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. The computer readable medium can be, for example but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device. More specific examples (a nonexhaustive list) of the computer-readable medium would include the following: an electrical connection (electronic) having one or more wires, a portable computer diskette (magnetic), a random access memory (RAM) (electronic), a read-only memory (ROM) (electronic), an erasable programmable read-only memory (EPROM or Flash memory) (electronic), an optical fiber (optical), and a portable compact disc read- only memory (CDROM) (optical).

[0049] In an example, operations can be performed by one or more programmable processors executing a computer program to perform functions by operating on input data and generating output. Examples of method operations can also be performed by, and example apparatus can be implemented as, special purpose logic circuitry (e.g., a field programmable gate array (FPGA) or an application-specific integrated circuit (ASIC)).Docket: 02962-02 (222117-2390)

[0050] The computing system can include clients and servers. A client and server are generally remote from each other and generally interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. In embodiments deploying a programmable computing system, it will be appreciated that both hardware and software architectures require consideration. Specifically, it will be appreciated that the choice of whether to implement certain functionality in permanently configured hardware (e.g., an ASIC), in temporarily configured hardware (e.g., a combination of software and a programmable processor), or a combination of permanently and temporarily configured hardware can be a design choice.

[0051] In a networked deployment, the computing system 500 can operate in the capacity of either a server or a client machine in server-client network environments. In an example, computing system 500 can act as a peer machine in peer-to-peer (or other distributed) network environments. The computing system 500 can be a personal computer (PC), a tablet PC, a set-top box (STB), a Personal Digital Assistant (PDA), a mobile telephone, a web appliance, a network router, switch or bridge, or any machine capable of executing instructions (sequential or otherwise) specifying actions to be taken (e.g., performed) by the computing system 500. Further, while only a single computing system 500 is illustrated, the term “machine” shall also be taken to include any collection of machines that individually or jointly execute a set (or multiple sets) of instructions to perform any one or more of the methodologies discussed herein.

[0052] In brief, the present disclosure discloses systems and methods for generating a quantum error correcting code by employing an iterative quantum optical procedureDocket: 02962-02 (222117-2390) driven or informed by machine learning. Accordingly, in various embodiments, an exemplary system or method can generate, using machine learning techniques, universal quantum resources, encoded over either discrete (qubit) or continuous (qumode) variables, usable for quantum sensing, quantum communication, and quantum computing, where such quantum resources are based on quantum error correction encodings that guarantee both sensitivity and resilience to physical noise, yielding quantum advantage for sensor acuity, entanglement channel distribution, and fault tolerant quantum computing.

[0053] For example, various embodiments of the present disclosure provide an all- optical quasi-deterministic method for generating GKP state precursors, which does not require coupling to a qubit and its success rate significantly exceeds that of all other qubitless methods. An aspect of an embodiment of the present disclosure achieves a nearly perfect theoretical success rate for generating essential quantum state resources for quantum error correction. This method and system outperforms all other qubit-less proposals known so far. Moreover, driving a quantum optical circuit used for the generation of essential quantum state resources with machine learning has never been done for qubit-less methods before. This ensures that the agent is able to adjust to situations it never encountered before, resulting in near-deterministic operation, with no need to rely on the low-probability post-selection of randomly occurring positive results. Quantum precursors or resources generated by the disclosed machine learning protocol enable at least the following: decoherence-free quantum information for quantum sensing (sensitivity to minute signals, viewed as errors); decoherence-free quantum communication (quantum repeaters for long-haul quantum transmission ofDocket: 02962-02 (222117-2390) entanglement); and decoherence-free quantum computing (via quantum error correction for fault tolerance).

[0054] While the present disclosure has been described with respect to specific embodiments, many modifications, variations, alterations, substitutions, and equivalents will be apparent to those skilled in the art. The present disclosure is not to be limited in scope by the specific embodiments described herein. Many variations and modifications may be made to the above-described embodiment(s) without departing substantially from the principles of the disclosure. All such modifications and variations are intended to be included herein within the scope of this disclosure.

Claims

Docket: 02962-02 (222117-2390) CLAIMS We claim:

1. A method for implementing a quantum error correction code with quantum light comprising: iteratively training, by a computing system using reinforcement learning, at least one neural network that is interacting with a model of a measurement-based quantum optical circuit to generate circuit parameters for the measurement-based quantum optical circuit, wherein the generated circuit parameters produce a target optical quantum state of the measurement-based quantum optical circuit; applying the generated circuit parameters to the measurement-based quantum optical circuit; and outputting a quantum state of the measurement-based quantum optical circuit.

2. The method of claim 1, wherein the quantum state is encoded as discrete qubit variables.

3. The method of claim 1, wherein the quantum state is encoded as continuous qumode variables.

4. The method of claim 1, wherein the quantum state comprises a GKP state.Docket: 02962-02 (222117-2390) 5. The method of claim 1, wherein the quantum state comprises a squeezed cat state.

6. The method of claim 1, wherein the circuit parameters comprise at least one of a field amplitude parameter, a phase displacement parameter, or a beam splitter reflectivity parameter.

7. The method of claim 1, wherein the measurement-based quantum optical circuit comprises an optical parametric oscillator, one or more variable beam splitters, and a photon-number resolving detector.

8. A system for implementing a quantum error correction code with quantum light comprising. a processor of a computing device; a memory in communication with the processor, the memory storing program instructions, the processor operative with the program instructions to perform operations of: iteratively training, by a computing system using reinforcement learning, at least one neural network that is interacting with a model of a measurement-based quantum optical circuit to generate circuit parameters for the measurement-based quantum optical circuit, wherein the generated circuit parameters produce a target optical quantum state of the measurement-based quantum optical circuit; andDocket: 02962-02 (222117-2390) outputting the generated circuit parameters to the measurement-based quantum optical circuit; and the measurement-based quantum optical circuit having the generated circuit parameters applied to the measurement-based quantum optical circuit, wherein the measurement-based quantum optical circuit is configured to output a quantum state of the measurement-based quantum optical circuit.

9. The system of claim 8, wherein the measurement-based quantum optical circuit is configured to encode the quantum state as discrete qubit variables.

10. The system of claim 8, wherein the measurement-based quantum optical circuit is configured to encode the quantum state as continuous qumode variables.

11. The system of claim 8, wherein the quantum state comprises a GKP state.

12. The system of claim 8, wherein the quantum state comprises a squeezed cat state.

13. The system of claim 8, wherein the circuit parameters comprise at least one of a field amplitude parameter, a phase displacement parameter, or a beam splitter reflectivity parameter.Docket: 02962-02 (222117-2390) 14. The system of claim 8, wherein the measurement-based quantum optical circuit comprises an optical parametric oscillator, one or more variable beam splitters, and a photon-number resolving detector.

15. A non-transitory, tangible computer readable storage medium having instructions stored thereon that, in response to execution by a computer-based system, cause the computer-based system to perform operations comprising: iteratively training, by a computing system using reinforcement learning, at least one neural network that is interacting with a model of a measurement-based quantum optical circuit to generate circuit parameters for the measurement-based quantum optical circuit, wherein the generated circuit parameters produce a target optical quantum state of the measurement-based quantum optical circuit; and outputting the generated circuit parameters to the measurement-based quantum optical circuit.

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