Method and apparatus for use in quantum processing

Abstract

A frequency-tunable coupler (130) couples first and second quantum systems (110, 120), the coupler (130) and the second quantum system (120) being arranged so that tuning the coupler (130) to the second quantum system (120) forms a hybridized mode with a symmetric state and an asymmetric state, coupled to a waveguide (140) The coupler (130) is driven with an excitation-preserving transition signal to transfer a first excited state of the first quantum system (110) to the asymmetric state of the hybridized mode, thereby emitting a photon encoded with a first part of a quantum state into the waveguide at a first frequency. The first quantum system (110) is simultaneously driven with a non-excitation-preserving transition signal to transfer a second excited state of the first quantum system (110) to the symmetric state of the hybridized mode, thereby emitting a second photon encoded with a second part of the quantum state, at a second frequency.

Description

[0001] METHOD AND APPARATUS FOR USE IN QUANTUM PROCESSING

[0002] TECHNICAL FIELD

[0003] The present disclosure is generally related to quantum processing and is more particularly related to methods and apparatus for use in a quantum processing unit, QPU. A related quantum-processing system is also disclosed.

[0004] BACKGROUND

[0005] Quantum computing emerges as a promising approach to enhance telecommunications networks, offering potential computational advantages based on the quantum mechanics principles of superposition and entanglement. These networks are evolving to support applications requiring low latency, such as augmented reality and cloud gaming, through intelligent platforms that utilize heterogeneous compute accelerators across the edge-to-cloud continuum. To meet the diverse needs of future applications, metrics like solution speed and quality are critical. Quantum computers are expected to address several telecom-related challenges, including Fourier transform computation, maximum likelihood-based soft MIMO detection, and efficient offloading of tasks to edge servers and micro base stations to improve service quality within macro cell coverage areas.

[0006] In the noisy intermediate-scale quantum (NISQ) era, quantum computers have limited number of qubits and are exposed to noise and errors. To solve this problem, quantum processors need to be scaled up. Aside from the traditional approach of simply building quantum chips that can each handle more and more qubits, another approach is to use a multi-QPU architecture, which can run a larger task on several quantum processors, in a cooperative way.

[0007] To implement multi-QPU architecture, quantum channels between the remotely distributed quantum processors are needed. These can be based on travelling photons, where a photon carrying quantum information is emitted by the sender processor, travels through the quantum channel, and is re-absorbed by the receiver processor. This process enables quantum state transfer and the building of remote entanglement between the qubits of both circuits.

[0008] A quantum information channel for sharing quantum information between spatially separated quantum processing units (QPUs) can be implemented, for example, by emitting a microwave photon from a sender processor into a microwave waveguide and absorbing it, at the other end of the waveguide, in a receiver processor. For this purpose, deterministically encoding the state of a stationary qubit into a travelling photon so that the quantum state can be reliably transferred to the receiver is of great interest. The transfer of quantum state via microwave photons transmitted through a microwave waveguide has been described, for example, by P. Kurpiers et al., “Deterministic quantum state transfer and remote entanglement using microwave photons,” Nature 558, 264 (2018) (hereinafter, “Kurpiers 2018”). In this example, first and second quantum nodes are coupled, respectively, to each end of a coaxial waveguide. Each quantum node includes a superconducting transmon qubit, coupled to one microwave resonator configured for qubit readout and another resonator configured for excitation transfer of photons to / from the coaxial waveguide. At one node, a cavity-assisted Raman process is used to transfer the qubit state of the transmon to a time-symmetric microwave photon emitted into the coaxial waveguide. The reverse process is then used to absorb the photon at the other node, resulting in a transfer of the qubit’s quantum state through the quantum channel to a receiver.

[0009] Previous work by the present inventors demonstrated a waveguide-quantum electrodynamics (QED) framework as a structure to implement emission of quantum-encoded photons into a waveguide. Yang, Jiaying, et al. "Deterministic generation of shaped single microwave photons using a parametrically driven coupler," arXiv preprint arXiv:2303.02899 (2023) (hereinafter “Yang 2023”).

[0010] During the transmission of the microwave photon in a quantum channel, there is a risk of photon loss due to the noise in the environment. In this scenario, quantum error detection techniques that allow monitoring for photon loss at the receiving end of the quantum channel while not disturbing the transmitted quantum state are needed. This has been previously addressed by literature that describes the encoding of quantum information into two photons that are emitted at different times, i.e., in different time bins. These techniques, described in Kurpiers, Philipp, et al. "Quantum communication with time-bin encoded microwave photons,” Physical Review Applied 12.4 (2019): 044067 (hereinafter “Kurpiers 2019”), and Ilves, Jesper, et al. "On-demand generation and characterization of a microwave time-bin qubit," npj Quantum Information 6.1 (2020): 34 (hereinafter “Ilves 2020”), may be used to implement an error detection protocol for quantum communication.

[0011] Hsuan-Hao Lu, Marco Liscidini, Alexander L. Gaeta, Andrew M. Weiner, and Joseph M. Lukens, "Frequency-bin photonic quantum information," Optica 10, 1655-1671 (2023) describes frequency-bin state generation techniques based on spontaneous parametric down conversion (SPDC) and spontaneous four-wave mixing (SFWM) methods that lead to optical photons. Improved structures and techniques for transferring quantum states through a channel while providing for error detection are needed.

[0012] SUMMARY

[0013] An object of the invention disclosed herein is to provide a more hardware-resource-efficient apparatus and method for generating frequency-bin encoded photons for the communication of quantum information. Methods described herein thus provide for the generating of frequencybin encoded photons using a waveguide QED structure, by driving superconducting qubits. The generated frequency-bin photons can carry “error-detectable” quantum information between two processors. The apparatus described herein uses the same superconducting qubit hardware modality as is used for computing qubits, enabling resource-efficient multi-chip quantum computing. The same hardware may be used for photon emission with or without an error detection protocol.

[0014] The techniques described herein are based on waveguide quantum electrodynamics and provide for the emission of photons where the transmitted quantum information is encoded into a pair of frequency bins, which may be regarded as simultaneously emitted photonic modes at two different frequencies . These generated frequency-bin photons allow for error detection at a receiving device, to deal with photon loss problems when transmitting microwave photons carrying quantum state between remotely distributed quantum processors. As detailed below, in the event of photon loss, the qubit at the receiving processor transitions to a distinguishable state, allowing for immediate detection of the photon loss.

[0015] Compared to time-bin encoding, the frequency-bin encoded photons described herein are emitted at the same time but at different frequencies, which makes the data rate twice as fast. Moreover, the techniques use a simple hardware structure that does not need any extra qubits compared to the single-photon emitting structure described in the inventors’ previous work referenced above (Yang 2023).

[0016] Embodiments of the apparatuses described herein transmit frequency-encode emitted photons using a frequency-tunable coupler coupling first and second quantum systems, the coupler and the second quantum system being arranged so that tuning the coupler to the second quantum system forms a hybridized mode with a symmetric state and an asymmetric state, coupled to a waveguide. The coupler is driven with an excitation-preserving transition signal to transfer a first excited state of the first quantum system to the asymmetric state of the hybridized mode, causing emission of a photon encoded with a first part of a quantum state into the waveguide at a first frequency. The first quantum system is simultaneously driven with a non-excitation- preserving transition signal to transfer a second excited state of the first quantum system to the symmetric state of the hybridized mode, causing emission of a second photon encoded with a second part of the quantum state at a second frequency.

[0017] More particularly, an example apparatus for use in a quantum processing unit, QPU, comprises a first quantum system and a second quantum system, which may be first and second superconducting transmons, respectively. The apparatus further comprises a waveguide system coupled to the second quantum system and arranged to receive quantum-encoded photons emitted from the second quantum system and a frequency-tunable coupler coupling the first quantum system to the second quantum system. The frequency-tunable coupler and the second quantum system are arranged so that tuning the frequency-tunable coupler to a resonant frequency of the second quantum system forms a hybridized mode with a symmetric state and an asymmetric state, each coupled to the waveguide system. The apparatus still further comprises first driver circuitry connected to the frequency-tunable coupler and configured to drive the frequency-tunable coupler with an excitation-preserving transition signal configured to transfer a first excited state of the first quantum system to the asymmetric state of the hybridized mode, causing an emission of a first photon encoded with a first part of a quantum state into the waveguide system at a first frequency, as well as second driver circuitry connected to the first quantum system and configured to drive the first quantum system with a non-excitation-preserving transition signal configured to transfer a second excited state of the first quantum system to the symmetric state of the hybridized mode, causing an emission of a second photon encoded with a second part of the quantum state into the waveguide system at a second frequency. The first driver circuitry and second driver circuitry are configured to drive the frequency-tunable coupler and the first quantum system substantially simultaneously, so that the emissions of the first and second photons are substantially simultaneous.

[0018] BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 is a schematic of a frequency-bin state generation system.

[0020] Figure 2 is another schematic of a frequency-bin state generation system.

[0021] Figure 3 shows the encoding of an arbitrary superposition state onto a pair of photonic modes emitted at two different frequencies. Figure 4 illustrates an example apparatus for frequency-bin encoding of a quantum state, accordingto some embodiments.

[0022] Figure 5A and Figure 5B show two techniques for transferring a state of a qubit into an emitted photon state.

[0023] Figure 6 shows an example of frequency-bin encoding using duplicated hardware.

[0024] Figure 7 shows an example of frequency-bin encoding according to techniques disclosed herein.

[0025] Figure 8 illustrates the hybridized mode formed by tuning a frequency-tunable coupler to the emitter qubit, in an example apparatus.

[0026] Figure 9 shows energy transitions for a process for transferring a single qubit state into frequency-bin encoded photons.

[0027] Figure 10 shows the state of the qubit in a receiver for fr the events of a lost photon and successful photon reception.

[0028] Figure 11 illustrates details of an example apparatus accordingto some embodiments.

[0029] Figure 12 is a process flow diagram illustrating an example method accordingto some embodiments.

[0030] DETAILED DESCRIPTION

[0031] The term “qubit,” in its formal sense, refers to a unit of quantum information, which may be embodied in a particle such as a photon, electron, or atom, where the particle may be manipulated so that it has one of two quantum states. The term may also be used, in a less formal sense, to refer to a physical structure that can store the unit of quantum information, or that can be used to create the desired quantum state.

[0032] In this document, the term “quantum system” is used to refer to a quantum-mechanical system, i.e., to a physical structure, that can store a qubit or that can be used to create a qubit. The quantum system may be manipulated to exist in a quantum superposition of states 0 and 1 , for example, using a property of the quantum system such as a polarization degree of freedom or spin. Thus, the quantum system may register a quantum bit such as a qubit. In general, a quantum system may store or be used to create one qubit or several qubits, or one or several of other units of quantum information. The specific examples described herein each correspond to a single qubit, for simplicity, but it should be understood that the techniques described herein may be extended to systems with multiple qubits.

[0033] Importantly, however, the term “qubit” may also be used herein in its less formal sense to refer to a quantum system, i.e. , to a physical structure in which a qubit is stored or created. Thus, the term “qubit” may be used herein to refer to a unit of quantum information in the abstract or to refer to a physical structure in which a qubit may be realized or stored. The context of each usage should make clear which meaning is intended.

[0034] When encoding a single particle, such as a photon, with a qubit and transmitting the particle through a quantum channel, there is a risk of particle loss during its transfer through the quantum channel, due to the noise in the environment. The time-bin encoding protocol described in previous work can be used to provide an error-detection code that overcomes this problem. As discussed in that work, if the time-bin encoded photon is lost, the loss can be detected at the receiver by measuring a state that is distinguishable from either of the two possible states of the qubit that was transmitted, without actually measuring (and thus destroying) the transmitted state. If photon loss is detected, the encoded time-bin photon can be transmitted again. However, due to the sequential emission of the time-bin encoded photon in an early time-bin and a late time-bin, the time needed for photon emission is doubled and the photon emission rate for a given apparatus is half of what it would be without the time-bin encoding.

[0035] A possible alternative to time-bin encoding is frequency-bin encoding, where quantum- encoded photons are transmitted using two different frequencies, i.e., in different frequency bins, rather than at two different times. As briefly discussed above, some methods for frequency-bin state generation are based on SPDC and SFWM. These methods provide optical photon generation that is not compatible with superconducting qubits. None of them can directly take a state from a superconducting quantum processor. Consequently, these techniques require additional hardware setup for generation, swap operations and / or frequency transducers to realize a multi-chip quantum computing system for scaling data-centric superconducting quantum computing.

[0036] The techniques described herein, on the other hand, include methods to generate frequencybin encoded photons using a waveguide QED structure, by driving superconducting qubits. The generated frequency-bin photons can convey “error-detectable” quantum information between two processors. The apparatuses described herein use the same superconducting qubit hardware modality as is used for computing qubits, enabling resource-efficient multi-chip quantum computing.

[0037] The techniques described herein are based on waveguide quantum electrodynamics and provide for the emission of quantum-state-encoded photons using two different frequencies, simultaneously. These generated frequency-bin-encoded photons allow for error detection at a receiving device, to deal with photon loss problems when transmitting microwave photons carrying quantum state between remotely distributed quantum processors. As detailed below, in the event of photon loss, the qubit at the receiving processor transitions to a distinguishable state, allowing for immediate detection of the photon loss. Compared to time-bin encoding, the frequency-bin encoded photons described herein are emitted using a single time interval but at different frequencies, which makes the data rate twice as fast. Moreover, the techniques use a simple hardware structure that does not need any extra qubits compared to the single-photon emitting structure described in the inventors’ previous work referenced above (Yang 2023).

[0038] As will be shown in further detail below, embodiments of the apparatuses described herein frequency-encode emitted photons using a frequency-tunable coupler coupling first and second quantum systems, the coupler and the second quantum system being arranged so that tuning the coupler to the second quantum system forms a hybridized mode with a symmetric state and an asymmetric state, coupled to a waveguide. The coupler is driven with an excitationpreservingtransition signal to transfer a first excited state of the first quantum system to the asymmetric state of the hybridized mode, causing emission of a photon encoded with a first part of a quantum state into the waveguide at a first frequency. The first quantum system is simultaneously driven with a non-excitation-preserving transition signal to transfer a second excited state of the first quantum system to the symmetric state of the hybridized mode, causing emission of a second photon encoded with a second part of the quantum state at a second frequency.

[0039] Figure 1 illustrates a basic schematic of a frequency-bin state generation system 100, annotated to indicate several of the features of the example systems described herein. As indicated in the figure, the system hardware includes superconducting data and emitter qubits, shown in the figure as first quantum system 110 and second quantum system 120, a frequency- tunable coupler 130 between the qubits, and a coplanarwaveguide 140 for carrying encoded photons from one quantum processing unit (QPU) to another. Control signals for this system, described in further detail below, include a parametric drive signal, applied by first driver circuitry 150 to a frequency-tunable coupler, and a second-order transition drive, applied by second driver circuitry 160 to the data qubit. The output of the system is robust frequency-bin encoded photons for multi-chip quantum computing (MCQC). Figure 2 is another schematic of a frequency-bin state generation system, in this case emphasizing the benefit of error detection, i.e., detection of interconnection photon loss, in an MCQC scenario.

[0040] To fully explain the inventive systems and techniques described herein, it is necessary to start with an explanation of frequency-bin encoding and frequency-bin encoded photons. Figure 3 illustrates the encoding of an arbitrary superposition state a\g) + (3\e) onto a pair of photonic modes (shown as a pair of wavelets on the right-hand side of the figure) emitted at two different frequencies, and )2. As briefly discussed above, frequency-bin encoding can be used as an error detection protocol to overcome photon loss during the interconnect of a multi-QPU system. To accomplish this, quantum information of a qubit must be encoded into two photons that are emitted at the same time but at two different frequencies. Note that from a quantum mechanical perspective, the qubit state is a quantum superposition of being in the ground (|g> state) or the first excited state (|e> state), meaning that while there is a probability for it to be found in either state, these events are mutually exclusive (it can never be both). The frequencybin emission protocol works in such a way that if the qubit is in |g>, a photon is emitted at a certain frequency, but if the qubit is instead in |e>, a photon is emitted at a different frequency. So, the superposition between the two possible qubit states is mapped into a superposition of a photon emitted at either of the two frequencies. However, whatever the state of the qubit, only one photon is actually emitted at a time, because the probabilities for the qubit to be in the ground or in the excited state are mutually exclusive. The discussion in this disclosure may occasionally refer to a “photon pair” or “pair of photons” being emitted, but it should be understood that what is meant here is a superposition of a photon emitted at one of the two frequencies. A more accurate term is “pair of photonic modes” - for the purposes of this discussion, the terms “photon pair” or “pair of photons” should be understood to refer to a pair of photonic modes where the quantum state of a qubit has been frequency-bin-encoded onto that pair.

[0041] To generate the frequency-bin encoded photons, it is necessary to implement the encoding protocol shown in Figure 3, in which a quantum state is transferred from a qubit into a frequency-bin photon state. Any arbitrary state a\g) + (3\e) can be transferred into two photons at frequency (J)^ and 61)2, where the photon with frequency (J)^ has the amplitude coefficient a and the photon with frequency 6c>2 has the amplitude coefficient . An example structure to generate frequency-bin encoded photons according to this protocol is the superconducting circuit shown in Figure 4. Note, however, that this is simply an example implementation - the techniques described herein do not necessarily require the use of superconducting qubits in the hardware implementation, as other types of qubit structures may be used in a similar manner. The example apparatus shown in Figure 4 includes two superconducting transmon bits, qubit QB1 and qubit QB2, each capacitively coupled to a frequency-tunable parametric coupler 400 arranged between them. A flux line 410 is inductively coupled to a superconducting quantum interference device (SQUID) loop 420 of the coupler 400, at the position indicated by the bold arrow in Figure 4, enabling the frequency tunability of the coupler 400. Qubit QB2 is strongly coupled to a coplanar waveguide 430, extending from the right-hand side of Figure 4, and is designed and fabricated to have a decay rate r of 2TT-8MHZ, for example, so that once qubit QB2 is populated, there will be a microwave photon emitted into the waveguide 430.

[0042] In the hardware implementation shown in Figure 4, there are two qubits (i.e., two single-qubit quantum systems), the data qubit and the emitter qubit, coupled by a frequency-tunable coupler between them. For single-photon emission, the data qubit is used to prepare the desired state to be transferred, which can be any arbitrary state a\g) + (3\e). The coupler’s frequency can be tuned by the flux that goes into the flux line that is inductively coupled to the coupler, which enables the coupler to operate two-qubit gate between the qubits. The emitter qubit is strongly coupled to a coplanarwaveguide, which can emit photons into the waveguide once it is being excited. To emit microwave photons into the waveguide, the state of the data qubit is transferred from the data qubit to the emitter qubit. Due to the high decay rate of the emitter qubit into the waveguide, the emitter qubit will decay into the ground state while emitting a photon into the waveguide, with the emitted photon having the same state as the initial state in the data qubit.

[0043] With this architecture, there are actually two methods of transferring a state a\g) + (3\e) in the data qubit into a same state of an emitted photon state a|0) + / ?|1). Figures 5A and 5B are energy diagrams showing the state transitions corresponding to these two methods of emitting a photon that has the same state as the initial state of the data qubit. Figure 5A shows the first method, while Figure 5B shows the second. In these illustrations, the first letter of each illustrated state represents the data qubit, the second letter represents the coupler and the third letter represents the emitter qubit. For example, state \gge) means the data qubit and the coupler are in the ground state and the emitter qubit is in the first excited state, while \fgg) means the data qubit is in the second excited state and the coupler and emitter qubit are in the ground state.

[0044] The first method may be understood with reference to Figure 5A. Applying a parametric drive to the coupler shown in Figure 4, through its flux line, causes an action like an iSWAP gate between the qubits, shown in the figure as an \egg) and \gge) transition, whereby the excitation in the data qubit is transferred to the emitter qubit. The data qubit is left in the ground state, but the emitter qubit is transitioned to the superposition state a\g) + (3\e). Due to the decay of the emitter qubit into the waveguide, the emitter qubit will return to the ground state immediately while emitting a photon a|0) + / ?|1) into the waveguide. Note that this is the same transition described in the inventor’s previous work, Yang 2023. The parametric drive signal may be referred to as an excitation-preserving drive, since the excitation state in the data qubit is transferred to the emitter qubit.

[0045] In a second method, the state of the data qubit is transitioned from a\g) + (3\e) to a\g) + utilizing the second excited state f. After that, by applying a second-order drive between \fgg) and \gge) by driving from the charge line of the data qubit, the data qubit’s state a\g) + (3\f) can be transferred into emitter qubit’s state a\g) + (3\e). These transitions are shown in Figure 5B. Again, due to the decay into the waveguide, the emitter qubit will decay to the ground state immediately while emitting a photon a|0) + / ?|1) into the waveguide. This is similar to the transition described in the previous work describing time-bin encoded photons referenced in the Background section above (Kurpiers 2019 and Ilves 2020). The second-order drive signal used here, which may be referred to more generally as a non-excitation-preserving drive, as the transition is from a state with two excitations in the data bit into a state with one excitation in the emitter qubit, exploits the Raman process described in Kurpiers 2018, with a key difference being that here it is between two qubit structures, instead of between a cavity and a qubit structure.

[0046] The transitions described above are each for the emission of a single photon into a waveguide, at a single frequency, using the architecture shown in Figure 4. Either of those transitions and the resulting emissions of a quantum-encoded photon transmission can be implemented with that structure. Accordingly, one straightforward approach to generating frequency-bin encoded photons, according to the protocol shown in Figure 3, is to simply duplicate the hardware shown in Figure 4, using each instantiation to generate a quantum-encoded photon, but at different frequencies, where one photon is encoded with a first component of the desired quantum state and the other is encoded with a second component of that quantum state. This approach is illustrated conceptually, in Figure 6, where the data bit and the auxiliary qubit are prepared in complementary fashion with the a and p components of the desired quantum state. As seen in the figure, the a component of the desired quantum state a|0) + / ?|1) is encoded onto a photon using the top data qubit and emitter qubit. The ft component is encoded onto a second photon using the bottom data qubit and emitter qubit. By tuning the respective couplers to different frequencies and driving the upper and lower transitions simultaneously, a pair of frequency- encoded photons can be emitted into the waveguide at the same time. Note that either of the two transition types described above may be used.

[0047] However, this approach requires twice as much hardware as the baseline single-photon apparatus. This problem can be avoided by simultaneously using both of the two transition types described above, simultaneously, with a proper tuning of the coupler. Conceptually, the result is the schematic shown in Figure 7. As seen there, only two qubits are needed to generate frequency-bin encoded photons, compared to the four qubits needed in the approach shown in Figure 6.

[0048] To generate frequency-bin encoding with the same structure shown in Figure 4, i.e., without replicating the data qubit, the emitter qubit, and the coupler between them, the coupler must first be tuned to the same frequency as the emitter qubit. Due to the direct coupling between the qubit and the coupler, the two components will form a hybridized mode having two states, a symmetric state |S) and an asymmetric state |A). This is shown in Figure 8. The frequencies of these two states are COs^emitter qubit + gar|d CO A ^emitter qubit g respectively, where g is the direct coupling strength between the coupler and the emitter qubit.

[0049] Secondly, the arbitrary superposition state a\g) + fi\e) in the data qubit is brought into the a\e) + fi\f) state by applying a single qubit gate between ef transition, followed by a single qubit gate between ge transition on the data qubit.

[0050] Thirdly, both the parametric drive and the second-order transition drive are applied simultaneously, according to the two methods described above. The parametric drive transfers the |e) (initial state \g)) part of the data qubit into the asymmetric state | A), which will immediately decay and emit a photon with frequency CO^. This parametric drive is a specific implementation of what may be referred to as an excitation-preserving drive, since the excitation state in the data qubit is transferred to the emitter qubit. At the same time, the second-order transition drive transfers the \f) (initial state |e)) part of the data qubit into the symmetric state | S), which will immediately decay and emit a photon with frequency OOg. The second-order drive is a specific implementation of what may be referred to more generally as a non-excitation-preserving drive, as the transition is from a state with two excitations in the data bit into a state with one excitation in the emitter qubit. Note that references herein to “at the same time” or “simultaneously” should be understood as referring to substantially simultaneous events, i.e., events that at least closely overlap, possiblywith minortiming differences arriving from imperfections or tolerances in the hardware used to implement the techniques.

[0051] The energy transitions for the whole process described above are shown in Figure 9. As shown in the figure, this process implements the transfer of a single qubit state a\g) + (β\e) into two photonic modes at frequency (i)sand (i)A, which is a frequency-bin encoded photon state

[0052] The benefits of emitting a frequency-bin-encoded photon according to the techniques above are manifested at the receiving end, where the encoding can be used to detect photon loss in a non-destructive manner, i.e., without disturbing the quantum state of a successfully received pair of photons.

[0053] The hardware for implementing the receiver is essentially the same as described above. To read the transmitted quantum state, conventional read-out circuitry is coupled to the data qubit circuitry. Detection of an error, i.e., detection of the loss of the photon carried by either of the two frequency bins is performed in the same way as with the time-bin encoding described in Kurpiers 2019, referenced above. In short, if a photon is lost or not successfully absorbed by the receiver, a vacuum state is received instead of the desired state of the frequency-bin encoded state. Receiving the vacuum state will result in the state of the data qubit comprising the second excitation state, i.e., the \f) state discussed above. A quantum non-demolition measurement that distinguishes between the \f) state and a subspace comprisingthe \g) state and the |e) state, without measuring within that subspace, can detect whether there has been photon loss without affecting the quantum state of a successfully transmitted frequency-bin encoded photon. This is shown in Figure 10. The right side of the illustrated table shows the state of the data qubit in the receiver for the case where the photon carried by either of the frequency bins is lost, and where the frequency-bin encoded photon is successfully received. As seen there, in the case where the photon carried by either of the frequency bins is lost, the state of the receiver qubit comprises the \f ) state, which can be detected with a measurement that does not disturb the quantum state of the qubit when there is no photon loss.

[0054] Notably, however, while the frequency-bin encoding scheme described above yields the same error- detection benefits as the time-bin encoding scheme described in, for example, Kurpiers 2019, the frequency-bin encoding scheme can be operated at twice as fast a rate, with similar hardware. Further, the techniques described above do not require a doubling of qubit hardware, compared to a single-photon emission scheme, requiring no new quantum hardware compared to that described in Yang 2023.

[0055] In view of the details and examples descried above, it will be appreciated that Figure 11 is a schematic diagram of an example apparatus in which the above techniques may be applied. The apparatus includes a microwave transceiver part 1110, and a superconducting circuit part 1150. The superconducting circuit part 1120 includes a qubit QB1 , a qubit QB2, and a parametrically driven coupler 400 arranged between them. (Qubits QB1 and QB2 can be more formally referred to as first and second one-qubit quantum systems.) The parametric coupler 400 includes a SQUID device 420, for applying the flux to the coupler, arranged in Figure 11 at roughly the midpoint of coupler 400, but its details are not illustrated in this figure. A waveguide interface 1155 couples qubit QB2 to waveguide 430.

[0056] The parametric coupler 400 is driven by a signal from arbitrary waveform generator (AWG) 1115, which forms part of the microwave transceiver part 1110. Likewise, qubit QB1 is excited to a desired superposition state with another signal from AWG 1115. Microwave photons emitted into waveguide 430 are passed through microwave circulator 1160 and microwave isolators 1165, as well as appropriate filters and amplifiers, and supplied to analog-to-digital converter 1125, for measurement and digitization. The digitized characterization of the frequency-bin photons can then be supplied to AWG 1115, for use in generating the AC flux pulse signal applied to the parametric coupler 400.

[0057] It will be appreciated that the apparatus shown in Figure 11 is but one example of an apparatus in which the techniques and concepts described herein may be employed - in this case utilizing two superconducting transmons with a parametric coupler between them. The term “parametric coupler” refers to a frequency-tunable coupler, i.e. , a coupling circuit or structure where the frequency of the coupling can be modulated in a controlled fashion, e.g., by application of a flux as in examples described herein, to induce a certain transition. In the present case, the modulation frequency corresponds to the frequency difference between the two states and the effect of the modulation is to activate an exchange interaction between the two states. The techniques may be applied more generally, with structures where the coupling strength between two quantum processing components, such as qubits, resonators, etc., changes as a function of a time-varying waveform driving the coupling. Thus, some embodiments of the presently disclosed invention can be considered as comprising first and second quantum systems, the second quantum system being configured to emit quantum- encoded particles into a waveguide coupled to the second quantum system, and parametric frequency-tunable coupling circuitry coupling the first quantum system to the second quantum system. In the examples detailed herein, these first and second quantum systems are first and second superconductingtransmon qubits, but other embodiments might comprise a resonator and a qubit, two realizations of quantum-encoded photons, one or more other sorts of qubits such as fluxonium-based qubits, etc. The apparatus shown in Figure 11 or described in more general terms above may form part of a quantum processing unit (QPU), quantum computing system, a telecommunications network node, etc.

[0058] This more generalized apparatus further comprises first driver circuitry connected to the frequency-tunable coupler and configured to connected to the frequency-tunable coupler and configured to drive the frequency-tunable coupler with an excitation-preserving transition signal configured to transfer a first excited state of the first quantum system to the asymmetric state of the hybridized mode, causing an emission of a first photon encoded with a first part of a quantum state into the waveguide system at a first frequency. Second driver circuitry is connected to the first quantum system and configured to drive the first quantum system with a non-excitation-preserving transition signal configured to transfer a second excited state of the first quantum system to the symmetric state of the hybridized mode, causing an emission of a second photon encoded with a second part of the quantum state into the waveguide system at a second frequency. The first driver circuitry and second driver circuitry are configured to drive the frequency-tunable coupler and the first quantum system substantially simultaneously, so that the emissions of the first and second photons are substantially simultaneous.

[0059] Figure 12 is a process flow diagram illustrating, in general terms, the steps for transmitting quantum information from a QPU like those described above, i.e., a QPU that comprises a first quantum system and a second quantum system, a waveguide system coupled to the second quantum system and arranged to receive quantum-encoded photons emitted from the second quantum system, and a frequency-tunable coupler coupling the first quantum system to the second quantum system, the frequency-tunable coupler and the second quantum system being arranged so that tuning the frequency-tunable coupler to a resonant frequency of the second quantum system forms a hybridized mode with a symmetric state and an asymmetric state each coupled to the waveguide system. As shown at block 1210, the illustrated method includes the step of exciting the first qubit to an arbitrary superposition of a ground state and a first excited state. As shown at block 1220, the method further includes the step of driving the frequency-tunable coupler with an excitation-preserving transition signal configured to transfer the first excited state of the first quantum system to the asymmetric state of the hybridized mode, causing an emission of a first photon encoded with a first part of a quantum state into the waveguide system at a first frequency. As shown at block 1230, the method further includes driving the first quantum system with a non-excitation-preserving transition signal configured to transfer a second excited state of the first quantum system to the symmetric state of the hybridized mode, causing an emission of a second photon encoded with a second part of the quantum state into the waveguide system at a second frequency. The frequency-tunable coupler and the first quantum system are driven substantially simultaneously, so that the emissions of the first and second photons are substantially simultaneous. Note that the “first photon” and “second photon” referred to here and elsewhere in this document are a quantum- encoded pair of photons in superposition, such that each has a certain probability of existing, with those probabilities adding to 1 , but where both do not exist at the same time. For convenience, this document refers to the simultaneous emission of both a first photon and a second photon, but it should be understood that these emissions are mutually exclusive from a quantum mechanical perspective.

[0060] In some embodiments of the illustrated method, the first and second quantum systems are superconducting transmons. In some of these and in some other embodiments, the frequency- tunable coupler is a parametrically-driven frequency-tunable coupler tunable with a DC flux to the resonant frequency of the second quantum system, in which case driving the frequency- tunable coupler comprises driving the parametrically-driven frequency-tunable couple with the DC flux and a parametric drive signal configured to transfer the first excited state of the first quantum system to the asymmetric state of the hybridized mode.

[0061] In some embodiments, driving the first quantum system comprises using second-order drive circuitry coupled to the first quantum system and further configured to first prepare the first quantum system in an arbitrary superposition state of a ground state and the first excited state and to subsequently transfer the arbitrary superposition state of the first quantum system to a superposition of the first excited state and the second excited state. This is shown in Figure 12 at block 1215.

[0062] The techniques described herein represent the first approach to generate frequency-bin photons based on superconducting modality using a waveguide QED structure. Key features of various embodiments of these techniques are:

[0063] • No new quantum hardware requirements compared to the apparatus described in Yang 2023, which describes an apparatus for quantum-encoded photon emission without error detection.

[0064] • The frequency-bin degree of freedom encoding forms the basis of a simple error detection protocol to deal with photon loss problems when transmitting microwave photons carrying quantum state between remotely distributed quantum processors.

[0065] • Compared to time-bin encoding in superconducting hardware, the encoded photons are emitted at the same time but at different frequencies, which makes the data-rate twice as fast.

[0066] • The scheme requires a simple hardware structure that does not need any extra qubits compared to a previously disclosed structure with no ability for error detection (Yang 2023).

Claims

CLAIMS1 . An apparatus for use in a quantum processing unit, QPU, the apparatus comprising: a first quantum system (110) and a second quantum system (120); a waveguide system (140) coupled to the second quantum system (120) and arranged to receive quantum-encoded photons emitted from the second quantum system (120); a frequency-tunable coupler (130) coupling the first quantum system (110) to the second quantum system (120), the frequency-tunable coupler (130) and the second quantum system (120) being arranged so that tuning the frequency- tunable coupler (130) to a resonant frequency of the second quantum system (120) forms a hybridized mode with a symmetric state and an asymmetric state, each coupled to the waveguide system (140); first driver circuitry (150) connected to the frequency-tunable coupler (120) and configured to drive the frequency-tunable coupler (120) with an excitationpreserving transition signal configured to transfer a first excited state of the first quantum system (110) to the asymmetric state of the hybridized mode, causing an emission of a first photon encoded with a first part of a quantum state into the waveguide system (140) at a first frequency; and second driver circuitry (160) connected to the first quantum system (110) and configured to drive the first quantum system (110) with a non-excitation- preserving transition signal configured to transfer a second excited state of the first quantum system (110) to the symmetric state of the hybridized mode, causing an emission of a second photon encoded with a second part of the quantum state into the waveguide system (140) at a second frequency, wherein the first driver circuitry (150) and second driver circuitry (160) are configured to drive the frequency-tunable coupler (130) and the first quantum system (110) substantially simultaneously so that the emissions of the first and second photons are substantially simultaneous.

2. The apparatus of claim 1 , wherein the first quantum system (110) and second quantum system (120) are superconducting transmons.

3. The apparatus of claim 1 or 2, wherein the frequency-tunable coupler (130) is a parametrically-driven frequency-tunable coupler tunable with a DC flux to the resonantfrequency of the second quantum system (120), and wherein the first driver circuitry (150) is configured to drive the parametrically-driven frequency-tunable coupler with the DC flux and an AC parametric drive signal configured to transfer the first excited state of the first quantum system to the symmetric state of the hybridized mode.

4. The apparatus of any one of claims 1 -3, wherein the second driver circuitry (160) comprises second-order drive circuitry coupled to the first quantum system (110) and is further configured to first prepare the first quantum system (110) in an arbitrary superposition state of a ground state and the first excited state and to subsequently transfer the arbitrary superposition state of the first quantum system (110) to a superposition of the first excited state and the second excited state.

5. A quantum processing unit, QPU, comprising an apparatus according to anyone of claims 1 - 4.

6. A quantum-processing system comprising a first QPU according to claim 5 and further comprising a second QPU, the second QPU comprising: a third quantum system (120) and a fourth quantum system (110), the third quantum (120) system being coupled to the waveguide system(140) so as to receive the first and second photons; a second frequency-tunable coupler (130) coupling the third quantum system (120) to the fourth quantum system (110), the second frequency-tunable coupler (130) and the third quantum system (120) being arranged so that tuning the frequency-tunable coupler (130) to a resonant frequency of the third quantum system (120) forms the same hybridized mode as in the first QPU; third driver circuitry (150) connected to the frequency-tunable coupler (130) and configured to drive the second frequency-tunable coupler (130) with an excitation-preserving transition signal configured to transfer the first part of the quantum state encoded in the first photon into a first excited state of the fourth quantum system (110); and fourth driver circuitry (160) connected to the fourth quantum system (110) and configured to drive the fourth quantum system (110) with a non-excitation- preserving transition signal configured to transfer the second part of the quantum state encoded in the second photon to a second excited state of thefourth quantum system (110), wherein the third driver circuitry (150) and fourth driver circuitry (160) are configured to drive the second frequency-tunable coupler (130) and the fourth quantum system (110) substantially simultaneously so that transfers of the first and second parts of the quantum state to the fourth quantum system (110) are substantially simultaneous.

7. A method for transmitting quantum information from a quantum processing unit, QPU, that comprises a first quantum system (110) and a second quantum system (120), a waveguide system (130) coupled to the second quantum system (120) and arranged to receive quantum- encoded photons emitted from the second quantum system (120), and a frequency-tunable coupler (130) coupling the first quantum system (110) to the second quantum system (120), the frequency-tunable coupler (130) and the second quantum system (120) being arranged so that tuning the frequency-tunable coupler (130) to a resonant frequency of the second quantum system (120) forms a hybridized mode with a symmetric state and an asymmetric state, each coupled to the waveguide system (140), the method comprising: exciting (1210) the first qubit to an arbitrary superposition of a ground state and a first excited state; driving (1220) the frequency-tunable coupler (130) with an excitation-preserving transition signal configured to transfer the first excited state of the first quantum system (110) to the asymmetric state of the hybridized mode, causing an emission of a first photon encoded with a first part of a quantum state into the waveguide system (140) at a first frequency; and driving (1230) the first quantum system (110) with a non-excitation-preserving transition signal configured to transfer a second excited state of the first quantum system (110) to the symmetric state of the hybridized mode, causing an emission of a second photon encoded with a second part of the quantum state into the waveguide system (140) at a second frequency, wherein said driving (1220) the frequency-tunable coupler (130) and driving (1230) the first quantum system (110) are performed substantially simultaneously so that the emissions of the first and second photons are substantially simultaneous.

8. The method of claim 7, wherein the first and second qubits are superconductingtransmons.

9. The method of claim 7 or 8, wherein the frequency-tunable coupler (130) is a parametrically- driven frequency-tunable coupler tunable with a DC flux to the resonant frequency of the second quantum system, and wherein said driving (1220) the frequency-tunable coupler (130) comprises driving the parametrically-driven frequency-tunable couple with the DC flux and an AC parametric drive signal configured to transfer the first excited state of the first quantum system to the symmetric state of the hybridized mode.

10. The method of any one of claims 7-9, wherein said driving (1220) the first quantum system (110) comprises using second-order drive circuitry coupled to the first quantum system (110) and further configured to first prepare the first quantum system (110) in an arbitrary superposition state of a ground state and the first excited state and to subsequently transfer the arbitrary superposition state of the first quantum system (110) to a superposition of the first excited state and the second excited state.

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