Abstract: Systems, methods, and quantum circuits for utilizing a joint modular multiplicative inverse operation to perform quantum decryption. First and second private keys are determined by applying first and second series of quantum phase estimation circuits to first and second pluralities of qubits. The private keys are determined further based on public keys and a base point P. The first and second series of quantum phase estimation circuits include application of a joint modular multiplicative inverse circuit on a first qubit of the first plurality of qubits and a second qubit of the second plurality of qubits that calculates a modular multiplicative inverse of a modular product of a first value of the first qubit and a second value of the second qubit. The first and second private keys are stored in a non-transitory computer-readable memory medium.

Abstract: A fault-tolerant quantum computer using topological codes such as surface codes can have an architecture that reduces the amount of idle volume generated. The architecture can include qubit modules that generate surface code patches for different qubits and a network of interconnections between different qubit modules. The interconnections can include “port” connections that selectably enable coupling of boundaries of surface code patches generated in different qubit modules and/or “quickswap” connections that selectably enable transferring the state of a surface code patch from one qubit module to another. Port and/or quickswap connections can be made between a subset of qubit modules. For instance port connections can connect a given qubit module to other qubit modules within a fixed range. Quickswap connections can provide a log-tree network of direct connections between qubit modules.

Abstract: Systems and methods for emulating a physical quantum system with a quantum computation. A model Hamiltonian that approximates a first quantization Hamiltonian of the physical quantum system is stored in memory. The physical system includes a plurality of particles. The first quantization Hamiltonian includes a plurality of first quantization energy operators, and the model Hamiltonian includes a plurality of energy terms corresponding to respective ones of the plurality of first quantization energy operators. Each energy term includes a respective energy operator, a respective energy register operator, and a respective inverse energy operator. The physical quantum system is emulated by performing a quantum computation on a plurality of qubits of the quantum computing system to emulate time evolution using the model Hamiltonian.

Abstract: Systems and methods for emulating a physical quantum system with a quantum computation. A model Hamiltonian that approximates a first quantization Hamiltonian of the physical quantum system is stored in memory. The physical system includes a plurality of particles. The first quantization Hamiltonian includes a plurality of first quantization energy operators, and the model Hamiltonian includes a plurality of energy terms corresponding to respective ones of the plurality of first quantization energy operators. Each energy term includes a respective energy operator, a respective energy register operator, and a respective inverse energy operator. The physical quantum system is emulated by performing a quantum computation on a plurality of qubits of the quantum computing system to emulate time evolution using the model Hamiltonian.

Abstract: A fault-tolerant quantum computer using topological codes such as surface codes can have an architecture that reduces the amount of idle volume generated. The architecture can include qubit modules that generate surface code patches for different qubits and a network of interconnections between different qubit modules. The interconnections can include “port” connections that selectably enable coupling of boundaries of surface code patches generated in different qubit modules and/or “quickswap” connections that selectably enable transferring the state of a surface code patch from one qubit module to another. Port and/or quickswap connections can be made between a subset of qubit modules. For instance port connections can connect a given qubit module to other qubit modules within a fixed range. Quickswap connections can provide a log-tree network of direct connections between qubit modules.

Abstract: A fault-tolerant quantum computer using topological codes such as surface codes can have an architecture that reduces the amount of idle volume generated. The architecture can include qubit modules that generate surface code patches for different qubits and a network of interconnections between different qubit modules. The interconnections can include “port” connections that selectably enable coupling of boundaries of surface code patches generated in different qubit modules and/or “quickswap” connections that selectably enable transferring the state of a surface code patch from one qubit module to another. Port and/or quickswap connections can be made between a subset of qubit modules. For instance port connections can connect a given qubit module to other qubit modules within a fixed range. Quickswap connections can provide a log-tree network of direct connections between qubit modules.

Abstract: A fault-tolerant quantum computer using topological codes such as surface codes can have an architecture that reduces the amount of idle volume generated. The architecture can include qubit modules that generate surface code patches for different qubits and a network of interconnections between different qubit modules. The interconnections can include “port” connections that selectably enable coupling of boundaries of surface code patches generated in different qubit modules and/or “quickswap” connections that selectably enable transferring the state of a surface code patch from one qubit module to another. Port and/or quickswap connections can be made between a subset of qubit modules. For instance port connections can connect a given qubit module to other qubit modules within a fixed range. Quickswap connections can provide a log-tree network of direct connections between qubit modules.

Abstract: A fault-tolerant quantum computer using topological codes such as surface codes can have an architecture that reduces the amount of idle volume generated. The architecture can include qubit modules that generate surface code patches for different qubits and a network of interconnections between different qubit modules. The interconnections can include “port” connections that selectably enable coupling of boundaries of surface code patches generated in different qubit modules and/or “quickswap” connections that selectably enable transferring the state of a surface code patch from one qubit module to another. Port and/or quickswap connections can be made between a subset of qubit modules. For instance port connections can connect a given qubit module to other qubit modules within a fixed range. Quickswap connections can provide a log-tree network of direct connections between qubit modules.

Abstract: Circuits are provided that create entanglement among qubits having Gottesman-Kitaev-Preskill (GKP) encoding using photonic systems and structures. For example, networks of beam splitters and homodyne measurement circuits can be used to perform projective entangling measurements on GKP qubits from different quantum systems. In some embodiments. GKP qubits can be used to implement quantum computations using fusion-based quantum computing or other fault-tolerant quantum computing approaches.

Abstract: Fusion-based quantum computations can be implemented using a network of interleaving modules. Each interleaving module can receive or produce resource states consisting of entangled physical qubits and can include a set of reconfigurable fusion circuits that can be controlled to perform either fusion operations or single qubit measurements on pairs of qubits from different resource states, routing paths connected to the reconfigurable fusion circuits, and delay lines and routing switches that operate to select routing paths for qubits of the resource states, thereby implementing a desired combination of fusion operations and single qubit measurements. The routing paths can include local routing paths that couple to reconfigurable fusion circuits in the same interleaving module and network routing paths that couple a routing switch in one interleaving module to a reconfigurable fusion circuit in a different interleaving module within the network.

Abstract: A fault-tolerant quantum computer using topological codes such as surface codes can have an architecture that reduces the amount of idle volume generated. The architecture can include qubit modules that generate surface code patches for different qubits and a network of interconnections between different qubit modules. The interconnections can include “port” connections that selectably enable coupling of boundaries of surface code patches generated in different qubit modules and/or “quickswap” connections that selectably enable transferring the state of a surface code patch from one qubit module to another. Port and/or quickswap connections can be made between a subset of qubit modules. For instance port connections can connect a given qubit module to other qubit modules within a fixed range. Quickswap connections can provide a log-tree network of direct connections between qubit modules.

Abstract: A fault-tolerant quantum computer using topological codes such as surface codes can have an architecture that reduces the amount of idle volume generated. The architecture can include qubit modules that generate surface code patches for different qubits and a network of interconnections between different qubit modules. The interconnections can include “port” connections that selectably enable coupling of boundaries of surface code patches generated in different qubit modules and/or “quickswap” connections that selectably enable transferring the state of a surface code patch from one qubit module to another. Port and/or quickswap connections can be made between a subset of qubit modules. For instance port connections can connect a given qubit module to other qubit modules within a fixed range. Quickswap connections can provide a log-tree network of direct connections between qubit modules.

Abstract: A fault-tolerant quantum computer using topological codes such as surface codes can have an architecture that reduces the amount of idle volume generated. The architecture can include qubit modules that generate surface code patches for different qubits and a network of interconnections between different qubit modules. The interconnections can include “port” connections that selectably enable coupling of boundaries of surface code patches generated in different qubit modules and/or “quickswap” connections that selectably enable transferring the state of a surface code patch from one qubit module to another. Port and/or quickswap connections can be made between a subset of qubit modules. For instance port connections can connect a given qubit module to other qubit modules within a fixed range. Quickswap connections can provide a log-tree network of direct connections between qubit modules.

Abstract: A fault-tolerant quantum computer using topological codes such as surface codes can have an architecture that reduces the amount of idle volume generated. The architecture can include qubit modules that generate surface code patches for different qubits and a network of interconnections between different qubit modules. The interconnections can include “port” connections that selectably enable coupling of boundaries of surface code patches generated in different qubit modules and/or “quickswap” connections that selectably enable transferring the state of a surface code patch from one qubit module to another. Port and/or quickswap connections can be made between a subset of qubit modules. For instance port connections can connect a given qubit module to other qubit modules within a fixed range. Quickswap connections can provide a log-tree network of direct connections between qubit modules.

Abstract: A fault-tolerant quantum computer using topological codes such as surface codes can have an architecture that reduces the amount of idle volume generated. The architecture can include qubit modules that generate surface code patches for different qubits and a network of interconnections between different qubit modules. The interconnections can include “port” connections that selectably enable coupling of boundaries of surface code patches generated in different qubit modules and/or “quickswap” connections that selectably enable transferring the state of a surface code patch from one qubit module to another. Port and/or quickswap connections can be made between a subset of qubit modules. For instance port connections can connect a given qubit module to other qubit modules within a fixed range. Quickswap connections can provide a log-tree network of direct connections between qubit modules.

Abstract: Systems and methods for emulating a physical quantum system with a quantum computation. A model Hamiltonian that approximates a first quantization Hamiltonian of the physical quantum system is stored in memory. The physical system includes a plurality of particles. The first quantization Hamiltonian includes a plurality of first quantization energy operators, and the model Hamiltonian includes a plurality of energy terms corresponding to respective ones of the plurality of first quantization energy operators. Each energy term includes a respective energy operator, a respective energy register operator, and a respective inverse energy operator. The physical quantum system is emulated by performing a quantum computation on a plurality of qubits of the quantum computing system to emulate time evolution using the model Hamiltonian.