Abstract: A method is provided for synthesizing quantum circuits while reducing the T-count, comprising, for a plurality of qubits: determining a target unitary and executing a set of candidate operations W with a single T gate and computing a specific function f of U W?1 keeping the values of W that correspond to specific multiplicities such that after the first collection of W operators is selected a collection of unitaries U W?1 is determined to consider in the next round to build a tree. A method of synthesizing quantum circuits while reducing the T-depth is also provided, comprising, for a plurality of qubits: determining a target unitary and execute a set of candidate operations W with T depth of one and computing a specific function f of U W?1, keeping the values of W that correspond to specific multiplicities such that after the first collection of W operators is selected a collection of unitaries U W?1 is determined to consider in the next round to build a tree.

Abstract: A method for signal suppression by increasing entropy in a system includes iteratively applying a set of electromagnetic (EM) pulses to the system, the set of EM pulses effecting swaps between the following pairs of system energy levels: a first system energy level in which the reset system is in a highest energy level and the target system is in a lowest target system energy level, and a corresponding second system energy level in which the reset system is in a highest energy level and the target system is in a highest target system energy level, and waiting a time period. This will suppress the signal of the target element. This for example can be a signal of a solvent in NMR.

Abstract: A system and method are provided for mitigating key-exhaustion attacks in a key exchange protocol. The method includes computationally confirming an exchange of key bits has provided fresh shared key material before information theoretically confirming the exchange of key bits has provided fresh shared key material, while maintaining synchronization between messaging parties. In one implementation, maintaining synchronization includes updating keys in between each post-processing message session and managing a local state of each messaging party in the key exchange protocol prior to sending a next post-processing message. In another implementation, maintaining synchronization includes hiding a message containing the information theoretic authenticator by executing a decoy authentication process, prior to using an information theoretical key.

Abstract: A system and method are provided for mitigating key-exhaustion attacks in a key exchange protocol. The method includes computationally confirming an exchange of key bits has provided fresh shared key material before information theoretically confirming the exchange of key bits has provided fresh shared key material, while maintaining synchronization between messaging parties. In one implementation, maintaining synchronization includes updating keys in between each post-processing message session and managing a local state of each messaging party in the key exchange protocol prior to sending a next post-processing message. In another implementation, maintaining synchronization includes hiding a message containing the information theoretic authenticator by executing a decoy authentication process, prior to using an information theoretical key.

Abstract: The present application recognizes the problem of reducing the CNOT-count in Clifford+ T circuits on connectivity constrained architectures. Here, one can “slice” the circuit at the position of Hadamard (H) gates and “build” the intermediate portions. Two kinds of partitioning are evaluated, namely: (i) a simple method of partitioning the gates of the input circuit based on the locality of H gates, and (ii) a second method of partitioning the phase polynomial of the input circuit. The intermediate {CNOT, T} sub-circuits can be synthesized using Steiner trees, similar to the work of Nash, Gheorghiu, Mosca [NGM20] and Kissinger, de Griend [KdG19]. The following algorithms have certain procedural differences that also help to further reduce the CNOT-count. The performances of the algorithms are compared while mapping different benchmark circuits as well as random circuits to some popular architectures like 9-qubit square grid, 16-qubit square grid, Rigetti 16qubit Aspen, 16-qubit IBM QX5, 20-qubit IBM Tokyo.

Abstract: A method is provided for synthesizing quantum circuits while reducing the T-count, comprising, for a plurality of qubits: determining a target unitary and executing a set of candidate operations W with a single T gate and computing a specific function f of U W?1 keeping the values of W that correspond to specific multiplicities such that after the first collection of W operators is selected a collection of unitaries U W?1 is determined to consider in the next round to build a tree. A method of synthesizing quantum circuits while reducing the T-depth is also provided, comprising, for a plurality of qubits: determining a target unitary and execute a set of candidate operations W with T depth of one and computing a specific function f of U W?1, keeping the values of W that correspond to specific multiplicities such that after the first collection of W operators is selected a collection of unitaries U W?1 is determined to consider in the next round to build a tree.

Abstract: Quantum Key Exchange (QKE, also known as Quantum Key Distribution or QKD) allows communicating parties to securely establish cryptographic keys. It is a well-established fact that all QKE protocols require that the parties have access to an authentic channel. Without this authenticated link, QKE is vulnerable to man-in-the-middle attacks. Overlooking this fact results in exaggerated claims and/or false expectations about the potential impact of QKE. In this paper we present a systematic comparison of QKE with traditional key establishment protocols in realistic secure communication systems.

Abstract: There is provided a method for implementing an algorithm for forming, or synthesizing, quantum circuits on a system capable of performing the quantum circuit synthesis by using a deterministic walk (i.e. a pseudo-random walk with a random or pseudo-random starting point). In one implementation, the deterministic walk is performed using a parallel search algorithm. In an implementation of the parallel search algorithm, a user utilizes a programming language to write instructions for a compiler. Then, a meet in the middle approach is utilized to separate the circuit into two halves. Next, the parallel search technique is used to find a claw, or a pair, which satisfies the circuit analysis. Subsequently there is the production of a result and/or a synthesis of the circuit if the pair is found.

Abstract: Quantum circuits include quantum gates that require a certain amount of physical resources. It is desirable to reduce the number of certain quantum gates in order to improve the hardware efficiency of a quantum circuit. A system and a method are provided for synthesizing a quantum circuit that includes the operations of determining an ordered set or vector of phase coefficients and specifying a linear permutation. The operations also include determining a sequence of CNOT and Rz gates using the set of phase coefficients and the linear permutation, such that the number of Rz gates is reduced.

Abstract: A method for decreasing entropy in a system includes iteratively applying a set of electromagnetic (EM) pulses to the system, the set of EM pulses effect swaps between the following pairs of system energy levels: a first system energy level in which the reset system is in a lowest energy level and the target system is in a first target system energy level that is not a lowest energy level, and a corresponding second system energy level in which the reset system is in a highest energy level and the target system is in a second target system energy level that is next lowest in energy after the first target system energy level, and waiting a time period.

Abstract: A method for decreasing entropy in a system includes iteratively applying a set of electromagnetic (EM) pulses to the system, the set of EM pulses effect swaps between the following pairs of system energy levels: a first system energy level in which the reset system is in a lowest energy level and the target system is in a first target system energy level that is not a lowest energy level, and a corresponding second system energy level in which the reset system is in a highest energy level and the target system is in a second target system energy level that is next lowest in energy after the first target system energy level, and waiting a time period.

Abstract: Quantum circuits include quantum gates that require a certain amount of physical resources. It is desirable to reduce the number of certain quantum gates in order to improve the hardware efficiency of a quantum circuit. A system and a method are provided for synthesizing a quantum circuit that includes the operations of determining an ordered set or vector of phase coefficients and specifying a linear permutation. The operations also include determining a sequence of CNOT and Rz gates using the set of phase coefficients and the linear permutation, such that the number of Rz gates is reduced.

Abstract: There is provided a method for implementing an algorithm for forming, or synthesizing, quantum circuits on a system capable of performing the quantum circuit synthesis by using a deterministic walk (i.e. a pseudo-random walk with a random or pseudo-random starting point). In one implementation, the deterministic walk is performed using a parallel search algorithm. In an implementation of the parallel search algorithm, a user utilizes a programming language to write instructions for a compiler. Then, a meet in the middle approach is utilized to separate the circuit into two halves. Next, the parallel search technique is used to find a claw, or a pair, which satisfies the circuit analysis. Subsequently there is the production of a result and/or a synthesis of the circuit if the pair is found.