Methods and systems for memory-based computing include combining multiple operations into a single lookup table and combining multiple memory-based operation requests into a single read request. Operation result values are read from a multi-operation lookup table that includes result values for a first operation above a diagonal of the lookup table and includes result values for a second operation below the diagonal. Numerical inputs are used as column and row addresses in the lookup table and the requested operation determines which input corresponds to the column address and which input corresponds to the row address. Multiple operations are combined into a single request by combining respective members from each operation into respective inputs an reading an operation result value from a lookup table to produce a combined result output. The combined result output is separated into a plurality of individual result outputs corresponding to the plurality of requests.

Methods and apparatus for optimizing a quantum circuit. In one aspect, a method includes identifying one or more sequences of operations in the quantum circuit that un-compute respective qubits on which the quantum circuit operates; generating an adjusted quantum circuit, comprising, for each identified sequence of operations in the quantum circuit, replacing the sequence of operations with an X basis measurement and a classically-controlled phase correction operation, wherein a result of the X basis measurement acts as a control for the classically-controlled correction phase operation; and executing the adjusted quantum circuit.

Methodology to reduce the running time of any string sorting algorithm is described. In one methodology, a prefix of each string from the input unsorted string array is converted to an integer and placed in an array. The array of integers is sorted using the given sorting algorithm. In subsequent methodology, the characters of the string prefix are placed in a record structure and stored in an array of character records. The array of character records is sorted using the given sorting algorithm. The input unsorted array of strings is then sorted using either the sorted array of integers or character records as a reference. Both methodologies showed performance improvements when running in sequential mode only. Therefore, parallel data sort methodology (PDS) was introduced allowing sorting algorithms to sort data in parallel, and its implementation made the two methodologies execute much faster in parallel mode.

Methods and apparatus for optimizing a quantum circuit. In one aspect, a method includes identifying one or more sequences of operations in the quantum circuit that un-compute respective qubits on which the quantum circuit operates; generating an adjusted quantum circuit, comprising, for each identified sequence of operations in the quantum circuit, replacing the sequence of operations with an X basis measurement and a classically-controlled phase correction operation, wherein a result of the X basis measurement acts as a control for the classically-controlled correction phase operation; and executing the adjusted quantum circuit.

Methods, systems and apparatus for performing windowed quantum arithmetic. In one aspect, a method for performing a product addition operation includes: determining multiple entries of a lookup table, comprising, for each index in a first set of indices, multiplying the index value by a scalar for the product addition operation; for each index in a second set of indices, determining multiple address values, comprising extracting source register values corresponding to indices between i) the index in the second set of indices, and ii) the index in the second set of indices plus the predetermined window size; and adjusting values of a target quantum register based on the determined multiple entries of the lookup table and the determined multiple address values.

Methods and apparatus for optimizing a quantum circuit. In one aspect, a method includes identifying one or more sequences of operations in the quantum circuit that un-compute respective qubits on which the quantum circuit operates; generating an adjusted quantum circuit, comprising, for each identified sequence of operations in the quantum circuit, replacing the sequence of operations with an X basis measurement and a classically-controlled phase correction operation, wherein a result of the X basis measurement acts as a control for the classically-controlled correction phase operation; and executing the adjusted quantum circuit.

Methods and apparatus for performing surface code computations using Auto-CCZ states. In one aspect, a method for implementing a delayed choice CZ operation on a first and second data qubit using a quantum computer includes: preparing a first and second routing qubit in a magic state; interacting the first data qubit with the first routing qubit and the second data qubit with the second routing qubit using a first and second CNOT operation, where the first and second data qubits act as controls for the CNOT operations; if a received first classical bit represents an off state: applying a first and second Hadamard gate to the first and second routing qubit; measuring the first and second routing qubit using Z basis measurements to obtain a second and third classical bit; and performing classically controlled fixup operations on the first and second data qubit using the second and third classical bits.

Methods and apparatus for piecewise addition into an accumulation register using one or more carry runway registers, where the accumulation register includes a first plurality of qubits with each qubit representing a respective bit of a first binary number and where each carry runway register includes multiple qubits representing a respective binary number. In one aspect, a method includes inserting the one or more carry runway registers into the accumulation register at respective predetermined qubit positions, respectively, of the accumulation register; initializing each qubit of each carry runway register in a plus state; applying one or more subtraction operations to the accumulation register, where each subtraction operation subtracts a state of a respective carry runway register from a corresponding portion of the accumulation register; and adding one or more input binary numbers into the accumulation register using piecewise addition.

A computer-implemented method for generating one or more random numbers includes configuring a mapper to feed inputs of a random number generation system using a subset of noise sources from multiple noise sources. The random number generation system generates a random number based on the inputs. The method further includes evaluating the subset of noise sources and detecting that a first noise source from the subset of noise sources has degraded in quality. The method further includes evaluating a second noise source from the available noise sources, the second noise source not being in the subset of noise sources. In response to the second noise source satisfying a predetermined threshold criterion, the first noise source is replaced with the second in the subset of noise sources for providing random bit streams to facilitate generating the random number by the random number generation system.

A computer-implemented method for generating one or more random numbers includes configuring a mapper to feed inputs of a random number generation system using a subset of noise sources from multiple noise sources. The random number generation system generates a random number based on the inputs. The method further includes evaluating the subset of noise sources and detecting that a first noise source from the subset of noise sources has degraded in quality. The method further includes evaluating a second noise source from the available noise sources, the second noise source not being in the subset of noise sources. In response to the second noise source satisfying a predetermined threshold criterion, the first noise source is replaced with the second in the subset of noise sources for providing random bit streams to facilitate generating the random number by the random number generation system.