Quantum Optical Memristor

Abstract

The quantum optical memristor (1) comprises a Mach-Zehnder interferometer (2) having a first optical input (3), a first optical output (5), and a second optical output (6), a detector (9) for detecting a time-dependent optical signal n(t) at the second optical output (6) of the Mach-Zehnder interferometer (2), and a target reflectivity R of the Mach-Zehnder interferometer (2). target The first optical input (3) and the first optical output (5) of the Mach-Zehnder interferometer (2) are the first optical input (7) and the first optical output (8) of the quantum optical memristor (1), respectively. The controller (10) calculates the calculated target reflectance R target The controller 10 updates the reflectivity R(t) of the Mach-Zehnder interferometer 2 to match the target reflectivity R(t) based on the derivative of the reflectivity with respect to time. target The derivative of the reflectivity with respect to time is a linear function of the detected signal n(t).

Description

[Technical field]

[0001] The present invention relates to a quantum optical memristor for manipulating photon quantum states, - a Mach-Zehnder interferometer having at least a first optical input and having a first optical output and a second optical output; - a detector configured to detect a time-dependent optical signal n(t) at the second optical output of the Mach-Zehnder interferometer; - Target reflectivity R of the Mach-Zehnder interferometer target and a controller configured to calculate the first optical input and the first optical output of the Mach-Zehnder interferometer are respectively the first optical input and the first optical output of the quantum optical memristor; The controller calculates the target reflectance R target The Mach-Zehnder interferometer is configured to update the reflectivity R(t) of the Mach-Zehnder interferometer to match

[0002] The present invention also relates to a method for manipulating optical qubits using quantum optical memristors, the quantum optical memristors comprising: - a Mach-Zehnder interferometer having at least a first optical input, a first optical output, and a second optical output; - a detector configured to detect a time-dependent optical signal n(t) at the second optical output of the Mach-Zehnder interferometer; - Target reflectivity R of the Mach-Zehnder interferometer target and a controller configured to calculate the first optical input and the first optical output of the Mach-Zehnder interferometer are respectively the first optical input and the first optical output of the quantum optical memristor; The controller calculates the target reflectance R target and configured to update the reflectivity R(t) of the Mach-Zehnder interferometer to match The method comprises: - providing one or more photons to a quantum optical memristor at an optical input of the quantum optical memristor; - measuring an optical signal n(t) at a detector; - Calculated target reflectance R target and updating the reflectivity R(t) of the Mach-Zehnder interferometer to match [Background technology]

[0003] The project leading to this application has received financial support from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 820474, financial support from the Austrian Science Fund (FWF): Forschergruppe FG5 and financial support from the Austrian Ministry of Education, Science and Research (BMBWF) and the Austrian Ministry for Digitalisation and Economic Location (BMDW) through their programme "QuantERA".

[0004] Memristors have been postulated as a fourth fundamental passive circuit element, in addition to resistors, capacitors, and inductors. A fundamental property of such devices is that they retain a memory of their past states in the form of resistive hysteresis. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Leon O Chua and Sung Mo Kang, "Memristive devices and systems", Proceedings of the IEEE 64, 209-223, 1976 [Non-Patent Document 2] Salmilehto, J., Deppe, F., Di Ventra, M., Sanz, M., & Solano, E., "Quantum memristors with superconducting circuits", Scientific reports, 7(1), 1-6, 2017 [Non-Patent Document 3] Pfeiffer, P., Egusquiza, IL, Di Ventra, M., Sanz, M., & Solano, E., "Quantum memristors", Scientific reports, 6(1), 1-6, 2016 [Non-Patent Document 4] Mikel Sanz, Lucas Lamata, and Enrique Solano, "Invited article: Quantum memristors in quantum photonics", APL Photonics 3, 080801, 2018 [Non-Patent Document 5] Gonzalez-Raya et al, "Quantum Memristors in Frequency-Entangled Optical Fields", 2019 Summary of the Invention [Problem to be solved by the invention]

[0006] In Non-Patent Document 1, a more general concept of a memristive device is introduced, which is defined by the following equation:

[0007]

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[0008] where u and y denote the input and output variables, respectively, and s denotes the state variable, all of which are implicitly assumed to depend on time t. The device is first demonstrated in an electronic circuit, where u and y are currents and voltages, and f is a generalized resistance. Quantum memristors should be able to go beyond their classical counterparts by enabling the same behavior, in addition to preserving quantum coherence when processing the information encoded in the quantum state. Depending on the choice of input and output variables, quantum memristors must offer the following characteristics: (a) To show the memristive behavior in the classical limit, i.e., the dynamics of the above formula when the expectation values ​​of the quantum observables are taken into account. (b) Quantum coherent processing, i.e., the ability to coherently map quantum input states onto output states. These two requirements are typically mutually exclusive, which represents a serious technical obstacle. The only situation in which a quantum photonic device can produce the memory behavior required for case (a) is through interaction with the environment over some form of measurement process. In practice, this is always associated with some level of decoherence, thus invalidating point (b) and making the device not different from a classical memristor. To overcome this contradiction, it is necessary to implement an open quantum system such that features (a) and (b) can coexist, and the interaction with the environment must be strong enough to provide a useful nonlinearity, but at the same time weak enough to fully preserve quantum coherence.

[0009] In non-patent document 2, quantum memristors in electronic circuits are presented. Non-patent document 2 introduces a quantum memristor based on tunneling induced by quasiparticles and the cancellation of supercurrents by tunneling. Memristors comprise superconducting quantum interference devices (SQUIDs) and superconducting circuits. However, electronic memristors are not suitable for photonics, i.e. for the operation of optical qubits. On the other hand, SQUIDs and superconducting circuits cannot process photons. On the other hand, electronic memristors are voltage controlled. It is essential that the voltage can take positive and negative values, which is not the case for optical signals. Therefore, the presented algorithm is also not suitable for photonic memristors.

[0010] In non-patent document 3, a protocol and numerical simulations are presented for quantum electronic memristors based on superconducting circuits. The proposed system consists of a quantum LC circuit with a shunt by a memristor. Therefore, this component cannot be used to process photons. The protocol is based on measuring the voltage applied to the memristor. Again, it is essential that the voltage can take positive and negative values, which is not the case for optical signals. Therefore, the protocol is not suitable for photonic memristors.

[0011] In the paper by , the possibility of realizing quantum memristors in the photon domain was pointed out. , proposes to use a Mach-Zehnder interferometer with an adjustable retarder. The Mach-Zehnder interferometer acts as an adjustable beam splitter, whereas its reflectivity can be changed by the retarder. A model is proposed for adapting the phase based on a previously detected signal. The proposed device theoretically fulfills the requirements of a memristor outlined above for coherent and squeezed states. The model shows the deviation behavior in the case of Fock states, which is probably the most relevant for quantum photonics applications. In those examples with Fock states, they obtain a hysteresis diagram that does not approach the origin. Physically, they are expressed as a function of the input quantity x, called the quadrature phase operator.in This occurs because the authors use a feedback function based on x = 1 / x, but an input state with zero quadrature does not always mean an output state with zero photons. Thus, even if their proposed device could exhibit memory behavior, it is inconsistent with the definition of a memristive device, and in particular with the required resistive hysteresis. Furthermore, the scheme proposed by [4] is very challenging, if not impossible, to implement in practice, since it requires tuning and measuring the quadrature operator, which generally requires mixing states with coherent beams, thus greatly complicating any experimental setup. Moreover, the input states are given by a superposition of Fock states, which, although realizable in linear optics, is impractical, especially considering that the average quadrature phase of such states depends on their relative phase terms, which should be tightly controlled. A further challenge lies in the fact that the subsequent manipulation of a qubit encoded in superposition with a vacuum state is always significantly far from trivial. Although they show diagrammatically a measurement performed at the second output of the beam splitter, [4] does not consider the proposed input quantity x in does not disclose how to derive from such measurements.

[0012] The paper by E. K. et al. describes different implementations of quantum memristors in a quantum photonics setup.

[0013] It is an object of the present invention to provide a quantum optical memristor and method capable of manipulating photon quantum states. [Means for solving the problem]

[0014] The present invention proposes a device as defined at the outset, The controller (10) calculates the derivative of the reflectance with respect to time.

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[0015] If a, b, and p are any nonzero real numbers, then

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[0016] Generally, within the scope of this disclosure, the derivative of reflectance with respect to time

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[0017] Optionally, the derivative of the reflectance with respect to time

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[0018] The present invention also relates to a method as defined at the beginning, The controller (10) calculates the derivative of the reflectance with respect to time.

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[0019] By Mach-Zehnder interferometer we understand any device that allows adjusting the probability P1 that a photon arriving at its input is emitted at a first of two or more (M) outputs, where:

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[0020] The Mach-Zehnder interferometer can act as a beam splitter, and the probability can be changed by changing the relative phase of the optical paths. In this embodiment, the interferometer can act as a tunable beam splitter, and thus P1 can be referred to as the "reflectivity" of the Mach-Zehnder interferometer.

[0021] In a typical embodiment, the Mach-Zehnder interferometer may be a device that splits the incident light into two paths using a first beam splitter, introduces a relative phase term between the two paths, for example by a delay, and recombines the two paths at a second beam splitter. The probability P1 that an incident photon is emitted at the first of the two outputs of the Mach-Zehnder can be changed by changing the relative phase term of the two paths. In this embodiment, the overall operation of the Mach-Zehnder interferometer is therefore equivalent to that of an adjustable beam splitter.

[0022] In another preferred embodiment, the controller calculates a derivative of the reflectance

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[0023] It should be noted that if the lower bound of the integral interval is a (positive) function of time, this will result in derivatives containing negative terms. For example,

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[0024] Optionally, the length T of the time frame can be configured, and preferably is configured, to be equal to or less than the modulation period of the optical input signal at the optical input of the Mach-Zehnder interferometer (2). Depending on the relationship between the modulation period of the optical input signal and the integration time T, two limiting schemes are accessible. If the integration time T is small compared to the modulation period, the input may be considered to be approximately constant. The behavior then simplifies to R(t)=n(t) for the case of a single photon. In contrast, if the input oscillates very fast, such that the modulation time is small compared to the integration time T, the integral approaches zero, resulting in R(t)=0.5, resulting in a constant reflectivity R of 50%. If the integration time is equal to the modulation period, the integral is over the entire modulation period and therefore zero. Integrating over a period longer than one therefore leads to redundant results. For this reason, the integration time is preferably equal to or less than the modulation period.

[0025] For example, the signal n(t) at the detector may be related to the number of photons detected (e.g., photon count). This is particularly advantageous for applications involving small numbers of photons, especially when the device is used to manipulate qubits encoded as single photons. The detector may be a single-photon detector (e.g., a photon counter). In a preferred embodiment, the quantum optical memristor comprises parallel paths having an optical input and an optical output, the optical input and optical output of the parallel paths being respectively a second optical input and a second optical output of the quantum optical memristor, the parallel paths and the Mach-Zehnder interferometer being configured to be fed from the same photon source, and the parallel paths do not essentially manipulate the state of the photons in the parallel paths. The parallel paths offer the possibility for the quantum optical memristor to transmit photons without interacting with the Mach-Zehnder interferometer. Thus, the photons may be manipulated or transmitted essentially in their original state.

[0026] Preferably, the parallel paths are configured to associate with a first spatial mode and the Mach-Zehnder interferometer is configured to associate with a second spatial mode of the qubit, where the qubit is encoded as a single photon that is a superposition of the first and second spatial modes. In this way, the qubit may be path-encoded rather than encoded as a superposition of energy states. Path-encoded qubits are easier to handle in quantum optics compared to qubits encoded as a superposition of two energy levels. This embodiment significantly expands the application possibilities.

[0027] Preferably, the quantum optical memristor comprises parallel paths having optical inputs and optical outputs; the optical input and the optical output of the parallel path are a second optical input and a second optical output of the quantum optical memristor, respectively; the first optical input and the second optical input of the quantum optical memristor are configured to be fed from the same photon source; The parallel paths do not inherently manipulate the state of the photons in the parallel paths, the parallel paths are configured to associate with a first spatial mode and the Mach-Zehnder interferometer is configured to associate with a second spatial mode of the qubit, where the qubit is encoded as a single photon that is a superposition of the first and second spatial modes; The method comprises: - providing a quantum optical memristor with qubits encoded as photons in a superposition of first and second spatial modes. The method is suitable for qubits encoded as a superposition of two spatial modes, which is a particularly beneficial and natural choice for integrated quantum photonics.

[0028] Optionally, the Mach-Zehnder interferometer comprises two beam splitters, the beam splitters having a 50 / 50 splitting ratio. To achieve maximum tunability of the reflectivity over the entire range between 0 and 1, the beam splitters should have a 50 / 50 splitting ratio.

[0029] Preferably, the quantum optical memristor is partially provided as part of an integrated photonic chip, and at least the Mach-Zehnder interferometer is part of the integrated photonic chip. The Mach-Zehnder interferometer includes two beam splitters and a retarder, which may also be part of the integrated photonic chip. The retarder is part of one of the two arms of the Mach-Zehnder interferometer and is used to change the relative phase between the two arms. The quantum optical memristor components, which are part of the integrated photonic chip, can be manufactured in a reliable and reproducible manner, reducing the cost per part. Furthermore, the optical path is rigidly mechanically connected, thus preventing phase decoherence. At least the detector and the controller are typically external components.

[0030] Optionally, the quantum optical memristor is partially provided as part of an integrated photonic chip, with at least the Mach-Zehnder interferometer and the parallel path being part of the integrated photonic chip. The quantum optical memristor components that are part of the integrated photonic chip can be manufactured in a reliable and reproducible manner, reducing the cost per part. Furthermore, the optical paths are rigidly mechanically connected, thus preventing phase decoherence. At least the detector and the controller are typically external components.

[0031] In preferred embodiments, the quantum optical memristor is at least partially based on and laser written into glass, and at least the Mach-Zehnder interferometer is based on and laser written into glass, which is particularly suitable as a substrate and for laser writing, which offers a high level of reproducibility.

[0032] In another preferred embodiment, the quantum optical memristor is at least partially based on and laser written into glass, and at least the Mach-Zehnder interferometer and the parallel path are based on and laser written into glass, which is particularly suitable as a substrate and for laser writing, which provides a high level of reproducibility.

[0033] Preferably, the Mach-Zehnder interferometer comprises two beam splitters, the beam splitters being guided directional couplers, which are off-the-shelf reliable components in integrated photonics and suitable for use as beam splitters in the present application.

[0034] In the following, preferred embodiments of the quantum optical memristor and the method of manipulating optical qubits with a quantum optical memristor according to the present invention are defined together with their preferred combinations.

[0035] 1. Quantum optical memristors for manipulating photon quantum states - a Mach-Zehnder interferometer having at least a first optical input and having a first optical output and a second optical output; - a detector configured to detect a time-dependent optical signal n(t) at the second optical output of the Mach-Zehnder interferometer; - Target reflectivity R of the Mach-Zehnder interferometer target and a controller configured to calculate the first optical input and the first optical output of the Mach-Zehnder interferometer are respectively the first optical input and the first optical output of the quantum optical memristor; The controller calculates the target reflectance R target and configured to update the reflectivity R(t) of the Mach-Zehnder interferometer to match Quantum optical memristors are The controller calculates the derivative of the reflectance with respect to time.

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[0036] 2. The quantum optical memristor according to embodiment 1 is The linear function is characterized by having a negative offset proportional to the maximum expected value of the signal n(t).

[0037] 3. The quantum optical memristor according to embodiment 1 or 2 is The controller calculates the derivative of the reflectance

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[0038] 4. The quantum optical memristor according to embodiment 3 is The length T of the time frame can be configured, and preferably is configured, to be less than or equal to the modulation period of the optical input signal at the optical input of the Mach-Zehnder interferometer (2).

[0039] 5. The quantum optical memristor according to any one of the first to fourth embodiments, The signal at the detector, n(t), is characterized as being related to the number of photons detected.

[0040] 6. The quantum optical memristor according to any one of the first to fifth embodiments, A parallel path is provided having an optical input and an optical output; the optical input and the optical output of the parallel paths are a second optical input and a second optical output of the quantum optical memristor, respectively; the parallel path and the Mach-Zehnder interferometer are configured to be fed by the same photon source; The parallel paths are characterized by essentially no manipulation of the state of the photons in the parallel paths.

[0041] 7. The quantum optical memristor according to embodiment 6 is The parallel paths are configured to associate with a first spatial mode and the Mach-Zehnder interferometer is configured to associate with a second spatial mode of the qubit, wherein the qubit is encoded as a single photon that is a superposition of the first and second spatial modes.

[0042] 8. The quantum optical memristor according to any one of the first to seventh embodiments, a Mach-Zehnder interferometer comprising two beam splitters (14, 15); The beam splitter (14, 15) is characterized by having a 50 / 50 split ratio.

[0043] 9. A quantum optical memristor according to any one of the first to eighth embodiments, The quantum optical memristor is provided at least in part as part of an integrated photonic chip; At least the Mach-Zehnder interferometer is characterized as being part of an integrated photonic chip.

[0044] 10. The quantum optical memristor according to embodiment 6 or 7, The quantum optical memristor is provided at least in part as part of an integrated photonic chip; The feature is that at least the Mach-Zehnder interferometer and the parallel path are part of an integrated photonic chip.

[0045] 11. The quantum optical memristor according to embodiment 9 or 10, The quantum optical memristor is based at least in part on glass and is laser written into the glass; At least the Mach-Zehnder interferometer is characterized in that it is based on glass and is laser written into the glass.

[0046] 12. The quantum optical memristor according to embodiment 10 is The quantum optical memristor is based at least in part on glass and is laser written into the glass; At least the Mach-Zehnder interferometer and the parallel path are glass based and laser written into the glass.

[0047] 13. The quantum optical memristor according to any one of the first to twelfth embodiments, a Mach-Zehnder interferometer comprising two beam splitters (14, 15); The beam splitters (14, 15) are characterized as being guided directional couplers (17, 18).

[0048] 14. A method of manipulating optical qubits using a quantum optical memristor, comprising: Quantum optical memristors are - a Mach-Zehnder interferometer having at least a first optical input, a first optical output, and a second optical output; - a detector configured to detect a time-dependent optical signal n(t) at the second optical output of the Mach-Zehnder interferometer; - Target reflectivity R of the Mach-Zehnder interferometer target and a controller configured to calculate the first optical input and the first optical output of the Mach-Zehnder interferometer are respectively the first optical input and the first optical output of the quantum optical memristor; The controller calculates the target reflectance R target and configured to update the reflectivity R(t) of the Mach-Zehnder interferometer to match The controller calculates the derivative of the reflectance with respect to time.

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[0049] 15. The method of embodiment 14, a quantum optical memristor comprising parallel paths having optical inputs and optical outputs; the optical input and the optical output of the parallel paths are a second optical input and a second optical output of the quantum optical memristor, respectively; a first optical input and a second optical input of the quantum optical memristor are configured to be fed from the same photon source; The parallel paths do not inherently manipulate the state of the photons in the parallel paths, the parallel paths are configured to associate with a first spatial mode and the Mach-Zehnder interferometer is configured to associate with a second spatial mode of the qubit, where the qubit is encoded as a single photon that is a superposition of the first and second spatial modes; The method further comprising: - providing a quantum optical memristor with qubits encoded as photons in a superposition of first and second spatial modes.

[0050] The invention is further explained below with reference to particularly preferred examples of embodiments and to drawings, however, the invention is not intended to be limited to these embodiments. [Brief description of the drawings]

[0051] [Figure 1] 1 illustrates a schematic diagram of a quantum optical memristor according to a first embodiment; [Diagram 2] 13A illustrates a schematic diagram of a quantum optical memristor in a second embodiment with parallel paths; [Diagram 3] FIG. 3 shows a schematic of an experimental setup for manipulating single photons using a quantum optical memristor according to FIG. 2. [Figure 4] Experimental results obtained using the experimental setup of FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0052] 1 shows a quantum optical memristor 1 for manipulating photon quantum states in a first embodiment. The quantum optical memristor 1 comprises a Mach-Zehnder interferometer 2 having a first optical input 3 and a second optical input 4, and having a first optical output 5 and a second optical output 6. The first optical input 3 and the first optical output 5 of the Mach-Zehnder interferometer are respectively a first optical input 7 and a first optical output 8 of the quantum optical memristor 1. A detector 9 is configured to detect a time-dependent optical signal n(t) at the second optical output 6 of the Mach-Zehnder interferometer 2.

[0053] Furthermore, the controller 10 controls the target reflectivity R of the Mach-Zehnder interferometer 2. target The controller 10 is configured to calculate the calculated target reflectance R target The controller 10 is configured to update the reflectivity R(t) of the Mach-Zehnder interferometer 2 to match the reflectivity R(t) of the Mach-Zehnder interferometer 2. The reflectivity of the Mach-Zehnder interferometer is the probability that a photon will change paths 11, 12 in the Mach-Zehnder interferometer 2. The controller 10 therefore controls the phase difference of the paths 11, 12 and thereby the reflectivity R(t). In one of the paths 11, 12, a means for changing the phase 13 is included, e.g. a phase retarder, which is controlled by the controller 10. The controller 11 calculates the derivative of the reflectivity with respect to time,

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[0054] Derivative of reflectance with respect to time in this exemplary embodiment

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[0055] Based on the signal n(t), target To estimate , the controller 10 calculates the derivative of the reflectance

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[0056] The behavior of the quantum optical memristor is adjustable by the choice of the length T of the time frame, which is configurable. The length T is preferably equal to or smaller than the modulation or oscillation period T of the optical input signal at the optical input 7 of the Mach-Zehnder interferometer 2. oscThe integral time T is chosen to be equal to or less than n(t). If a low-pass filter, for example an RC filter, is used, the integral time T must be greater than the time constant of the filter. Depending on the relationship between the modulation period and the length T of the optical input signal, two limiting schemes are accessible. If the integral time T is small compared to the modulation period, the input may be considered to be (nearly) constant. The behavior simplifies to R(t)=n(t). In contrast, if the input oscillates very fast, such that the modulation time is small compared to the integral time T, the integral approaches zero, resulting in R(t)=0.5, resulting in a constant reflectance R of 50%. If the integral time is equal to the modulation period, the integral will be over the entire modulation period and therefore be zero. Integrating over a period longer than one therefore leads to redundant results. For this reason, the integral time is preferably less than or equal to the modulation period.

[0057] The signal n(t) at the detector 9 is related to the number of detected photons. In this case the detector is a single photon detector. The Mach-Zehnder interferometer comprises two beam splitters 14, 15, each with a 50 / 50 splitting ratio. This splitting ratio is particularly useful for controlling the reflectivity R(t).

[0058] The quantum optical memristor 1 is partially provided as part of an integrated photonic chip 16. That is, the Mach-Zehnder interferometer 2, including the beam splitters 14, 15 and the means for modifying the phase 13, such as a retarder, are part of the integrated photonic chip. The detector 9 and the controller 10 are external components. By using advanced processes and techniques known in the field of integrated photonics, the quantum optical memristor 1 can be manufactured in a reliable, stable and reproducible manner. These processes can also be scaled relatively easily, resulting in a low cost per device. Also, it is possible to realize a quantum optical memristor 1 with small dimensions and inherent compatibility with further integrated photonics components. Moreover, the relevant components of the quantum optical memristor 1 are mechanically tightly connected to each other via the integrated photonic chip 16. This prevents undesired levels of phase decoherence of the qubits, which could adversely affect the properties of the quantum optical memristor 1. In this context, a thermal phase shifter may be used as a means for modifying the phase 13. For example, the quantum optical memristor 1 may be based on glass and is laser written into the glass. The beam splitters 14, 15 are guided directional couplers 17, 18. Guided directional couplers 17, 18 are off-the-shelf reliable components in integrated photonics and are suitable for use as beam splitters 14, 15 according to the present application.

[0059] The quantum optical memristor 1 is configured to provide one or more photons to the quantum optical memristor at the optical input 7 of the quantum optical memristor 1, measure the optical signal n(t) at the detector 9, and obtain a calculated target reflectance R target This can be used to manipulate the photon quantum state by updating the reflectivity R(t) of the Mach-Zehnder interferometer 2 to match

[0060] The fabrication of integrated photonic chips may be based on femtosecond laser micromachining processes. Single-mode optical waveguides optimized for operation at 1550 nm are written in aluminoborosilicate glass (Corning EAGLE XG, 1.1 mm thick) by focusing laser pulses (Yb:KYW cavity-dumped mode-locked laser: 1030 nm wavelength, 300 fs pulse duration, 520 nJ energy per pulse, 1 MHz repetition rate) with a 50x objective lens (0.65 NA) equipped with an anomalous aberration correction collar. The entire optical circuit is written at 25 μm from the bottom surface of the substrate by translating the substrate with a uniform speed of 40 mm / s. In particular, six overlapping laser scans are performed along the desired waveguide path. To achieve single mode operation and reduce waveguide birefringence, the writing process is followed by a thermal annealing process that includes a fast rise ramp of 12°C per minute to 750°C, followed by two slower fall ramps of 12°C per hour to 630°C and 24°C per hour to 500°C. The cooling process is then completed without any controlled temperature ramps. At the end of the waveguide fabrication process, the measured insertion loss is 1.2 dB, corresponding to a transmission of 76%.

[0061] The Mach-Zehnder interferometer 2 consists of two balanced directional couplers 17, 18 (zero interaction length and coupling distance of 7.5 μm), which can be connected to the rest of the circuit by an S-shaped bent waveguide (40 mm radius of curvature) and a straight waveguide (separation p=127 μm and length L=2 mm). To ensure maximum efficiency of the phase-shifting operation and minimum crosstalk, thermal isolation trenches are formed by ablation on both sides of the optical waveguide considered to be phase-adjusted. To manufacture the trenches, laser pulses (Light Conversion PHAROS: 1030 nm wavelength, 1 picosecond pulse duration, 1.5 μJ energy per pulse, 20 kHz repetition rate) are used, which are focused by a 20× water immersion objective (0.50 NA) on the bottom side of the substrate. The latter is then translated at 4 mm per second completely immersed in distilled water. This manufacturing technique is usually called water-assisted laser ablation. Depth D t =300μm, width W t = 97 μm, and length L t Four rectangular glass blocks (depth D) were cut to realize a single trench with a depth of 0.2 mm. b =D t4 = 75 μm) are alternately removed by ablating only the periphery of each block, separating it and immersing it in water. Thus, a deep trench is produced on the bottom side of the substrate with a yield of almost 1. The substrate is then turned over and the process continues with the production of the thermal phase shifter on the bottom side. First, after a standard piranha cleaning bath, a metallic multilayer film consisting of 3 nm chromium and 100 nm gold is deposited on the entire area of ​​the chip by using a magnetron sputtering system. Secondly, to reach a stable value of the electrical resistivity and to prevent electrical drifts that would impair the stability of the phase shifter operation, a further thermal annealing (a ramp up to 500 °C with 10 °C per minute, a period of 60 minutes maintained at this temperature, followed by a cooling process without thermal operation) is used. Finally, the thermal phase shifter is patterned by laser pulses (Yb:KYW cavity-dumped mode-locked laser: 1030 nm wavelength, 300 fs pulse duration, 200 nJ energy per 669 pulses, 1 MHz repetition rate) focused on the chip surface by a 10x objective lens (0.25 NA). By translating the substrate at 2 mm / s, the contact pads and electrodes are isolated by selectively removing the metal. Instead, a thermal phase shifter with width W r =pW t = 30 μm and length L r A resistive microheater with a length of φ = L = 2 mm is isolated by the presence of a trench. The average electrical resistance of the microheater is 38 Ω, while the resulting power required to produce a phase shift of 2π is small, about 55 mW. Finally, the photonic chip is mounted on an aluminum heat sink, wire-bonded to a printed circuit board, and connected by pigtails to both input and output single-mode optical fibers. After the pigtailing process, the total insertion loss from the input to the output fiber is 2 dB, corresponding to a transmission of 63%.

[0062] FIG. 2 shows another embodiment of the quantum optical memristor 1. In addition to the embodiment shown in FIG. 1, the quantum optical memristor comprises a parallel path 19 having an optical input 20 and an optical output 21. The optical input 20 and the optical output 21 of the parallel path 19 are the second optical input 22 and the second optical output 2) of the quantum optical memristor 1, respectively. The parallel path 19 and the Mach-Zehnder interferometer 2 are configured to be fed from the same photon source, in other words, the quantum optical memristor 1 is fed from one photon source. The parallel path 1) does not inherently manipulate the state of the photons in the parallel path 19. Additional components that may change the state of the photons are not part of the parallel path 19. The parallel path 19 is configured to be associated with a first spatial mode and the Mach-Zehnder interferometer 2 is configured to be associated with a second spatial mode of the qubit, where the qubit is encoded as a single photon that is a superposition of the first and second spatial modes. Thus, the quantum optical memristor 1 is suitable for manipulating qubits that are path-encoded rather than encoded as a superposition of energy states. Path-encoded qubits are easier to handle in quantum optics compared to qubits encoded as a superposition of two energy levels. In addition to the Mach-Zehnder interferometer 2, a parallel path 19 may also be realized as part of an integrated photonic chip 16 (not shown).

[0063] FIG. 3 shows an experimental setup for manipulating single photons, including and using a quantum optical memristor 1 according to FIG. 2. A collinear type II SPDC source emits pairs of identical photons at 1550 nm. The source is based on a 30 mm PPKTP crystal 24 with a poling period of 46.2 μm adapted for downconversion from 775 to 1550 nm. The crystal is pumped by a CW amplified diode laser 25 (Toptica TA Pro 780) with a pump power of about 80 mW. The crystal is inserted into a Sagnac interferometer 26, which generates photons with polarization entanglement, although in this particular case no entanglement is used.

[0064] The optical components used to generate photons are labeled as follows: m…Mirror dm...Dichroic mirror QWP...quarter wave plate HWP…half wave plate PBS...Polarizing beam splitter PPKTB…PPKTB crystal 24 Logic: logic operation unit

[0065] One of the photons, called the idler, is sent directly to the detector 27 for prediction, and the other, called the signal, is connected to the integrated photonic chip 16 through a single mode fiber 28 directly glued to the surface of the photonic chip 16. In the photonic chip 16, the signal photons pass through a state preparation stage 29 including a Mach-Zehnder interferometer 2a with a delay 13a, and then through a quantum optical memristor 1 including a parallel path 19, so that the qubits encoded by the two rails or paths can be manipulated. Thus, there is a state tomography stage 35 including a Mach-Zehnder interferometer 2b and a delay 13b. The state tomography stage 35 is used to show that the device preserves any of the initial quantum coherences. The controller 10 is connected by a pigtail to a single mode fiber 30 attached to the detector. We use superconducting nanowire single photon detectors 9, 27, 34 (PhotonSpot Inc.), with an average detection efficiency of more than 95%. We use three detectors 27, 9, 34: one for the leading (idler) photons 27, one for the signal n(t) 9, and one for the output signal 34 of the quantum optical memristor 1.

[0066] After the detectors 9, 27, 34, a logic unit 31 analyses the signal. Each coincidence of the idler and the signal n(t) triggers the generation of a rectangular voltage pulse in the signal channel. The resulting signal is shown diagrammatically in oscilloscope 33a (lower pulse train). Similarly, each coincidence of the idler and the signal triggers a voltage pulse in the output channel (upper pulse train of oscilloscope 33a). With a pump power of about 80 mW at the source, the maximum coincidence rate in each channel is about 3×10 per second. 4 counts. Both channels are then low pass filtered using a filter 32 with RC=100 ms. This has the effect of averaging the pulse train and providing a continuous voltage signal, which is now proportional to the pulse rate and in turn to the number of photons. Measuring the output voltage of the RC filter 32 therefore constitutes a measurement of the number of photons. Note that the time constant RC should be much smaller than the integration time T. Here T=10 s is used.

[0067] At this point, the output signal goes to an oscilloscope 33b for eventual data logging, while the feedback signal goes to the controller 10, which determines n(t) and R target and updates the value of the reflectivity R(t) of the quantum optical memristor 1. The controller 10 changes the value of the reflectivity R(t) by changing the voltage applied to the thermal phase shifter of the Mach-Zehnder interferometer 2. The phase shifter generates a phase shift proportional to the power consumed.

[0068] Figure 4 shows experimental results (dots) and simulations (lines) obtained with the experimental setup shown in Figure 3. in is the signal at the input, and n out is the output signal. The oscillation period T osc is kept constant at 10 seconds, and the integration time T is one oscillation period T oscThe device does not approach the origin, but instead exhibits a hysteresis diagram that is linear at high frequencies and nonlinear at low frequencies. The high frequency limit is, in this case, T = T osc Since the experimental results provide a complete characterization of the dynamic response of the device, the experimental data are in good agreement with the simulated dynamics. In particular, in the low frequency limit n out =n in -n in 2 and the high frequency limit n out =0.5*n in is as expected. This is also consistent with the original definition of a memristive device.

Claims

1. A quantum optical memristor (1) for manipulating photon quantum states, comprising: a Mach-Zehnder interferometer (2) having at least a first optical input (3) and having a first optical output (5) and a second optical output (6); a detector (9) configured to detect a time-dependent optical signal n(t) at the second optical output (6) of said Mach-Zehnder interferometer (2); - the target reflectivity R of the Mach-Zehnder interferometer (2) ｔａｒｇｅｔ and a controller (10) configured to calculate a first optical input (3) and a first optical output (5) of the Mach-Zehnder interferometer (2) are respectively a first optical input (7) and a first optical output (8) of the quantum optical memristor (1); The controller (10) calculates the target reflectance R ｔａｒｇｅｔ configured to update the reflectivity R(t) of the Mach-Zehnder interferometer (2) to correspond to The quantum optical memristor (1) is The controller (10) calculates a derivative of the reflectance with respect to time. [0010] Based on this, the target reflectance R ｔａｒｇｅｔ configured to calculate The derivative of the reflectance with respect to time [0025] is a function of the detected signal n(t), The function includes a negative term. Quantum optical memristor (1).

2. the function is a linear function of the detected signal n(t), Quantum optical memristor (1) according to claim 1.

3. the negative term being a negative offset proportional to a maximum expected value of the signal n(t), Quantum optical memristor (1) according to claim 2.

4. The controller (10) calculates a derivative of the reflectance [0030] , and perform an integration step for the target reflectance R ｔａｒｇｅｔ The method is characterized in that the method is configured to obtain A quantum optical memristor (1) according to any one of claims 1 to 3.

5. The controller (10) performs a time window integration step over a time frame of length T to obtain a target reflectance R ｔａｒｇｅｔ The method is characterized in that the method is configured to obtain Quantum optical memristor (1) according to claim 4.

6. The length T of the time frame is configurable. Quantum optical memristor (1) according to claim 5.

7. The length T of the time frame is configured to be equal to or less than the modulation period of the optical input signal at the optical input of the Mach-Zehnder interferometer (2).

7. A quantum optical memristor (1) according to claim 6.

8. the signal n(t) at the detector (9) is related to the number of detected photons, Quantum optical memristor (1) according to claim 1.

9. A parallel path (19) is provided having an optical input (20) and an optical output (21); the optical input (20) and the optical output (21) of the parallel path (19) are respectively a second optical input (22) and a second optical output (23) of the quantum optical memristor (1); the parallel path and the Mach-Zehnder interferometer (2) are configured to be fed by the same photon source; the parallel paths (19) are characterized in that they do not essentially manipulate the state of the photons in the parallel paths (19); Quantum optical memristor (1) according to claim 1.

10. the parallel paths (19) are configured to associate with a first spatial mode and the Mach-Zehnder interferometer (2) is configured to associate with a second spatial mode of a qubit, the qubit being encoded as a single photon that is a superposition of the first and second spatial modes.

10. The quantum optical memristor (1) according to claim 9.

11. The Mach-Zehnder interferometer (2) comprises two beam splitters (14, 15); The beam splitter (14, 15) has a split ratio of 50 / 50. Quantum optical memristor (1) according to claim 1.

12. The quantum optical memristor (1) is provided at least in part as part of an integrated photonic chip (16), At least the Mach-Zehnder interferometer (2) is a part of the integrated photonic chip (16). Quantum optical memristor (1) according to claim 1 or 11.

13. The quantum optical memristor (1) is provided at least in part as part of an integrated photonic chip (16), At least the Mach-Zehnder interferometer (2) and the parallel path (19) are part of the integrated photonic chip (16). Quantum optical memristor (1) according to claim 9 or 10.

14. The quantum optical memristor (1) is at least partially based on glass and is laser written into the glass; characterised in that at least the Mach-Zehnder interferometer (2) is based on glass and is laser written into the glass, Quantum optical memristor (1) according to claim 12.

15. The quantum optical memristor (1), at least in part based on glass and laser written into the glass; characterised in that at least the Mach-Zehnder interferometer (2) is based on glass and is laser written into the glass, Quantum optical memristor (1) according to claim 13.

16. The quantum optical memristor (1) is at least partially based on glass and is laser written into the glass; characterised in that at least the Mach-Zehnder interferometer (2) and the parallel path (19) are based on glass and are laser written into the glass, Quantum optical memristor (1) according to claim 13.

17. The Mach-Zehnder interferometer (2) comprises two beam splitters (14, 15); The beam splitters (14, 15) are guided directional couplers (17, 18). Quantum optical memristor (1) according to claim 1 or 11.

18. A method for manipulating optical qubits using a quantum optical memristor (1), comprising the steps of: The quantum optical memristor (1) is a Mach-Zehnder interferometer (2) having at least a first optical input (3), a first optical output (5), and a second optical output (6); a detector (9) configured to detect a time-dependent optical signal n(t) at the second optical output (6) of said Mach-Zehnder interferometer (2); - the target reflectivity R of the Mach-Zehnder interferometer (2) ｔａｒｇｅｔ and a controller (10) configured to calculate a first optical input (3) and a first optical output (5) of the Mach-Zehnder interferometer (2) are respectively a first optical input (7) and a first optical output (8) of the quantum optical memristor (1); The controller (10) calculates the target reflectance R ｔａｒｇｅｔ configured to update the reflectivity R(t) of the Mach-Zehnder interferometer (2) to correspond to The above method is - providing one or more photons to said quantum optical memristor (1) at a first optical input (7) of said quantum optical memristor (1); - measuring the optical signal n(t) at said detector (9); - the target reflectance R calculated above ｔａｒｇｅｔ and updating the reflectivity R(t) of the Mach-Zehnder interferometer (2) so that it coincides with The target reflectance R ｔａｒｇｅｔ is the derivative of the reflectance with respect to time [0045] It is calculated based on The reflectance above [0050] is a function of the detected signal n(t), The function includes a negative term. method.

19. The quantum optical memristor (1) comprises a parallel path (19) having an optical input (20) and an optical output (21); the optical input (20) and the optical output (21) of the parallel path (19) are respectively a second optical input (22) and a second optical output (23) of the quantum optical memristor (1); a first optical input (7) and a second optical input (22) of said quantum optical memristor (1) configured to be fed from the same photon source; the parallel path (19) does not essentially manipulate the state of the photons in the parallel path (19); the parallel paths (19) are configured to associate with a first spatial mode and the Mach-Zehnder interferometer (2) is configured to associate with a second spatial mode of a qubit, the qubit being encoded as a single photon that is a superposition of the first and second spatial modes; The above method is providing said quantum optical memristor (1) with qubits encoded as photons in a superposition of said first and second spatial modes, 20. The method of claim 18.

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