Google Inc.

Austin Greig Fowler

John Martinis

Rami Barends

Craig Gidney

Ryan Babbush

Hartmut Neven

Yu Chen

Alireza Shabani Barzegar

Jonathan Arthur Gross

Alexandru Paler

Chen Yu

Methods, systems, and apparatus for performing low overhead quantum computations using lattice surgery. In one aspect, an apparatus includes a multi-qubit lattice defining a plurality of qubit rows and plurality of qubit columns, comprising: two or more separate row portions of rotated logical qubits, each row portion comprising a plurality of rotated logical qubits that are each adjacent to each other, each rotated logical qubit comprising: a plurality of data qubits, and a plurality of measure qubits; two or more separate row portions of inactive qubits, each row portion defining a plurality of inactive qubits; wherein: each row portion of rotated logical qubits is adjacent a row portion of inactive qubits.

Low overhead quantum computation using lattice surgery

Methods, systems, and apparatus for operating a system of qubits. In one aspect, a method includes operating a first qubit from a first plurality of qubits at a first qubit frequency from a first qubit frequency region, and operating a second qubit from the first plurality of qubits at a second qubit frequency from a second first qubit frequency region, the second qubit frequency and the second first qubit frequency region being different to the first qubit frequency and the first qubit frequency region, respectively, wherein the second qubit is diagonal to the first qubit in a two-dimensional grid of qubits.

Frequency pattern for reducing parasitic interactions in a qubit grid

Systems and methods for tracking errors in a quantum computing system are provided. In one example, a method can include matching data associated with one or more detection events associated with a quantum computing system using a successive pattern structure comprising a plurality of processing layers. Each processing layer in the plurality of processing layers can be associated with a pattern including a plurality of sections. Each section can be associated with a processing unit operable to match one or more detection events near a center of the section. The method can include tracking one or more errors of a quantum computing system based at least in part on a matching of one or more detection events.

Low latency scalable parallel streaming matching for quantum computing systems

Methods, systems and apparatus for quantum error correction. A layered representation of error propagation through quantum error detection circuits is constructed. The layered representation includes multiple line circuit layers that each represent a probability of local detection events in a quantum computing system associated with potential error processes in an execution of a quantum algorithm. To construct the layered representation, potential detection events associated with each potential error process occurring at quantum gates in the quantum circuit are determined. Lines are associated with each potential error process, the lines each connecting a potential detection event associated with the potential error process to another potential detection event associated with the same potential error process or a boundary of the quantum circuit. Similar lines are merged and used to construct unique line circuit layers. The layered representation is transmitted to the quantum computing system prior to execution of the quantum algorithm.

Quantum error correction

Methods, systems, and apparatus for producing CCZ states and T states. In one aspect, a method for transforming a CCZ state into three T states includes obtaining a first target qubit, a second target qubit and a third target qubit in a CCZ state; performing a Xgate on the third target qubit; performing an X gate on the first target qubit and the second target qubit using the third target qubit as a control; performing a Z gate on the first target qubit and the second target qubit using the third qubit as a X axis control; performing a Zgate on the third target qubit; and performing a Z gate on the first target qubit and the second target qubit using the third qubit as a X axis control to obtain the three T states.

Magic state factory constructions for producing CCZ and T states

Methods, systems and apparatus for approximating a target quantum state that is defined as a result of applying a specific rotation operation to an initial quantum state. A method includes determining multiple configurations of T-gates. Each configuration of T-gates includes a number of T-gates that is less than or equal to a predefined total number of T-gates and represents a rotation operation that, when applied to the initial quantum state, produces an evolved quantum state that is an approximation of the target quantum state. A configuration of T-gates that represents a rotation operation with a rotation angle that is closest to a rotation angle of the specific rotation operation is selected from the multiple configurations of T-gates. A rotation operation represented by the selected configuration of T-gates is applied to the initial quantum state to obtain the approximation of the target quantum state.

Error corrected variational algorithms

Apparatus for quantum error correction is disclosed. The apparatus includes an array of processing cores, each processing core comprising: a processor on a first chip; and a processor cache on the first chip; and a bus for interconnecting neighbouring processing cores in the array of processing cores; wherein each processing core includes: control code which, when executed by the processor, causes the processor to access a processor cache of at least one neighbouring processing core.

Methods and systems for performing a surface code error detection cycle. In one aspect, a method includes initializing and applying Hadamard gates to multiple measurement qubits; performing entangling operations on a first set of paired qubits, wherein each pair comprises a measurement qubit coupled to a neighboring data qubit in a first direction; performing entangling operations on a second set of paired qubits, wherein each pair comprises a measurement qubit coupled to a neighboring data qubit in a second or third direction, the second and third direction being perpendicular to the first direction, the second direction being opposite to the third direction; performing entangling operations on a third set of paired qubits, wherein each pair comprises a measurement qubit coupled to a neighboring data qubit in a fourth direction, the fourth direction being opposite to the first direction; applying Hadamard gates to the measurement qubits; and measuring the measurement qubits.

Reducing parasitic interactions in a qubit grid for surface code error correction

A computer-implemented method for correcting one or more errors in a quantum computing system can include obtaining, by a computing system comprising one or more computing devices, a plurality of weighted detection graphs, each of the plurality of weighted detection graphs being descriptive of a plurality of error detection measurements and having a plurality of weights, each of the weights respectively determined according to an error probability. The method can include generating, by the computing system, a plurality of reweighted detection graphs based at least in part on a correlation between physical errors in the quantum computing system. The method can include correcting, by the computing system, one or more errors in a quantum computing system based at least in part on a global decoding of the plurality of reweighted detection graphs.

Preprocessing for correlated topological quantum error correction

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.

Surface code computations using Auto-CCZ quantum states

Methods, systems, and apparatus for producing CCZ states and T states. In one aspect, a method for distilling a CCZ state includes preparing multiple target qubits, ancilla qubits and stabilizer qubits in a zero state, performing an X gate for each stabilizer qubit on multiple ancilla qubits or multiple ancilla qubits and one of the target qubits using the stabilizer qubit as a control, measuring the stabilizer qubits, performing, on each of the ancilla qubits, a Zgate and a Hadamard gate, measuring each of the ancilla qubits, performing, conditioned on each measured ancilla qubit state, a NOT operation on a selected stabilizer qubit, or a NOT operation on the selected stabilizer qubit and a Z gate on one or more respective target qubits, performing, on each target qubit and conditioned on a measured state of a respective stabilizer qubit, a Z gate on the target qubit, and performing an X gate on each of the target qubits.

Methods, systems and apparatus for approximating a target quantum state. In one aspect, a method for determining a target quantum state includes the actions of receiving data representing a target quantum state of a quantum system as a result of applying a quantum circuit to an initial quantum state of the quantum system; determining an approximate quantum circuit that approximates the specific quantum circuit by adaptively adjusting a number of T gates available to the specific quantum circuit; and applying the determined approximate quantum circuit to the initial quantum state to obtain an approximation of the target quantum state.

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Reseda, CA, United States of America

Austin Greig Fowler