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.

A domino full adder based on delayed gating positive feedback comprises a first PMOS transistor, a second PMOS transistor, a third PMOS transistor, a fourth PMOS transistor, a fifth PMOS transistor, a sixth PMOS transistor, a seventh PMOS transistor, an eighth PMOS transistor, a ninth PMOS transistor, a first NMOS transistor, a second NMOS transistor, a third NMOS transistor, a fourth NMOS transistor, a fifth NMOS transistor, a sixth NMOS transistor, a seventh NMOS transistor, an eighth NMOS transistor, a ninth NMOS transistor, a tenth NMOS transistor, an eleventh NMOS transistor, a first inverter, a second inverter, a third inverter and a fourth inverter.

Massively parallel neural inference computing elements are provided. A plurality of multipliers is arranged in a plurality of equal-sized groups. Each of the plurality of multipliers is adapted to, in parallel, apply a weight to an input activation to generate an output. A plurality of adders is operatively coupled to one of the groups of multipliers. Each of the plurality of adders is adapted to, in parallel, add the outputs of the multipliers within its associated group to generate a partial sum. A plurality of function blocks is operatively coupled to one of the plurality of adders. Each of the plurality of function blocks is adapted to, in parallel, apply a function to the partial sum of its associated adder to generate an output value.

Massively parallel neural inference computing elements are provided. A plurality of multipliers is arranged in a plurality of equal-sized groups. Each of the plurality of multipliers is adapted to, in parallel, apply a weight to an input activation to generate an output. A plurality of adders is operatively coupled to one of the groups of multipliers. Each of the plurality of adders is adapted to, in parallel, add the outputs of the multipliers within its associated group to generate a partial sum. A plurality of function blocks is operatively coupled to one of the plurality of adders. Each of the plurality of function blocks is adapted to, in parallel, apply a function to the partial sum of its associated adder to generate an output value.

An arithmetic logic unit (ALU) including a binary, parallel adder and multiplier to perform arithmetic operations is described. The ALU includes an adder circuit coupled to a multiplexer to receive input operands that are directed to either an addition operation or a multiplication operation. During the multiplication operation, the ALU is configured to determine partial product operands based on first and second operands and provide the partial product operands to the adder circuit via the multiplexer, and the adder circuit is configured to provide an output having a value equal to a product of the first operand second operands. During an addition operation, the ALU is configured to provide the first and second operands to the adder circuit via the multiplexer, and the adder circuit is configured to provide the output having a value equal to a sum of the first and second operands.

An arithmetic logic unit (ALU) including a binary, parallel adder and multiplier to perform arithmetic operations is described. The ALU includes an adder circuit coupled to a multiplexer to receive input operands that are directed to either an addition operation or a multiplication operation. During the multiplication operation, the ALU is configured to determine partial product operands based on first and second operands and provide the partial product operands to the adder circuit via the multiplexer, and the adder circuit is configured to provide an output having a value equal to a product of the first operand second operands. During an addition operation, the ALU is configured to provide the first and second operands to the adder circuit via the multiplexer, and the adder circuit is configured to provide the output having a value equal to a sum of the first and second operands.

Disclosed is a method for configuring an MSD parallel adder based on ternary logic operators. Five ternary logic operators that satisfy a sufficient condition for MSD addition are used to configure an MSD parallel adder. During the arrangement of a ternary logic operator, any method in the following may be used: each of ternary operators of n bits is reconfigured into a ternary logic operator each time, and reconfiguration is performed five times for implementation; each of ternary operators of n bits is reconfigured into two ternary logic operators having the same input each time, and reconfiguration is performed three times for implementation; each of ternary operators of n bits is reconfigured into five ternary logic operators of the same time, and reconfiguration is performed once for implementation; corresponding unreconfigurable ternary logic operators are used instead for the foregoing reconfiguration process.

Disclosed is a method for configuring an MSD parallel adder based on ternary logic operators. Five ternary logic operators that satisfy a sufficient condition for MSD addition are used to configure an MSD parallel adder. During the arrangement of a ternary logic operator, any method in the following may be used: each of ternary operators of n bits is reconfigured into a ternary logic operator each time, and reconfiguration is performed five times for implementation; each of ternary operators of n bits is reconfigured into two ternary logic operators having the same input each time, and reconfiguration is performed three times for implementation; each of ternary operators of n bits is reconfigured into five ternary logic operators of the same time, and reconfiguration is performed once for implementation; corresponding unreconfigurable ternary logic operators are used instead for the foregoing reconfiguration process.

An in-memory vector addition method for a dynamic random access memory (DRAM) is disclosed which includes consecutively transposing two numbers across a plurality of rows of the DRAM, each number transposed across a fixed number of rows associated with a corresponding number of bits, assigning a scratch-pad including two consecutive bits for each bit of each number being added, two consecutive bits for carry-in (C.sub.in), and two consecutive bits for carry-out-bar (C.sub.out), assigning a plurality of bits in a transposed orientation to hold results as a sum of the two numbers, for each bit position of the two numbers: computing the associated sum of the bit position; and placing the computed sum in the associated bit of the sum.

An integrated circuit that includes very large adder circuitry is provided. The very large adder circuitry receives more than two inputs each of which has hundreds or thousands of bits. The very large adder circuitry includes multiple adder nodes arranged in a tree-like network. The adder nodes divide the input operands into segments, computes the sum for each segment, and computes the carry for each segment independently from the segment sums. The carries at each level in the tree are accumulated using population counters. After the last node in the tree, the segment sums can then be combined with the carries to determine the final sum output. An adder tree network implemented in this way asymptotically approaches the area and performance latency as an adder network that uses infinite speed ripple carry adders.