Related papers: Measurement-Assisted Clifford Synthesis

A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-K\"onig bound for $n$-dimensional topological stabilizer codes. In this work, we extend…

We propose a method for classical simulation of finite-dimensional quantum systems, based on sampling from a quasiprobability distribution, i.e., a generalized Wigner function. Our construction applies to all finite dimensions, with the…

We reduce the extra qubits needed for two fault-tolerant quantum computing protocols: error correction, specifically syndrome bit measurement, and cat state preparation. For distance-three fault-tolerant syndrome extraction, we show an…

The Clifford group is the set of gates generated by controlled-Z gates, the phase gate and the Hadamard gate. We will say that a n-qubit state is a Clifford state if it can be prepared using Clifford gates. These states are known as the…

In this paper we study the potential of using reinforcement learning (RL) in order to synthesize quantum circuits, while optimizing the T-count and CS-count, of unitaries that are exactly implementable by the Clifford+T and Clifford+CS gate…

Stabilizer simulation can efficiently simulate an important class of quantum circuits consisting exclusively of Clifford gates. However, all existing extensions of this simulation to arbitrary quantum circuits including non-Clifford gates…

We propose a calculus of local equations over one-way computing patterns, which preserves interpretations, and allows the rewriting of any pattern to a standard form where entanglement is done first, then measurements, then local…

We present an algorithm for manipulating quantum information via a sequence of projective measurements. We frame this manipulation in the language of stabilizer codes: a quantum computation approach in which errors are prevented and…

In this work we establish lower bounds on the size of Clifford circuits that measure a family of commuting Pauli operators. Our bounds depend on the interplay between a pair of graphs: the Tanner graph of the set of measured Pauli…

Let $n\geq 8$ be divisible by 4. The Clifford-cyclotomic gate set $\mathcal{G}_n$ is the universal gate set obtained by extending the Clifford gates with the $z$-rotation $T_n = \mathrm{diag}(1,\zeta_n)$, where $\zeta_n$ is a primitive…

It is important for performance studies in quantum technologies to analyze quantum circuits in the presence of noise. We introduce an error probability tensor, a tool to track generalized Pauli error statistics of qudits within quantum…

We show that qubit stabilizer states can be represented by non-negative quasi-probability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by…

As experimental platforms for quantum information processing continue to mature, characterization of the quality of unitary gates that can be applied to their quantum bits (qubits) becomes essential. Eventually, the quality must be…

Quantum error correction is the art of protecting fragile quantum information through suitable encoding and active interventions. After encoding $k$ logical qubits into $n>k$ physical qubits using a stabilizer code, this amounts to…

We present a quantum circuit model which emulates the interface growth of the classical raise-and-peel model. Our model consists of Clifford unitary gates interspersed with projective measurements, applied according to prescribed feedback…

We examine the following problem: given a collection of Clifford gates, describe the set of unitaries generated by circuits composed of those gates. Specifically, we allow the standard circuit operations of composition and tensor product,…

We describe and analyze an error mitigation technique that uses multiple pairs of parity checks to detect the presence of errors. Each pair of checks uses one ancilla qubit to detect a component of the error operator and represents one…

Clifford gates and transformations, which map products of elementary Pauli or Majorana operators to other such products, are foundational in quantum computing, underpinning the stabilizer formalism, error-correcting codes, magic state…

We study ancilla-free approximation of single-qubit unitaries $U\in {\rm SU}(2)$ by gate sequences over Clifford+$G$, where $G\in\{T,V\}$ or their generalization. Let $p$ denote the characteristic factor of the gate set (e.g., $p=2$ for…

We start by studying the subgroup structures underlying stabilizer circuits. Then we apply our results to provide two normal forms for stabilizer circuits. These forms are computed by induction using simple conjugation rules in the Clifford…