Twirling noise affecting quantum gates is essential in understanding and controlling errors, but applicable operations to noise are usually restricted by symmetries inherent in quantum gates. In this work, we propose symmetric Cli...
Quantum computingClifford algebrasWe propose to represent both n n --qubits and quantum gates acting on them as elements in the complex Clifford algebra defined on a complex vector space of dimension 2n. 2n. In this framework, the Dirac formalism can be realized in straightforward way. We ...
Motivated by their central role in fault-tolerant quantum computation, we study the sets of gates of the third-level of the Clifford hierarchy and their distinguished subsets of ‘nearly diagonal’ semi-Clifford gates. The Clifford hierarchy gates can be implemented via gate teleportation given appro...
The conventional circuit paradigm, utilizing a small set of gates to construct arbitrary quantum circuits, is hindered by significant noise. In the quantum Fourier transform, for instance, the standard gate paradigm employs two CNOT gates for the partial
the two-qubit gate has notably lower fidelity than a single-qubit gate. Thus, to the first degree of approximation, the fidelity of an entire quantum computation depends on the number of two-qubit gates it uses. To make a more subtle point, since the single-qubit gates are most frequently...
circuits composed of only CNOT, Hadamard, and \pi/4 \pi/4 phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and Knill states that Clifford circuits are efficiently classically simulable. We...
Reaching useful fault-tolerant quantum computation relies on successfully implementing quantum error correction (QEC). In QEC, quantum gates and measurements are performed to encode quantum logic in a spatially nonlocal wavefunction within an error protected Hilbert space. To reach protected logic, clas...
We show that the Clifford gates and stabilizer circuits in the quantum computing literature, which admit efficient classical simulation, are equivalent to affine signatures under a unitary condition. The latter is a known class of tractable functions under the Holant framework....
Unlike other libraries considered so far, it consists of only a small number of gates for all of which robust, fault-tolerant realizations are known for many technologies that seem to be promising for large-scale quantum computing. As a consequence, (logic) synthesis of Clifford+T quantum ...
Efficient design of a quantum absolute-value circuit using Clifford+T gatesReversible gateQuantum circuitT-countAbsolute-valueQuantum computingCurrent quantum computers have a limited number of resources and are heavily affected by internal and external noise. Therefore, small, noise-tolerant circuits are...