Abstract: A method of training a quantum computer employs quantum algorithms. The method comprises loading, into the quantum computer, a description of a quantum Boltzmann machine, and training the quantum Boltzmann machine according to a protocol, wherein a classification error is used as a metric for the protocol.

Abstract: This disclosure focuses on example embodiments of a classical approach to the problem of quantum error correction in the presence of faults. Linear codes equipped with faulty parity measurements are disclosed. Example definitions of fault tolerance are introduced and embodiments of a fault tolerant scheme are disclosed that reduce the number of parity measurements required compared with Shor method. Such schemes are well suited to be implemented in the classical control device of a quantum computer in order to ensure quantum fault tolerance.

Abstract: This disclosure concerns tools and techniques for debugging a quantum program (e.g., a program used to configure and control a quantum computing device). Because the state space of a quantum program is so much larger and less structured than the state space for a classical program, new techniques are required to help the program developer and coder determine whether or not their program is working correctly and to identify errors if not. The disclosed technology provides tools and techniques for debugging quantum programs using a classical computer.

Abstract: This disclosure concerns tools and techniques for debugging a quantum program (e.g., a program used to configure and control a quantum computing device). Because the state space of a quantum program is so much larger and less structured than the state space for a classical program, new techniques are required to help the program developer and coder determine whether or not their program is working correctly and to identify errors if not. The disclosed technology provides tools and techniques for debugging quantum programs using a classical computer.

Abstract: This disclosure concerns tools and techniques for debugging a quantum program (e.g., a program used to configure and control a quantum computing device). Because the state space of a quantum program is so much larger and less structured than the state space for a classical program, new techniques are required to help the program developer and coder determine whether or not their program is working correctly and to identify errors if not. The disclosed technology provides tools and techniques for debugging quantum programs using a classical computer.

Abstract: The disclosed technology includes, among other innovations, a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. In particular embodiments, the disclosed technology reduces the memory footprint of a reversible network implemented in a quantum computer and generated from a higher-level program. Such a reduced-memory footprint is desirable in that it addresses the limited availability of qubits available in many target quantum computer architectures.

Abstract: Boltzmann machines are trained using an objective function that is evaluated by sampling quantum states that approximate a Gibbs state. Classical processing is used to produce the objective function, and the approximate Gibbs state is based on weights and biases that are refined using the sample results. In some examples, amplitude estimation is used. A combined classical/quantum computer produces suitable weights and biases for classification of shapes and other applications.

Abstract: A Probabilistic Quantum Circuit with Fallback (PQFs) is composed as a series of circuit stages that are selected to implement a target unitary. A final stage is conditioned on unsuccessful results of all the preceding stages as indicated by measurement of one or more ancillary qubits. This final stage executes a fallback circuit that enforces deterministic execution of the target unitary at a relatively high cost (mitigated by very low probability of the fallback). Specific instances of general PQF synthesis method and are disclosed with reference to the specific Clifford+T, Clifford+V and Clifford+?/12 bases. The resulting circuits have expected cost in logb(1/?)+O(log(log(1/?)))+const wherein b is specific to each basis. The three specific instances of the synthesis have polynomial compilation time guarantees.

Abstract: This disclosure focuses on example embodiments of a classical approach to the problem of quantum error correction in the presence of faults. Linear codes equipped with faulty parity measurements are disclosed. Example definitions of fault tolerance are introduced and embodiments of a fault tolerant scheme are disclosed that reduce the number of parity measurements required compared with Shor method. Such schemes are well suited to be implemented in the classical control device of a quantum computer in order to ensure quantum fault tolerance.

Abstract: The disclosed technology includes, among other innovations, a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. In particular embodiments, the disclosed technology reduces the memory footprint of a reversible network implemented in a quantum computer and generated from a higher-level program. Such a reduced-memory footprint is desirable in that it addresses the limited availability of qubits available in many target quantum computer architectures.

Abstract: Embodiments of a new approach for training a class of quantum neural networks called quantum Boltzmann machines are disclosed. in particular examples, methods for supervised training of a quantum Boltzmann machine are disclosed using an ensemble of quantum states that the Boltzmann machine is trained to replicate. Unlike existing approaches to Boltzmann training, example embodiments as disclosed herein allow for supervised training even in cases where only quantum examples are known (and not probabilities from quantum measurements of a set of states). Further, this approach does not require the use of approximations such as the Golden-Thompson inequality.

Abstract: The disclosed technology includes, among other innovations, a framework for resource efficient compilation of higher-level programs into lower-level reversible circuits. In particular embodiments, the disclosed technology reduces the memory footprint of a reversible network implemented in a quantum computer and generated from a higher-level program. Such a reduced-memory footprint is desirable in that it addresses the limited availability of qubits available in many target quantum computer architectures.

Abstract: Ripple-carry and carry look-ahead adders for ternary addition and other operations include circuits that produce carry values or carry status indicators that can be stored on qutrit registers associated with input values to be processed. Inverse carry circuits are situated to reverse operations associated with the production of carry values or carry status indicators, and restored values are summed with corresponding carry values to produce ternary sums.

Abstract: Quantum algorithms to solve practical problems in quantum chemistry, materials science, and matrix inversion often involve a significant amount of arithmetic operations. These arithmetic operations are to be carried out in a way that is amenable to the underlying fault-tolerant gate set, leading to an optimization problem to come close to the Pareto-optimal front between number of qubits and overall circuit size. In this disclosure, a quantum circuit library is provided for floating-point addition and multiplication. Circuits are presented that are automatically generated from classical Verilog implementations using synthesis tools and compared with hand-generated and hand-optimized circuits. Example circuits were constructed and tested using the software tools LIQUi| and RevKit.

Abstract: Nearest neighbor distances are obtained by coherent majority voting based on a plurality of available distance estimates produced using amplitude estimation without measurement in a quantum computer. In some examples, distances are Euclidean distances or are based on inner products of a target vector with vectors from a training set of vectors. Distances such as mean square distances and distances from a data centroid can also be obtained.

Abstract: The generation of reversible circuits from high-level code is desirable in a variety of application domains, including low-power electronics and quantum computing. However, little effort has been spent on verifying the correctness of the results, an issue of particular importance in quantum computing where such circuits are run on all inputs simultaneously. Disclosed herein are example reversible circuit compilers as well as tools and techniques for verifying the compilers. Example compilers disclosed herein compile a high-level language into combinational reversible circuits having a reduced number of ancillary bits (ancilla bits) and further having provably clean temporary values.

Abstract: In this application, example methods for performing quantum Montgomery arithmetic are disclosed. Additionally, circuit implementations are disclosed for reversible modular arithmetic, including modular addition, multiplication and inversion, as well as reversible elliptic curve point addition. This application also shows that elliptic curve discrete logarithms on an elliptic curve defined over an n-bit prime field can be computed on a quantum computer with at most 9n+2?log2(n)?+10 qubits using a quantum circuit of at most 512n3 log2(n)+3572n3 Toffoli gates.

Abstract: Among the embodiments disclosed herein are quantum circuits (and associated compilation techniques) for performing Shor's quantum algorithm to factor n-bit integers. Example embodiments of the circuits use only 2n+2 qubits. In contrast to previous space-optimized implementations, embodiments of the disclosed technology feature a purely Toffoli-based modular multiplication circuit. Certain other example modular multiplication circuits disclosed herein are based on an (in-place) constant-adder that uses dirty ancilla qubits to achieve a size in (n log n) and a depth in (n).

Abstract: Quantum circuits and circuit designs are based on factorizations of diagonal unitaries using a phase context. The cost/complexity of phase sparse/phase dense approximations is compared, and a suitable implementation is selected. For phase sparse implementations in the Clifford+T basis, required entangling circuits are defined based on a number of occurrences of a phase in the phase context in a factor of the diagonal unitary.

Abstract: This disclosure concerns tools and techniques for debugging a quantum program (e.g., a program used to configure and control a quantum computing device). Because the state space of a quantum program is so much larger and less structured than the state space for a classical program, new techniques are required to help the program developer and coder determine whether or not their program is working correctly and to identify errors if not. The disclosed technology provides tools and techniques for debugging quantum programs using a classical computer.