Abstract: Aspects of the disclosure for reducing a qubit count employed by a quantum circuit include performing a geometric transformation to boundaries of a three-dimensional (3D) toric code, wherein a Hermite normal form is utilized to parameterize the geometric transformation. Aspects include transforming the 3D toric code to a two-dimensional (2D) toric code for the quantum circuit and causing the quantum circuit to execute the 2D toric code.

Abstract: Aspects of the disclosure for reducing a qubit count employed by a quantum circuit include performing a geometric transformation to boundaries of a three-dimensional (3D) toric code, wherein a Hermite normal form is utilized to parameterize the geometric transformation. Aspects include transforming the 3D toric code to a two-dimensional (2D) toric code for the quantum circuit and causing the quantum circuit to execute the 2D toric code.

Abstract: Aspects of the disclosure include removing a faulty qubit in a quantum circuit. The faulty qubit is determined to be in the quantum circuit, the faulty qubit being associated with a plaquette having other qubits, where adjacent plaquettes are neighboring the plaquette. A route is determined to isolate the plaquette from the adjacent plaquettes. Measurements are caused to be performed on the quantum circuit for the route that isolates the plaquette having the faulty qubit and the other qubits.

Abstract: A method and apparatus for performing quantum error correction using an automorphism code related to the honeycomb code. The automorphism code is based on Kramers-Wannier (KW) duality. For embodiments on a hexagonal lattice using three repeated time steps, ? of the pixels are active in a given time steps. In a given time step r, a KW circuit is applied to plaquettes labeled r mod 3, transferring quantum information from the active qubits at the beginning to a new set of active qubits at the end of the time step. Each of the three plaquette types is associated with one stabilizer either given by a product of six Z operators or three X operators. The KW circuit maps the product of X operators to the product of Z operators and vice-versa. The stabilizer group of the superlattice toric code changes every round.

Abstract: In a quantum-computation method, quantum-computer code is received for execution on a quantum computer. The quantum computer includes a plurality of qubits associated with a corresponding plurality of particles, and the plurality of particles define a quantum state. The quantum-computer code is decomposed into a sequence of operations including a total spin-state measurement on particles corresponding to two or more of the qubits. Then the sequence of operations is applied on the plurality of particles to thereby transform the quantum state according to the quantum-computer code initially received.

Abstract: Examples are disclosed that relate to, on a quantum computing device, distilling magic states encoded in a [[n,k,d]] block code comprising an outer code. One example provides a method comprising preparing encoded noisy magic states using data qubits, and measuring Clifford stabilizers on the data qubits, thereby applying an inner code. The method further comprises initializing output qubits and initiating a teleportation of distilled magic states derived from the encoded noisy magic states to the output qubits. The method further comprises measuring X-stabilizers on the data qubits, postselecting based on the outcomes, measuring each data qubit destructively utilizing Z-stabilizers, and applying one or more postselection conditions to the data qubits to complete the teleportation of the distilled magic states to the output qubits.

Abstract: Classical and quantum computational systems and methods for principal component analysis of multi-dimensional datasets are presented. A dataset is encoded in a tensor of rank p, where p is a positive integer that may be greater than 2. The classical methods are based on linear algebra. The quantum methods achieve a quartic speedup while using exponentially smaller space than the fastest classical algorithm, and a super-polynomial speedup over classical algorithms that use only polynomial space. In particular, an improved threshold for recovery is achieved. The presented classical and quantum methods work for both even and odd ranked tensors. Accordingly, quantum computation may be applied to large-scale inference problems, e.g., machine learning applications or other applications that involve highly-dimensional datasets.

Abstract: Performance management systems and methods may utilize a plurality of modules. A performance network module may receive a post from a user and cause the post to be displayed on a display, and receive a comment associated with the post from the user and cause the post to be displayed on the display. A report module may generate a report including a question and send the report to the user, and receive an answer to the question in the report from the user and store the answer in a database. A goal module may receive a goal and/or an update to the goal, and update a status associated with the goal. A review module may generate a review including a question and send the review to the user, and receive an answer to the question in the review from the user and store the answer in the database.