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 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.

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.

In-memory arithmetic processors for the “n-bit” by “n-bit” multiplication, the “n-bit” by “n-bit” addition, and the “n-bit” by “n-bit” subtraction operations are disclosed. The in-memory arithmetic processors of the invention can obtain the operational resultant integer in the binary format for two inputted integers represented by two “n-bit” binary codes in one-step processing with no sequential multiple-step operations as for the conventional arithmetic binary processors. The in-memory arithmetic processors are implemented by a 2-dimensional memory array with X and Y decoding for the two inputted operational integers in the arithmetic binary operations.

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 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.

An adder device for binary magnetic applied fields uses Interlayer Exchange Coupling (IEC) structure where two layers of ferromagnetic material are separated from each other by non-magnetic layers of electrically conductive material of atomic thickness, sufficient to generate anti-magnetic response in a magnetized layer. A set of regions are positioned on a top layer above a continuous bottom layer, and the regions excited with magnetization for A and not A, B and not B, and C and not C to form a sum and an inverse carry output magnetization.

An adder device for binary magnetic applied fields uses Interlayer Exchange Coupling (IEC) structure where two layers of ferromagnetic material are separated from each other by non-magnetic layers of electrically conductive material of atomic thickness, sufficient to generate anti-magnetic response in a magnetized layer. A set of regions are positioned on a top layer above a continuous bottom layer, and the regions excited with magnetization for A and not A, B and not B, and C and not C to form a sum and an inverse carry output magnetization.

A combined adder for N logical bits to produce a sum from a first addend having N first addend bits and a second addend having N second addend bits. A least significant adder produces a segment sum of the least significant bits and a carry out. Segment adder pairs are used for each higher order of significant sums. One segment adder produces a segment sum portion, and the other produces an incremented segment sum portion. Carry logic associated with each segment is utilized with a multiplexer to select the incremented segment sum portion or the segment sum portion. The selected segment sum portions are assembled with a most significant carry out to produce the sum.

A combined adder for N logical bits to produce a sum from a first addend having N first addend bits and a second addend having N second addend bits. A least significant adder produces a segment sum of the least significant bits and a carry out. Segment adder pairs are used for each higher order of significant sums. One segment adder produces a segment sum portion, and the other produces an incremented segment sum portion. Carry logic associated with each segment is utilized with a multiplexer to select the incremented segment sum portion or the segment sum portion. The selected segment sum portions are assembled with a most significant carry out to produce the sum.