A multi-addend adder circuit used for multi-addend addition in a polar representation in stochastic computing. The multi-addend adder circuit includes a buffer circuit and a computing circuit, where the buffer circuit is configured to store to-be-buffered data for at least one cycle and output buffer data, and the computing circuit is configured to process a plurality of pieces of bitstream data and the buffer data and output one piece of bitstream data and the to-be-buffered data, where the piece of output bitstream data is a quotient of dividing a sum of summation data and the buffer data by a scale-down coefficient, the output to-be-buffered data is a remainder of dividing a sum of all summation data until a current cycle by the scale-down coefficient, and the summation data is a quantity of bits whose values are 1 in the plurality of pieces of first bitstream data.

A multi-addend adder circuit used for multi-addend addition in a polar representation in stochastic computing. The multi-addend adder circuit includes a buffer circuit and a computing circuit, where the buffer circuit is configured to store to-be-buffered data for at least one cycle and output buffer data, and the computing circuit is configured to process a plurality of pieces of bitstream data and the buffer data and output one piece of bitstream data and the to-be-buffered data, where the piece of output bitstream data is a quotient of dividing a sum of summation data and the buffer data by a scale-down coefficient, the output to-be-buffered data is a remainder of dividing a sum of all summation data until a current cycle by the scale-down coefficient, and the summation data is a quantity of bits whose values are 1 in the plurality of pieces of first bitstream data.

An adding circuit, device and method for adding M binary operands/numbers. The binary operand (i) of the M binary operands has Ni bits. First, for i=1, . . . , M and j=1, . . . , Ni, the bit (i,j) is applied to a switch (i,j) that might be on if the bit (i,j) is 1, and off if the bit (i,j) is 0. Then a direct current (i,j) is sent through the switch (i,j), the direct current (i,j) having a value of (a) 2.sup.j1 if the switch (i,j) is on, and (b) zero if the switch (i,j) is off. All the direct currents (i,j) with their self-summing capabilities are merged into a combined current on an electrically conductive line. An ammeter on the electrically conductive line displays the decimal value of the sum of the M binary operands.

An adding circuit, device and method for adding M binary operands/numbers. The binary operand (i) of the M binary operands has Ni bits. First, for i=1, . . . , M and j=1, . . . , Ni, the bit (i,j) is applied to a switch (i,j) that might be on if the bit (i,j) is 1, and off if the bit (i,j) is 0. Then a direct current (i,j) is sent through the switch (i,j), the direct current (i,j) having a value of (a) 2.sup.j1 if the switch (i,j) is on, and (b) zero if the switch (i,j) is off. All the direct currents (i,j) with their self-summing capabilities are merged into a combined current on an electrically conductive line. An ammeter on the electrically conductive line displays the decimal value of the sum of the M binary operands.

The present embodiments relate to circuitry that efficiently performs floating-point arithmetic operations and fixed-point arithmetic operations. Such circuitry may be implemented in specialized processing blocks. If desired, the specialized processing blocks may include configurable interconnect circuitry to support a variety of different use modes. For example, the specialized processing block may efficiently perform a fixed-point or floating-point addition operation or a portion thereof, a fixed-point or floating-point multiplication operation or a portion thereof, a fixed-point or floating-point multiply-add operation or a portion thereof, just to name a few. In some embodiments, two or more specialized processing blocks may be arranged in a cascade chain and perform together more complex operations such as a recursive mode dot product of two vectors of floating-point numbers or a Radix-2 Butterfly circuit, just to name a few.

The present embodiments relate to circuitry that efficiently performs floating-point arithmetic operations and fixed-point arithmetic operations. Such circuitry may be implemented in specialized processing blocks. If desired, the specialized processing blocks may include configurable interconnect circuitry to support a variety of different use modes. For example, the specialized processing block may efficiently perform a fixed-point or floating-point addition operation or a portion thereof, a fixed-point or floating-point multiplication operation or a portion thereof, a fixed-point or floating-point multiply-add operation or a portion thereof, just to name a few. In some embodiments, two or more specialized processing blocks may be arranged in a cascade chain and perform together more complex operations such as a recursive mode dot product of two vectors of floating-point numbers or a Radix-2 Butterfly circuit, just to name a few.

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.

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 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.