Related papers: Depth reduction for quantum Clifford circuits thro…
In this paper we investigate the encoding of operator quantum error correcting codes i.e. subsystem codes. We show that encoding of subsystem codes can be reduced to encoding of a related stabilizer code making it possible to use all the…
We present an algorithm for building a circuit that approximates single qubit unitaries with precision {\epsilon} using O(log(1/{\epsilon})) Clifford and T gates and employing up to two ancillary qubits. The algorithm for computing our…
For random quantum circuits on $n$ qubits of depth $\Theta(\log n)$ with depolarizing noise, the task of sampling from the output state can be efficiently performed classically using a Pauli path method [Aharonov et al. Proceedings of the…
Given some group $G$ of logical gates, for instance the Clifford group, what are the quantum encodings for which these logical gates can be implemented by simple physical operations, described by some physical representation of $G$? We…
Universal fault-tolerant quantum computers will require the use of efficient protocols to implement encoded operations necessary in the execution of algorithms. In this work, we show how solvers for satisfiability modulo theories (SMT…
$k$-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:…
Simulating Clifford and near-Clifford circuits using the extended stabilizer formalism has become increasingly popular, particularly in quantum error correction. Compared to the state-vector approach, the extended stabilizer formalism can…
To address the challenge posed by noise in real quantum devices, quantum error mitigation techniques play a crucial role. These techniques are resource-efficient, making them suitable for implementation in noisy intermediate-scale quantum…
Recent work of Bravyi et al. and follow-up work by Bene Watts et al. demonstrates a quantum advantage for shallow circuits: constant-depth quantum circuits can perform a task which constant-depth classical (i.e., AC$^0$) circuits cannot.…
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 provide a recursively defined sequence of flag circuits which will detect logical errors induced by non-fault-tolerant $R_{\overline{Z}}(\frac{\pi}{2^l})$ gates on CSS codes with a fault distance of two. As applications, we give a family…
A powerful method for analyzing quantum error-correcting codes is to map them onto classical statistical mechanics models. Such mappings have thus far mostly focused on static codes, possibly subject to repeated syndrome measurements.…
Fault-tolerant, error-corrected quantum computation is commonly acknowledged to be crucial to the realisation of large-scale quantum algorithms that could lead to extremely impactful scientific or commercial results. Achieving a universal…
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…
The Gottesman-Knill theorem holds that operations from the Clifford group, when combined with preparation and detection of qubit states in the computational basis, are insufficient for universal quantum computation. Indeed, any measurement…
The preparation of quantum states using short quantum circuits is one of the most promising near-term applications of small quantum computers, especially if the circuit is short enough and the fidelity of gates high enough that it can be…
We describe a simple algorithm for sampling $n$-qubit Clifford operators uniformly at random. The algorithm outputs the Clifford operators in the form of quantum circuits with at most $5n + 2n^2$ elementary gates and a maximum depth of…
A decision diagram (DD) is a graph-like data structure for homomorphic compression of Boolean and pseudo-Boolean functions. Over the past decades, decision diagrams have been successfully applied to verification, linear algebra, stochastic…
We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be…
We study the computational power of unitary Clifford circuits with solely magic state inputs (CM circuits), supplemented by classical efficient computation. We show that CM circuits are hard to classically simulate up to multiplicative…