Related papers: Five-qubit states generated by Clifford gates
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
We introduce magic-augmented Clifford circuits -- architectures in which Clifford circuits are preceded and/or followed by constant-depth circuits of non-Clifford (``magic") gates -- as a resource-efficient way to realize approximate…
Stabilizer states admit compact classical descriptions, but many downstream tasks still require their full amplitude vectors. Since the output itself has size $2^n$, the main algorithmic question is whether one can materialize an $n$-qubit…
$k$-uniform states are valuable resources in quantum information, enabling tasks such as teleportation, error correction, and accelerated quantum simulations. The practical realization of $k$-uniform states, at scale, faces major obstacles:…
We consider the task of deciding whether an unknown qubit state falls in a prescribed neighborhood of a reference state. We assume that several copies of the unknown state are given and apply a unitary operation pairwise on them combined…
This work classifies stabilizer codes by the set of diagonal Clifford gates that can be implemented transversally on them. We show that, for any stabilizer code, its group of diagonal transversal Clifford gates on $\ell$ code blocks must be…
A scheme for implementing 2-qubit quantum controlled phase gate (QCPG) is proposed with two superconducting quantum interference devices (SQUIDs) in a cavity. The gate operations are realized within the two lower flux states of the SQUIDs…
We develop a simple and systematic route to higher levels of the qubit Clifford hierarchy by coherently controlling Clifford operations. Our approach is based on Pauli periodicity, defined for a Clifford unitary $U$ as the smallest integer…
A Hadamard-free Clifford transformation is a circuit composed of quantum Phase (P), CZ, and CNOT gates. It is known that such a circuit can be written as a three-stage computation, -P-CZ-CNOT-, where each stage consists only of gates of the…
We systematically construct and classify fault-tolerant logical gates implemented by constant-depth circuits for quantum codes using cohomology operations and symmetry. These logical gates are obtained from unitary operators given by…
We consider a model of two interacting always-on, exchange-only qubits for which controlled phase ($CPHASE$), controlled NOT ($CNOT$), quantum Fourier transform ($QFT$) and $SWAP$ operations can be implemented only in a few electrical…
We investigate stabilizer codes with carrier qudits of equal dimension $D$, an arbitrary integer greater than 1. We prove that there is a direct relation between the dimension of a qudit stabilizer code and the size of its corresponding…
We describe in detail the application of four qubit cluster states, built on the simultaneous entanglement of two photons in the degrees of freedom of polarization and linear momentum, for the realization of a complete set of basic one-way…
Achieving near-term quantum advantage will require accurate estimation of quantum observables despite significant hardware noise. For this purpose, we propose a novel, scalable error-mitigation method that applies to gate-based quantum…
We consider the problem of synthesizing Clifford quantum circuits for devices with all-to-all qubit connectivity. We approach this task as a reinforcement learning problem in which an agent learns to discover a sequence of elementary…
A quantum computer can solve hard problems - such as prime factoring, database searching, and quantum simulation - at the cost of needing to protect fragile quantum states from error. Quantum error correction provides this protection, by…
In scenarios where full access to all qubits of a multipartite quantum system is available and global operations can be implemented, the preparation of arbitrary entangled states is theoretically straightforward. However, practical…
Up to now every good quantum error-correcting code discovered has had the structure of an eigenspace of an Abelian group generated by tensor products of Pauli matrices; such codes are known as stabilizer or additive codes. In this letter we…
Identifying stabilizer codes that admit fault-tolerant implementations of the full logical Clifford group would significantly advance fault-tolerant quantum computation. Motivated by this goal, we study several classes of fault-tolerant…
Clifford codes are a class of quantum error control codes that form a natural generalization of stabilizer codes. These codes were introduced in 1996 by Knill, but only a single Clifford code was known, which is not already a stabilizer…