Related papers: Clifford testing: algorithms and lower bounds
We propose a scheme that converts a stabilizer code into another stabilizer code in a fault tolerant manner. The scheme first puts both codes in specific forms, and proceeds the conversion from a source code to a target code by applying…
We developed a general framework for synthesizing target gates by using a finite set of basic gates, which is a crucial step in quantum compilation. When approximating a gate in SU($n$), a naive brute-force search requires a computational…
Recently, Bravyi and K\"onig have shown that there is a tradeoff between fault-tolerantly implementable logical gates and geometric locality of stabilizer codes. They consider locality-preserving operations which are implemented by a…
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…
Quantum key distribution (QKD) promises provably secure cryptography, even to attacks from an all-powerful adversary. However, with quantum computing development lagging behind QKD, the assumption that there exists an adversary equipped…
Stabilizer codes are a simple and successful class of quantum error-correcting codes. Yet this success comes in spite of some harsh limitations on the ability of these codes to fault-tolerantly compute. Here we introduce a new metric for…
We initiate the study of parameterized complexity of $\textsf{QMA}$ problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists…
We introduce a new model for testing graph properties which we call the \emph{rejection sampling model}. We show that testing bipartiteness of $n$-nodes graphs using rejection sampling queries requires complexity $\widetilde{\Omega}(n^2)$.…
We revisit the Pauli-Clifford connection to introduce a real, grade-preserving algebraic framework for $n$-qubit quantum computation based on the tensor product $C\ell_{2,0}(\mathbb{R})^{\otimes n}$. In this setting, the bivector $J =…
In the property testing model, the task is to distinguish objects possessing some property from the objects that are far from it. One of such properties is monotonicity, when the objects are functions from one poset to another. This is an…
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…
Randomized benchmarking is a widely used experimental technique to characterize the average error of quantum operations. Benchmarking procedures that scale to enable characterization of $n$-qubit circuits rely on efficient procedures for…
Prior work of Beverland et al. has shown that any exact Clifford+$T$ implementation of the $n$-qubit Toffoli gate must use at least $n$ $T$ gates. Here we show how to get away with exponentially fewer $T$ gates, at the cost of incurring a…
We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of…
Benchmarking methods that can be adapted to multi-qubit systems are essential for assessing the overall or "holistic" performance of nascent quantum processors. The current industry standard is Clifford randomized benchmarking (RB), which…
Classical simulation of quantum circuits plays a crucial role in validating quantum hardware and delineating the boundaries of quantum advantage. Among the most effective simulation techniques are those based on the stabilizer extent, which…
This paper explores the representation of quantum computing in terms of unitary reflections (unitary transformations that leave invariant a hyperplane of a vector space). The symmetries of qubit systems are found to be supported by…
In quantum computation the target fidelity of the qubit gates is very high, with the admissible error being in the range from $10^{-3}$ to $10^{-4}$ and even less, depending on the protocol. The direct experimental determination of such an…
A unitary t-design is a set of unitaries that is "evenly distributed" in the sense that the average of any t-th order polynomial over the design equals the average over the entire unitary group. In various fields -- e.g. quantum information…
We prove a $k^{-\Omega(\log(\varepsilon_2 - \varepsilon_1))}$ lower bound for adaptively testing whether a Boolean function is $\varepsilon_1$-close to or $\varepsilon_2$-far from $k$-juntas. Our results provide the first superpolynomial…