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# n.quantum Computing

### n.quantum Computing

#### n.quantum Computing

**Neuromorphic Quantum Computing** (abbreviated as ‘**n.quantum computing**’) [1,2] is an unconventional computing type of computing that uses neuromorphic computing to perform quantum operations [3,4]. It was suggested that quantum algorithms, which are algorithms that run on a realistic model of quantum computation, can be computed equally efficiently with neuromorphic quantum computing [5,6,7,8,9].

Both traditional quantum computing and neuromorphic quantum computing [1] are physics-based unconventional computing approaches to computations and don’t follow the von Neumann architecture. They both construct a system (a circuit) that represents the physical problem at hand, and then leverage their respective physics properties of the system to seek the “minimum”. Neuromorphic quantum computing [1] and quantum computing share similar physical properties during computation [9,10].

**n.quantum Entanglement Effects**

Quantum computing utilise certain principles of quantum mechanics, such as entanglement, to enable their components to be interconnected over vast distances. This interconnection means that a change in one component can instantly affect others, no matter how far apart they are. This characteristic facilitates the computer's ability to swiftly determine the most energy-efficient state. Similarly, n.quantum computing exhibits a related phenomenon through long-distance connections stemming from a state known as criticality [11]. In this setup, each gate within the circuit is designed to be responsive to distant gates, creating a network where each gate can influence and be influenced by others across the system. As the circuit evolves, the connections between different gates reach a critical state, making the system prone to sudden, large-scale changes or "avalanches" triggered by minor disturbances anywhere in the circuit. These avalanches, driven by the circuit's long-range correlations, enable the system to quickly find the lowest energy state, significantly speeding up computation compared to traditional methods [9,11].

**n.quantum Tunnelling Effects**

Quantum computing also harness the principle of quantum tunnelling to find the most efficient solution. This process enables them to bypass energy barriers and access lower energy states that represent improved solutions. In contrast, n.quantum computing circuits [12] utilise the behaviour of electrical currents and voltages to expedite the transition to more favourable states. The concept of an instanton [9,11], borrowed from the study of dynamical systems, explains how these circuits navigate through energy barriers. This happens as the system encounters "saddle" points within the electrical landscape, which possess characteristics that attract the system initially but then repel it as it gets closer. This interaction results in the system being propelled away from these points at high speed, effectively allowing it to jump from one state to another across the landscape. This phenomenon [11] mirrors quantum tunnelling but occurs in the realm of voltages and currents. In neuromorphic quantum computing circuits, this behaviour emerges from the collective action of memristor based gates, which induce widespread fluctuations in voltages, thereby swiftly steering the circuit towards superior configurations.

These inherent physical mechanisms enable both, n.quantum computing circuits and quantum computing to navigate towards the best possible solution out of a vast array of potential configurations, by effectively mapping the solution into their system [9].

**Scalability & Real-World Applications**

There are currently a number of significant engineering obstacles to construct useful quantum computers capable of solving real-world problems at scale. The major challenge in quantum computing is maintaining the coherence of entangled qubits’ quantum states; they suffer from quantum decoherence and state fidelity from outside noise (vibrations, fluctuations in temperature, electromagnetic waves). To overcome noise interference, quantum computers are often isolated in large refrigerators cooled to near absolute zero (colder than outer space) to shield them and in turn, reduce errors in calculation. Although there are error-correcting techniques being deployed, there are currently no existing quantum computers capable of maintaining the full coherence required to solve industrial-sized problems at scale today. Therefore, they are mostly limited to solving toy-sized problems. In contrast to quantum computing, n.quantum computing possesses the capability to be efficiently emulated on contemporary computers through software, as well as to be physically constructed using conventional electrical components. Quantum algorithms can be computed efficiently with n.quantum computing at scale, potentially solving real-world problems [9,11].

##### EU Horizon 2020 Project “Neuromorphic Quantum Computing”

The European Union-funded project "Neuromorphic Quantum Computing" [2] resulted in the publication of eighteen peer-reviewed articles. Its objective was to introduce hardware inspired by the human brain with quantum functionalities. The project aimed to construct superconducting quantum neural networks to facilitate the creation of dedicated neuromorphic quantum machine learning hardware, which could potentially outperform traditional von Neumann architectures in future generations. This achievement represented the merger of two forefront developments in information processing: machine learning and quantum computing, into a novel technology. Contrary to conventional machine learning techniques that simulate neural functions in software on von Neumann hardware, neuromorphic quantum hardware was projected to provide a significant advantage by enabling parallel training on various batches of real-world data. This feature was anticipated to confer a quantum benefit. Neuromorphic hardware architectures were seen as critically important for both classical and quantum computing, especially for distributed and embedded computing tasks where the extensive scaling of current architectures could not offer a sustainable solution.

> Medium: Benchmarking the Dynex Neuromorphic Platform with the Q-Score

**References:**

[1] Pehle, Christian; Wetterich, Christof (2021-03-30), *Neuromorphic quantum computing*, arXiv:2005.01533

[2] "Neuromrophic Quantum Computing | Quromorphic Project | Fact Sheet | H2020". *CORDIS | European Commission*. doi:10.3030/828826. Retrieved 2024-03-18

[3] Wetterich, C. (2019-11-01). "Quantum computing with classical bits". *Nuclear Physics B*. **948**: 114776. arXiv:1806.05960. Bibcode:2019NuPhB.94814776W. doi:10.1016/j.nuclphysb.2019.114776. ISSN 0550-3213

[4] Pehle, Christian; Meier, Karlheinz; Oberthaler, Markus; Wetterich, Christof (2018-10-24), *Emulating quantum computation with artificial neural networks*, arXiv:1810.10335

[5] Carleo, Giuseppe; Troyer, Matthias (2017-02-10). "Solving the quantum many-body problem with artificial neural networks". *Science*. **355** (6325): 602–606. arXiv:1606.02318. Bibcode:2017Sci...355..602C. doi:10.1126/science.aag2302. ISSN 0036-8075. PMID 28183973

[6] Torlai, Giacomo; Mazzola, Guglielmo; Carrasquilla, Juan; Troyer, Matthias; Melko, Roger; Carleo, Giuseppe (2018-02-26). "Neural-network quantum state tomography". *Nature Physics*. **14** (5): 447–450. arXiv:1703.05334. Bibcode:2018NatPh..14..447T. doi:10.1038/s41567-018-0048-5. ISSN 1745-2481

[7] Sharir, Or; Levine, Yoav; Wies, Noam; Carleo, Giuseppe; Shashua, Amnon (2020-01-16). "Deep Autoregressive Models for the Efficient Variational Simulation of Many-Body Quantum Systems". *Physical Review Letters*. **124** (2): 020503. arXiv:1902.04057. Bibcode:2020PhRvL.124b0503S. doi:10.1103/PhysRevLett.124.020503. PMID 32004039

[8] Broughton, Michael; Verdon, Guillaume; McCourt, Trevor; Martinez, Antonio J.; Yoo, Jae Hyeon; Isakov, Sergei V.; Massey, Philip; Halavati, Ramin; Niu, Murphy Yuezhen (2021-08-26), *TensorFlow Quantum: A Software Framework for Quantum Machine Learning*, arXiv:2003.02989

[9] Broughton, Michael; Verdon, Guillaume; McCourt, Trevor; Martinez, Antonio J.; Yoo, Jae Hyeon; Isakov, Sergei V.; Massey, Philip; Halavati, Ramin; Niu, Murphy Yuezhen (2021-08-26), *TensorFlow Quantum: A Software Framework for Quantum Machine Learning*, arXiv:2003.02989

[10] Wilkinson, Samuel A.; Hartmann, Michael J. (2020-06-08). "Superconducting quantum many-body circuits for quantum simulation and computing". *Applied Physics Letters*. **116** (23). arXiv:2003.08838. Bibcode:2020ApPhL.116w0501W. doi:10.1063/5.0008202. ISSN 0003-6951

[11] Di Ventra, Massimiliano; Traversa, Fabio L.; Ovchinnikov, Igor V. (2017-08-07). "Topological Field Theory and Computing with Instantons". *Annalen der Physik*. **529** (12). arXiv:1609.03230. Bibcode:2017AnP...52900123D. doi:10.1002/andp.201700123. ISSN 0003-3804

[12] Gonzalez-Raya, Tasio; Lukens, Joseph M.; Céleri, Lucas C.; Sanz, Mikel (2020-02-14). "Quantum Memristors in Frequency-Entangled Optical Fields". *Materials*. **13** (4): 864. arXiv:1912.10019. Bibcode:2020Mate...13..864G. doi:10.3390/ma13040864. ISSN 1996-1944. PMC 7079656. PMID 32074986

**Neuromorphic Quantum Computing** (abbreviated as ‘**n.quantum computing**’) [1,2] is an unconventional computing type of computing that uses neuromorphic computing to perform quantum operations [3,4]. It was suggested that quantum algorithms, which are algorithms that run on a realistic model of quantum computation, can be computed equally efficiently with neuromorphic quantum computing [5,6,7,8,9].

Both traditional quantum computing and neuromorphic quantum computing [1] are physics-based unconventional computing approaches to computations and don’t follow the von Neumann architecture. They both construct a system (a circuit) that represents the physical problem at hand, and then leverage their respective physics properties of the system to seek the “minimum”. Neuromorphic quantum computing [1] and quantum computing share similar physical properties during computation [9,10].

**n.quantum Entanglement Effects**

Quantum computing utilise certain principles of quantum mechanics, such as entanglement, to enable their components to be interconnected over vast distances. This interconnection means that a change in one component can instantly affect others, no matter how far apart they are. This characteristic facilitates the computer's ability to swiftly determine the most energy-efficient state. Similarly, n.quantum computing exhibits a related phenomenon through long-distance connections stemming from a state known as criticality [11]. In this setup, each gate within the circuit is designed to be responsive to distant gates, creating a network where each gate can influence and be influenced by others across the system. As the circuit evolves, the connections between different gates reach a critical state, making the system prone to sudden, large-scale changes or "avalanches" triggered by minor disturbances anywhere in the circuit. These avalanches, driven by the circuit's long-range correlations, enable the system to quickly find the lowest energy state, significantly speeding up computation compared to traditional methods [9,11].

**n.quantum Tunnelling Effects**

Quantum computing also harness the principle of quantum tunnelling to find the most efficient solution. This process enables them to bypass energy barriers and access lower energy states that represent improved solutions. In contrast, n.quantum computing circuits [12] utilise the behaviour of electrical currents and voltages to expedite the transition to more favourable states. The concept of an instanton [9,11], borrowed from the study of dynamical systems, explains how these circuits navigate through energy barriers. This happens as the system encounters "saddle" points within the electrical landscape, which possess characteristics that attract the system initially but then repel it as it gets closer. This interaction results in the system being propelled away from these points at high speed, effectively allowing it to jump from one state to another across the landscape. This phenomenon [11] mirrors quantum tunnelling but occurs in the realm of voltages and currents. In neuromorphic quantum computing circuits, this behaviour emerges from the collective action of memristor based gates, which induce widespread fluctuations in voltages, thereby swiftly steering the circuit towards superior configurations.

These inherent physical mechanisms enable both, n.quantum computing circuits and quantum computing to navigate towards the best possible solution out of a vast array of potential configurations, by effectively mapping the solution into their system [9].

**Scalability & Real-World Applications**

There are currently a number of significant engineering obstacles to construct useful quantum computers capable of solving real-world problems at scale. The major challenge in quantum computing is maintaining the coherence of entangled qubits’ quantum states; they suffer from quantum decoherence and state fidelity from outside noise (vibrations, fluctuations in temperature, electromagnetic waves). To overcome noise interference, quantum computers are often isolated in large refrigerators cooled to near absolute zero (colder than outer space) to shield them and in turn, reduce errors in calculation. Although there are error-correcting techniques being deployed, there are currently no existing quantum computers capable of maintaining the full coherence required to solve industrial-sized problems at scale today. Therefore, they are mostly limited to solving toy-sized problems. In contrast to quantum computing, n.quantum computing possesses the capability to be efficiently emulated on contemporary computers through software, as well as to be physically constructed using conventional electrical components. Quantum algorithms can be computed efficiently with n.quantum computing at scale, potentially solving real-world problems [9,11].

##### EU Horizon 2020 Project “Neuromorphic Quantum Computing”

The European Union-funded project "Neuromorphic Quantum Computing" [2] resulted in the publication of eighteen peer-reviewed articles. Its objective was to introduce hardware inspired by the human brain with quantum functionalities. The project aimed to construct superconducting quantum neural networks to facilitate the creation of dedicated neuromorphic quantum machine learning hardware, which could potentially outperform traditional von Neumann architectures in future generations. This achievement represented the merger of two forefront developments in information processing: machine learning and quantum computing, into a novel technology. Contrary to conventional machine learning techniques that simulate neural functions in software on von Neumann hardware, neuromorphic quantum hardware was projected to provide a significant advantage by enabling parallel training on various batches of real-world data. This feature was anticipated to confer a quantum benefit. Neuromorphic hardware architectures were seen as critically important for both classical and quantum computing, especially for distributed and embedded computing tasks where the extensive scaling of current architectures could not offer a sustainable solution.

> Medium: Benchmarking the Dynex Neuromorphic Platform with the Q-Score

**References:**

[1] Pehle, Christian; Wetterich, Christof (2021-03-30), *Neuromorphic quantum computing*, arXiv:2005.01533

[2] "Neuromrophic Quantum Computing | Quromorphic Project | Fact Sheet | H2020". *CORDIS | European Commission*. doi:10.3030/828826. Retrieved 2024-03-18

[3] Wetterich, C. (2019-11-01). "Quantum computing with classical bits". *Nuclear Physics B*. **948**: 114776. arXiv:1806.05960. Bibcode:2019NuPhB.94814776W. doi:10.1016/j.nuclphysb.2019.114776. ISSN 0550-3213

[4] Pehle, Christian; Meier, Karlheinz; Oberthaler, Markus; Wetterich, Christof (2018-10-24), *Emulating quantum computation with artificial neural networks*, arXiv:1810.10335

[5] Carleo, Giuseppe; Troyer, Matthias (2017-02-10). "Solving the quantum many-body problem with artificial neural networks". *Science*. **355** (6325): 602–606. arXiv:1606.02318. Bibcode:2017Sci...355..602C. doi:10.1126/science.aag2302. ISSN 0036-8075. PMID 28183973

[6] Torlai, Giacomo; Mazzola, Guglielmo; Carrasquilla, Juan; Troyer, Matthias; Melko, Roger; Carleo, Giuseppe (2018-02-26). "Neural-network quantum state tomography". *Nature Physics*. **14** (5): 447–450. arXiv:1703.05334. Bibcode:2018NatPh..14..447T. doi:10.1038/s41567-018-0048-5. ISSN 1745-2481

[7] Sharir, Or; Levine, Yoav; Wies, Noam; Carleo, Giuseppe; Shashua, Amnon (2020-01-16). "Deep Autoregressive Models for the Efficient Variational Simulation of Many-Body Quantum Systems". *Physical Review Letters*. **124** (2): 020503. arXiv:1902.04057. Bibcode:2020PhRvL.124b0503S. doi:10.1103/PhysRevLett.124.020503. PMID 32004039

[8] Broughton, Michael; Verdon, Guillaume; McCourt, Trevor; Martinez, Antonio J.; Yoo, Jae Hyeon; Isakov, Sergei V.; Massey, Philip; Halavati, Ramin; Niu, Murphy Yuezhen (2021-08-26), *TensorFlow Quantum: A Software Framework for Quantum Machine Learning*, arXiv:2003.02989

[9] Broughton, Michael; Verdon, Guillaume; McCourt, Trevor; Martinez, Antonio J.; Yoo, Jae Hyeon; Isakov, Sergei V.; Massey, Philip; Halavati, Ramin; Niu, Murphy Yuezhen (2021-08-26), *TensorFlow Quantum: A Software Framework for Quantum Machine Learning*, arXiv:2003.02989

[10] Wilkinson, Samuel A.; Hartmann, Michael J. (2020-06-08). "Superconducting quantum many-body circuits for quantum simulation and computing". *Applied Physics Letters*. **116** (23). arXiv:2003.08838. Bibcode:2020ApPhL.116w0501W. doi:10.1063/5.0008202. ISSN 0003-6951

[11] Di Ventra, Massimiliano; Traversa, Fabio L.; Ovchinnikov, Igor V. (2017-08-07). "Topological Field Theory and Computing with Instantons". *Annalen der Physik*. **529** (12). arXiv:1609.03230. Bibcode:2017AnP...52900123D. doi:10.1002/andp.201700123. ISSN 0003-3804

[12] Gonzalez-Raya, Tasio; Lukens, Joseph M.; Céleri, Lucas C.; Sanz, Mikel (2020-02-14). "Quantum Memristors in Frequency-Entangled Optical Fields". *Materials*. **13** (4): 864. arXiv:1912.10019. Bibcode:2020Mate...13..864G. doi:10.3390/ma13040864. ISSN 1996-1944. PMC 7079656. PMID 32074986

**Neuromorphic Quantum Computing** (abbreviated as ‘**n.quantum computing**’) [1,2] is an unconventional computing type of computing that uses neuromorphic computing to perform quantum operations [3,4]. It was suggested that quantum algorithms, which are algorithms that run on a realistic model of quantum computation, can be computed equally efficiently with neuromorphic quantum computing [5,6,7,8,9].

Both traditional quantum computing and neuromorphic quantum computing [1] are physics-based unconventional computing approaches to computations and don’t follow the von Neumann architecture. They both construct a system (a circuit) that represents the physical problem at hand, and then leverage their respective physics properties of the system to seek the “minimum”. Neuromorphic quantum computing [1] and quantum computing share similar physical properties during computation [9,10].

**n.quantum Entanglement Effects**

Quantum computing utilise certain principles of quantum mechanics, such as entanglement, to enable their components to be interconnected over vast distances. This interconnection means that a change in one component can instantly affect others, no matter how far apart they are. This characteristic facilitates the computer's ability to swiftly determine the most energy-efficient state. Similarly, n.quantum computing exhibits a related phenomenon through long-distance connections stemming from a state known as criticality [11]. In this setup, each gate within the circuit is designed to be responsive to distant gates, creating a network where each gate can influence and be influenced by others across the system. As the circuit evolves, the connections between different gates reach a critical state, making the system prone to sudden, large-scale changes or "avalanches" triggered by minor disturbances anywhere in the circuit. These avalanches, driven by the circuit's long-range correlations, enable the system to quickly find the lowest energy state, significantly speeding up computation compared to traditional methods [9,11].

**n.quantum Tunnelling Effects**

Quantum computing also harness the principle of quantum tunnelling to find the most efficient solution. This process enables them to bypass energy barriers and access lower energy states that represent improved solutions. In contrast, n.quantum computing circuits [12] utilise the behaviour of electrical currents and voltages to expedite the transition to more favourable states. The concept of an instanton [9,11], borrowed from the study of dynamical systems, explains how these circuits navigate through energy barriers. This happens as the system encounters "saddle" points within the electrical landscape, which possess characteristics that attract the system initially but then repel it as it gets closer. This interaction results in the system being propelled away from these points at high speed, effectively allowing it to jump from one state to another across the landscape. This phenomenon [11] mirrors quantum tunnelling but occurs in the realm of voltages and currents. In neuromorphic quantum computing circuits, this behaviour emerges from the collective action of memristor based gates, which induce widespread fluctuations in voltages, thereby swiftly steering the circuit towards superior configurations.

These inherent physical mechanisms enable both, n.quantum computing circuits and quantum computing to navigate towards the best possible solution out of a vast array of potential configurations, by effectively mapping the solution into their system [9].

**Scalability & Real-World Applications**

There are currently a number of significant engineering obstacles to construct useful quantum computers capable of solving real-world problems at scale. The major challenge in quantum computing is maintaining the coherence of entangled qubits’ quantum states; they suffer from quantum decoherence and state fidelity from outside noise (vibrations, fluctuations in temperature, electromagnetic waves). To overcome noise interference, quantum computers are often isolated in large refrigerators cooled to near absolute zero (colder than outer space) to shield them and in turn, reduce errors in calculation. Although there are error-correcting techniques being deployed, there are currently no existing quantum computers capable of maintaining the full coherence required to solve industrial-sized problems at scale today. Therefore, they are mostly limited to solving toy-sized problems. In contrast to quantum computing, n.quantum computing possesses the capability to be efficiently emulated on contemporary computers through software, as well as to be physically constructed using conventional electrical components. Quantum algorithms can be computed efficiently with n.quantum computing at scale, potentially solving real-world problems [9,11].

##### EU Horizon 2020 Project “Neuromorphic Quantum Computing”

The European Union-funded project "Neuromorphic Quantum Computing" [2] resulted in the publication of eighteen peer-reviewed articles. Its objective was to introduce hardware inspired by the human brain with quantum functionalities. The project aimed to construct superconducting quantum neural networks to facilitate the creation of dedicated neuromorphic quantum machine learning hardware, which could potentially outperform traditional von Neumann architectures in future generations. This achievement represented the merger of two forefront developments in information processing: machine learning and quantum computing, into a novel technology. Contrary to conventional machine learning techniques that simulate neural functions in software on von Neumann hardware, neuromorphic quantum hardware was projected to provide a significant advantage by enabling parallel training on various batches of real-world data. This feature was anticipated to confer a quantum benefit. Neuromorphic hardware architectures were seen as critically important for both classical and quantum computing, especially for distributed and embedded computing tasks where the extensive scaling of current architectures could not offer a sustainable solution.

> Medium: Benchmarking the Dynex Neuromorphic Platform with the Q-Score

**References:**

[1] Pehle, Christian; Wetterich, Christof (2021-03-30), *Neuromorphic quantum computing*, arXiv:2005.01533

[2] "Neuromrophic Quantum Computing | Quromorphic Project | Fact Sheet | H2020". *CORDIS | European Commission*. doi:10.3030/828826. Retrieved 2024-03-18

[3] Wetterich, C. (2019-11-01). "Quantum computing with classical bits". *Nuclear Physics B*. **948**: 114776. arXiv:1806.05960. Bibcode:2019NuPhB.94814776W. doi:10.1016/j.nuclphysb.2019.114776. ISSN 0550-3213

[4] Pehle, Christian; Meier, Karlheinz; Oberthaler, Markus; Wetterich, Christof (2018-10-24), *Emulating quantum computation with artificial neural networks*, arXiv:1810.10335

[5] Carleo, Giuseppe; Troyer, Matthias (2017-02-10). "Solving the quantum many-body problem with artificial neural networks". *Science*. **355** (6325): 602–606. arXiv:1606.02318. Bibcode:2017Sci...355..602C. doi:10.1126/science.aag2302. ISSN 0036-8075. PMID 28183973

[6] Torlai, Giacomo; Mazzola, Guglielmo; Carrasquilla, Juan; Troyer, Matthias; Melko, Roger; Carleo, Giuseppe (2018-02-26). "Neural-network quantum state tomography". *Nature Physics*. **14** (5): 447–450. arXiv:1703.05334. Bibcode:2018NatPh..14..447T. doi:10.1038/s41567-018-0048-5. ISSN 1745-2481

[7] Sharir, Or; Levine, Yoav; Wies, Noam; Carleo, Giuseppe; Shashua, Amnon (2020-01-16). "Deep Autoregressive Models for the Efficient Variational Simulation of Many-Body Quantum Systems". *Physical Review Letters*. **124** (2): 020503. arXiv:1902.04057. Bibcode:2020PhRvL.124b0503S. doi:10.1103/PhysRevLett.124.020503. PMID 32004039

[8] Broughton, Michael; Verdon, Guillaume; McCourt, Trevor; Martinez, Antonio J.; Yoo, Jae Hyeon; Isakov, Sergei V.; Massey, Philip; Halavati, Ramin; Niu, Murphy Yuezhen (2021-08-26), *TensorFlow Quantum: A Software Framework for Quantum Machine Learning*, arXiv:2003.02989

[9] Broughton, Michael; Verdon, Guillaume; McCourt, Trevor; Martinez, Antonio J.; Yoo, Jae Hyeon; Isakov, Sergei V.; Massey, Philip; Halavati, Ramin; Niu, Murphy Yuezhen (2021-08-26), *TensorFlow Quantum: A Software Framework for Quantum Machine Learning*, arXiv:2003.02989

[10] Wilkinson, Samuel A.; Hartmann, Michael J. (2020-06-08). "Superconducting quantum many-body circuits for quantum simulation and computing". *Applied Physics Letters*. **116** (23). arXiv:2003.08838. Bibcode:2020ApPhL.116w0501W. doi:10.1063/5.0008202. ISSN 0003-6951

[11] Di Ventra, Massimiliano; Traversa, Fabio L.; Ovchinnikov, Igor V. (2017-08-07). "Topological Field Theory and Computing with Instantons". *Annalen der Physik*. **529** (12). arXiv:1609.03230. Bibcode:2017AnP...52900123D. doi:10.1002/andp.201700123. ISSN 0003-3804

[12] Gonzalez-Raya, Tasio; Lukens, Joseph M.; Céleri, Lucas C.; Sanz, Mikel (2020-02-14). "Quantum Memristors in Frequency-Entangled Optical Fields". *Materials*. **13** (4): 864. arXiv:1912.10019. Bibcode:2020Mate...13..864G. doi:10.3390/ma13040864. ISSN 1996-1944. PMC 7079656. PMID 32074986