A multiplier-accumulator includes: a plurality of exclusive negative OR (XNOR) gates provided along one or more input lines and configured to receive signals corresponding to an input bit sequence and a weight bit sequence corresponding to each of the one or more input lines and to output partial product results between the input bit sequence and the weight bit sequence; an encoder configured to apply, to the plurality of XNOR gates, a signal corresponding to a sequence in which a logical value of a most significant bit (MSB) is converted from an original sequence expressed in 2's complement of a corresponding sequence for either one or both of the input bit sequence and the weight bit sequence; and an outputter configured to generate an output in which a correction value is applied to operation results in which the partial product results output from the plurality of XNOR gates are summed.

The present invention discloses a computing array based on 1T1R device, operation circuits and operating methods thereof. The computing array has 1T1R arrays and a peripheral circuit; the 1T1R array is configured to achieve operation and storage of an operation result, and the peripheral circuit is configured to transmit data and control signals to control operation and storage processes of the 1T1R arrays; the operation circuits are respectively configured to implement a 1-bit full adder, a multi-bit step-by-step carry adder and optimization design thereof, a 2-bit data selector, a multi-bit carry select adder and a multi-bit pre-calculation adder; and in the operating method corresponding to the operation circuit, initialized resistance states of the 1T1R devices, word line input signals, bit line input signals and source line input signals are controlled to complete corresponding operation and storage processes.

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.

An apparatus with multi-format data support includes: a receiver configured to receive a plurality of data corresponding to a plurality of data formats; one or more processors configured to: multiply the plurality of data using one or more multipliers; perform a first alignment on a result of the multiplication based on an exponent value of the plurality of data; add a result of the first alignment; and perform a second alignment on a result of the addition based on the exponent value and an operation result of a previous cycle.

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.

Systems, apparatuses and methods may provide for technology that conducts, by a differential signal path, signed multiply-accumulate (MAC) operations on first analog signals and multibit weight data stored in the differential signal path, and outputs, by the differential signal path, second analog signals based on the signed MAC operations.

A binary logic circuit converts a number in floating point format having an exponent E of ew bits, an exponent bias B given by B = 2.sup.ew-1 - 1, and a significand comprising a mantissa M of mw bits into a fixed point format with an integer width of iw bits and a fractional width of fw bits. The circuit includes a shifter operable to receive a significand input comprising a contiguous set of the most significant bits of the significand and configured to left-shift the significand input by a number of bits equal to the value represented by k least significant bits of the exponent to generate a shifter output, wherein min{(ew - 1), bitwidth(iw - 2 - s.sub.y)} ≤ k ≤ (ew - 1) where s.sub.y = 1 for a signed floating point number and s.sub.y = 0 for an unsigned floating point number, and a multiplexer coupled to the shifter and configured to: receive an input comprising a contiguous set of bits of the shifter output; and output the input if the most significant bit of the exponent is equal to one.

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.

Floating point Multiply-Add, Accumulate Unit, supporting BF16 format for Multiply-Accumulate operations, and FP32 Single-Precision Addition complying with the IEEE 754 Standard. The Multiply-Accumulate unit uses higher radix and longer internal 2's complement significand representation to facilitate precision as well as comparison and operation with negative numbers. The addition is performed using Carry-Save format to avoid long carry propagation and speed up the operation. Operations including overflow detection, zero detection and sign extension are adopted for 2s complement and Carry-Save format. Handling of Overflow and Sign Extension allows for fast operation relatively independent on the size of the accumulator.

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.