Abstract: Quantum repeater systems and apparatus for quantum communication. In one aspect, a system includes a quantum signal receiver configured to receive a quantum field signal; a quantum signal converter configured to: sample quantum analog signals from a quantum field signal received by the quantum signal receiver; encode sampled quantum analog signals as corresponding digital quantum information in one or more qudits, comprising applying a hybrid analog-digital encoding operation to each quantum analog signal and a qudit in an initial state; decode digital quantum information stored in the one or more qudits as a recovered quantum field signal, comprising applying a hybrid digital-analog decoding operation to each qudit and a quantum analog register in an initial state; a quantum memory comprising qudits and configured to store digital quantum information encoded by the quantum signal converter; and a quantum signal transmitter configured to transmit the recovered quantum field signal.

Abstract: Methods, systems, and apparatus for quantum analog-digital conversion. In one aspect, a method includes obtaining a quantum analog signal; applying a hybrid analog-digital encoding operation to the quantum analog signal and a qudit in an initial state to obtain an evolved state of the qudit, wherein the hybrid analog-digital encoding operation is based on a swap operation comprising multiple adder operations; and providing the qudit in the evolved state as a quantum digital encoding of the quantum analog signal.

Abstract: Quantum repeater systems and apparatus for quantum communication. In one aspect, a system includes a quantum signal receiver configured to receive a quantum field signal; a quantum signal converter configured to: sample quantum analog signals from a quantum field signal received by the quantum signal receiver; encode sampled quantum analog signals as corresponding digital quantum information in one or more qudits, comprising applying a hybrid analog-digital encoding operation to each quantum analog signal and a qudit in an initial state; decode digital quantum information stored in the one or more qudits as a recovered quantum field signal, comprising applying a hybrid digital-analog decoding operation to each qudit and a quantum analog register in an initial state; a quantum memory comprising qudits and configured to store digital quantum information encoded by the quantum signal converter; and a quantum signal transmitter configured to transmit the recovered quantum field signal.

Abstract: Methods, systems, and apparatus for quantum analog-digital conversion. In one aspect, a method includes obtaining a quantum analog signal; applying a hybrid analog-digital encoding operation to the quantum analog signal and a qudit in an initial state to obtain an evolved state of the qudit, wherein the hybrid analog-digital encoding operation is based on a swap operation comprising multiple adder operations; and providing the qudit in the evolved state as a quantum digital encoding of the quantum analog signal.

Abstract: Quantum repeater systems and apparatus for quantum communication. In one aspect, a system includes a quantum signal receiver configured to receive a quantum field signal; a quantum signal converter configured to: sample quantum analog signals from a quantum field signal received by the quantum signal receiver; encode sampled quantum analog signals as corresponding digital quantum information in one or more qudits, comprising applying a hybrid analog-digital encoding operation to each quantum analog signal and a qudit in an initial state; decode digital quantum information stored in the one or more qudits as a recovered quantum field signal, comprising applying a hybrid digital-analog decoding operation to each qudit and a quantum analog register in an initial state; a quantum memory comprising qudits and configured to store digital quantum information encoded by the quantum signal converter; and a quantum signal transmitter configured to transmit the recovered quantum field signal.

Abstract: Quantum repeater systems and apparatus for quantum communication. In one aspect, a system includes a quantum signal receiver configured to receive a quantum field signal; a quantum signal converter configured to: sample quantum analog signals from a quantum field signal received by the quantum signal receiver; encode sampled quantum analog signals as corresponding digital quantum information in one or more qudits, comprising applying a hybrid analog-digital encoding operation to each quantum analog signal and a qudit in an initial state; decode digital quantum information stored in the one or more qudits as a recovered quantum field signal, comprising applying a hybrid digital-analog decoding operation to each qudit and a quantum analog register in an initial state; a quantum memory comprising qudits and configured to store digital quantum information encoded by the quantum signal converter; and a quantum signal transmitter configured to transmit the recovered quantum field signal.

Abstract: Methods, systems, and apparatus for quantum analog-digital conversion. In one aspect, a method includes obtaining a quantum analog signal; applying a hybrid analog-digital encoding operation to the quantum analog signal and a qudit in an initial state to obtain an evolved state of the qudit, wherein the hybrid analog-digital encoding operation is based on a swap operation comprising multiple adder operations; and providing the qudit in the evolved state as a quantum digital encoding of the quantum analog signal.

Abstract: Methods, systems, and apparatus for quantum analog-digital conversion. In one aspect, a method includes obtaining a quantum analog signal; applying a hybrid analog-digital encoding operation to the quantum analog signal and a qudit in an initial state to obtain an evolved state of the qudit, wherein the hybrid analog-digital encoding operation is based on a swap operation comprising multiple adder operations; and providing the qudit in the evolved state as a quantum digital encoding of the quantum analog signal.

Abstract: A magnetoencephalography apparatus includes: a lead configured to be secured to a user's head; a first magnetic field sensor attached to the lead, the first magnetic field sensor including a substrate, and an electron spin defect layer on the substrate, the electron spin defect layer including at least one lattice defect, in which a first spin energy level of the at least one lattice defect splits upon exposure to a microwave; and cabling, in which the cabling includes a first microwave transmission line arranged to provide a first microwave field to the electron spin defect layer and in which the cabling includes an optical fiber arranged to provide, from a first end of the optical fiber, a first light signal to the electron spin defect layer and to receive, at the first end of the optical fiber, a second light signal emitted by the electron spin defect layer.

Abstract: Methods, systems, and apparatus for quantum analog-digital conversion. In one aspect, a method includes obtaining a quantum analog signal; applying a hybrid analog-digital encoding operation to the quantum analog signal and a qudit in an initial state to obtain an evolved state of the qudit, wherein the hybrid analog-digital encoding operation is based on a swap operation comprising multiple adder operations; and providing the qudit in the evolved state as a quantum digital encoding of the quantum analog signal.

Abstract: Methods, systems, and apparatus for generating a Gottesman-Kitaev-Preskill (GKP) quantum state that includes a series of Gaussian peaks of target width and target separation embedded in a Gaussian envelope. In one aspect, a method includes obtaining a fourth qudit in an initial state, wherein the initial state comprises a tensor product of a state of a first qudit encoding the Gaussian envelope, a state of a second qudit encoding the target separation, and a state of a third qudit encoding the target width; applying a hybrid digital-analog swap operation to the fourth qudit and a quantum analog register in an initial state to obtain a modified state of the quantum analog register, where the hybrid digital-analog swap operation is based on a swap operation comprising multiple adder operations; and providing the modified state of the quantum analog register as an approximate GKP quantum state.

Abstract: Methods, systems, and apparatus for preparing a target mixed state of a quantum system. In some aspects a method includes preparing a parameterized ansatz quantum state as an initial approximation to the target mixed state, wherein the parameterized ansatz quantum state comprises a first set of variational parameters and a second set of variational parameters; determining, by classical and quantum computation, values of the first set of variational parameters and second set of variational parameters that minimize a quantum relative entropy of the target mixed state with respect to the parameterized ansatz quantum state; and preparing the parameterized ansatz quantum state with the determined values of the first set of variational parameters and second set of variational parameters as a final approximation to the target mixed state.