Abstract: A method of generating an m-photon entangled state includes inputting photons into a plurality of sets of modes. Each set of modes is coupled to a different set of modes. The method includes detecting photons in the plurality of sets of modes. The method includes, in accordance with a determination, based on a number of photons detected, that more than m-photons remain in the plurality of sets of modes: performing a second detection operation that includes detecting photons in the plurality of sets of modes; determining, based at least in part on a number of photons detected, whether the photons remaining in the plurality of sets of modes after the second detection operation are in the m-photon entangled state; and in accordance with a determination that the photons remaining in the plurality of sets of modes are in the m-photon entangled state, outputting the remaining photons.

Abstract: A method includes receiving a plurality of quantum systems, wherein each quantum system of the plurality of quantum system includes a plurality of quantum sub-systems in an entangled state, and wherein respective quantum systems of the plurality of quantum systems are independent quantum systems that are not entangled with one another. The method further includes performing a plurality of joint measurements on different quantum sub-systems from respective ones of the plurality of quantum systems, wherein the joint measurements generate joint measurement outcome data and determining, by a decoder, a plurality of syndrome graph values based on the joint measurement outcome data.

Abstract: A device includes a plurality of first switches. Each first switch includes a set of two or more first channels. Each first switch is configured to shift photons in the set of first channels by zero or more channels, based on first configuration information provided to the first switch. The device further includes a plurality of second switches. Each second switch includes a corresponding set of two or more second channels. The plurality of second switches is coupled to two or more output channels. Each second switch is coupled, by the set of second channels, to outputs of two or more first switches. Each second switch is configured to shift photons in the set of second channels by zero or more channels, based on second configuration information provided to the second switch so that photons are provided to respective output channels of the two or more output channels.

Abstract: A method includes receiving a plurality of quantum systems, wherein each quantum system of the plurality of quantum system includes a plurality of quantum sub-systems in an entangled state, and wherein respective quantum systems of the plurality of quantum systems are independent quantum systems that are not entangled with one another. The method further includes performing a plurality of joint measurements on different quantum sub-systems from respective ones of the plurality of quantum systems, wherein the joint measurements generate joint measurement outcome data and determining, by a decoder, a plurality of syndrome graph values based on the joint measurement outcome data.

Abstract: An expanded Bell state generator can generate a Bell state on four output modes of a set of m output modes, where m is greater than four. Some expanded Bell state generators can receive inputs on any four of a set of 2m input modes. Subsets of the m output modes can be multiplexed to reduce the number of modes to four. According to some embodiments, a set of 2×2 muxes can be used to rearrange the output modes prior to reducing the number of modes.

Abstract: A method of generating an m-photon entangled state includes inputting photons into a plurality of sets of modes. Each set of modes is coupled to a different set of modes. The method includes detecting photons in the plurality of sets of modes. The method includes, in accordance with a determination, based on a number of photons detected, that more than m-photons remain in the plurality of sets of modes: performing a second detection operation that includes detecting photons in the plurality of sets of modes; determining, based at least in part on a number of photons detected, whether the photons remaining in the plurality of sets of modes after the second detection operation are in the m-photon entangled state; and in accordance with a determination that the photons remaining in the plurality of sets of modes are in the m-photon entangled state, outputting the remaining photons.

Abstract: A method includes receiving a plurality of quantum systems, wherein each quantum system of the plurality of quantum system includes a plurality of quantum sub-systems in an entangled state, and wherein respective quantum systems of the plurality of quantum systems are independent quantum systems that are not entangled with one another. The method further includes performing a plurality of joint measurements on different quantum sub-systems from respective ones of the plurality of quantum systems, wherein the joint measurements generate joint measurement outcome data and determining, by a decoder, a plurality of syndrome graph values based on the joint measurement outcome data.

Abstract: A device (e.g., a photonic multiplexer) is provided that includes a plurality of first switches. Each first switch in the plurality of first switches includes a plurality of first channels. Each first switch is configured to shift photons in the plurality of first channels by zero or more channels, based on first configuration information provided to the first switch. The device further includes a plurality of second switches Each second switch includes a plurality of second channels. Each second channel is coupled with a respective first channel from a distinct first switch of the plurality of first switches. Each second switch is configured to shift photons in the plurality of second channels by zero or more channels, based on second configuration information provided to the second switch.

Abstract: A method of fusing qubits includes providing, to a Hadamard gate: a first qubit; a second qubit; and a Bell pair comprising a fourth qubit that is entangled with a fifth qubit. The method further includes determining whether the Hadamard gate was successful in producing a fused qubit. The method further includes in accordance with the determination that the Hadamard gate was successful in producing fused qubit, outputting the fused qubit.

Abstract: A multirail-encoded qubit can be implemented using a quantum system having a state space that includes a number M of distinct modes, where M is an integer greater than 2. The M modes are logically partitioned into two disjoint subsets (or “bands”), with each mode assigned to exactly one of the bands. The multirail encoding is defined such that a state in which any one of the modes in the first band is occupied and all modes in the second band are unoccupied maps to a logical 0 state of the qubit, and a state in which any one of the modes in the second band is occupied and all modes of the first band are unoccupied maps to a logical 1 state. Systems and methods for generating, measuring, and operating on multirail-encoded qubits are disclosed.

Abstract: A device includes a plurality of photon sources coupled to a plurality of output terminals. The plurality of photon sources are coupled together, by a first switch layer, into a plurality of photon source groups. The first switch layer comprises a plurality of switches. The device further includes a second switch layer coupled to output terminals of the first switch layer. The second switch layer includes a plurality of second layer n-by-n switches and a plurality of second layer l-by-l switches, wherein l is less than n. At least two output terminals from two respective photon sources residing within a first photon source group of the plurality of photon source groups and a second photon source group of the plurality of photon source groups are coupled directly to respective output terminals of the device without being coupled to any intervening second switch from the second switch layer.

Abstract: A device (e.g., a photonic multiplexer) is provided that includes a plurality of first switches. Each first switch in the plurality of first switches includes a plurality of first channels. Each first switch is configured to shift photons in the plurality of first channels by zero or more channels, based on first configuration information provided to the first switch. The device further includes a plurality of second switches. Each second switch includes a plurality of second channels. Each second channel is coupled with a respective first channel from a distinct first switch of the plurality of first switches. Each second switch is configured to shift photons in the plurality of second channels by zero or more channels, based on second configuration information provided to the second switch.

Abstract: An expanded Bell state generator can generate a Bell state on four output modes of a set of m output modes, where m is greater than four. Some expanded Bell state generators can receive inputs on any four of a set of 2m input modes. Subsets of the m output modes can be multiplexed to reduce the number of modes to four. According to some embodiments, a set of 2×2 muxes can be used to rearrange the output modes prior to reducing the number of modes.

Abstract: A method of generating an m photon entangled state includes inputting a photon into each of a first plurality of modes including first and second pairs of modes. The first plurality of modes is coupled with a second plurality of modes. Zero or more photons are detected in the second plurality of modes. The method includes, when more than m photons remain in the first plurality of modes: detecting zero or more photons in a third plurality of modes coupled with the first plurality of modes; determining, based on a number of photons detected, whether the photons remaining in the first plurality of modes are in the entangled state. The method includes, when the photons remaining in the first plurality of modes after the second detection operation are in the entangled state, outputting the photons remaining in the first plurality of modes.

Abstract: A method includes receiving a plurality of quantum systems, wherein each quantum system of the plurality of quantum system includes a plurality of quantum sub-systems in an entangled state, and wherein respective quantum systems of the plurality of quantum systems are independent quantum systems that are not entangled with one another. The method further includes performing a plurality of joint measurements on different quantum sub-systems from respective ones of the plurality of quantum systems, wherein the joint measurements generate joint measurement outcome data and determining, by a decoder, a plurality of syndrome graph values based on the joint measurement outcome data.

Abstract: A device includes a plurality of photon sources coupled to a plurality of output terminals. The plurality of photon sources are coupled together, by a first switch layer, into a plurality of photon source groups. The first switch layer comprises a plurality of switches. The device further includes a second switch layer coupled to output terminals of the first switch layer. The second switch layer includes a plurality of second layer n-by-n switches and a plurality of second layer l-by-l switches, wherein l is less than n. At least two output terminals from two respective photon sources residing within a first photon source group of the plurality of photon source groups and a second photon source group of the plurality of photon source groups are coupled directly to respective output terminals of the device without being coupled to any intervening second switch from the second switch layer.

Abstract: A method for obtaining a plurality of entangled qubits represented by a lattice structure that includes a plurality of contiguous lattice cells. A respective edge of a respective lattice cell corresponds to one or more edge qubits, and a respective face of the respective lattice cell corresponding to one or more face qubits. Each face qubit is entangled with adjacent edge qubits. A first face of the respective lattice cell corresponds to two or more face qubits, and/or a first edge corresponds to two or more edge qubits. A device for obtaining the plurality of entangled qubits represented by the above-described lattice structure is also described.

Abstract: A device (e.g., a photonic multiplexer) is provided that includes a plurality of first switches. Each first switch in the plurality of first switches includes a plurality of first channels. Each first switch is configured to shift photons in the plurality of first channels by zero or more channels, based on first configuration information provided to the first switch. The device further includes a plurality of second switches. Each second switch includes a plurality of second channels. Each second channel is coupled with a respective first channel from a distinct first switch of the plurality of first switches. Each second switch is configured to shift photons in the plurality of second channels by zero or more channels, based on second configuration information provided to the second switch.

Abstract: A device (e.g., a photonic multiplexer) is provided that includes a plurality of first switches. Each first switch in the plurality of first switches includes a plurality of first channels. Each first switch is configured to shift photons in the plurality of first channels by zero or more channels, based on first configuration information provided to the first switch. The device further includes a plurality of second switches. Each second switch includes a plurality of second channels. Each second channel is coupled with a respective first channel from a distinct first switch of the plurality of first switches. Each second switch is configured to shift photons in the plurality of second channels by zero or more channels, based on second configuration information provided to the second switch.

Abstract: A device (e.g., a photonic multiplexer) is provided that includes a plurality of first switches. Each first switch in the plurality of first switches includes a plurality of first channels. Each first switch is configured to shift photons in the plurality of first channels by zero or more channels, based on first configuration information provided to the first switch. The device further includes a plurality of second switches. Each second switch includes a plurality of second channels. Each second channel is coupled with a respective first channel from a distinct first switch of the plurality of first switches. Each second switch is configured to shift photons in the plurality of second channels by zero or more channels, based on second configuration information provided to the second switch.