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Fidelity is one of the most valuable and commonly used metrics for assessing the performance of quantum circuits on error-prone quantum processors. Several approaches have been proposed to estimate circuit fidelity without executing it on…
Quantum computing hardware has grown sufficiently complex that it often can no longer be simulated by classical computers, but its computational power remains limited by errors. These errors corrupt the results of quantum algorithms, and it…
We study the complexity of learning quantum states in various models with respect to the stabilizer formalism and obtain the following results: - We prove that $\Omega(n)$ $T$-gates are necessary for any Clifford+$T$ circuit to prepare…
As quantum computers and simulators begin to produce results that cannot be verified classically, it becomes imperative to develop a variety of tools to detect and diagnose experimental errors on these devices. While state or process…
We calculate the fidelity with which an arbitrary state can be encoded into a [7,1,3] CSS quantum error correction code in a non-equiprobable Pauli operator error environment with the goal of determining whether this encoding can be used…
Quantum computations are expressed in general as quantum circuits, which are specified by ordered lists of quantum gates. The resulting specifications are used during the optimisation and execution of the expressed computations. However,…
The quantum stabilizer formalism became foundational for understanding error correction soon after the realization of the first useful quantum error correction codes. Stabilizers provide a way to describe sets of quantum states which are…
Correcting errors due to noise in quantum circuits run on current and near-term quantum hardware is essential for any convincing demonstration of quantum advantage. Indeed, in many cases it has been shown that noise renders quantum circuits…
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 two classical algorithms for the simulation of universal quantum circuits on $n$ qubits constructed from $c$ instances of Clifford gates and $t$ arbitrary-angle $Z$-rotation gates such as $T$ gates. Our algorithms complement each…
Stabilizer circuits play an important role in quantum error correction protocols, and will be vital for ensuring fault tolerance in future quantum hardware. While stabilizer circuits are defined on the Clifford generating set, {H, S, CX},…
Recent advancements in quantum technologies have highlighted the importance of mitigating system imperfections, including parameter uncertainties and decoherence effects, to improve the performance of experimental platforms. However, most…
We present two new constructions for the Toffoli gate which substantially reduce resource costs in fault-tolerant quantum computing. The first contribution is a Toffoli gate requiring Clifford operations plus only four $T =…
To approximate arbitrary unitary transformations on one or more qubits, one must perform transformations which are outside of the Clifford group. The gate most commonly considered for this purpose is the T = diag(1, exp(i \pi/4)) gate. As T…
Quantum message authentication codes are families of keyed encoding and decoding maps that enable the detection of tampering on encoded quantum data. Here, we study a new class of simulators for quantum message authentication schemes, and…
Fault-tolerant operations based on stabilizer codes are the state of the art in suppressing error rates in quantum computations. Most such codes do not permit a straightforward implementation of non-Clifford logical operations, which are…
The Clifford hierarchy is a nested sequence of sets of quantum gates that can be fault-tolerantly performed using gate teleportation within standard quantum error correction schemes. The groups of Pauli and Clifford gates constitute the…
Post-selection strategies that discard low-confidence computational results can significantly improve the effective fidelity of quantum error correction at the cost of reduced acceptance rates, which can be particularly useful for offline…
Semiconductor spin qubits demonstrated single-qubit gates with fidelities up to $99.9\%$ benchmarked in the single-qubit subspace. However, tomographic characterizations reveals non-negligible crosstalk errors in a larger space.…
The stabilization of a quantum computer by repeated error correction can be reduced almost entirely to repeated preparation of blocks of qubits in quantum codeword states. These are multi-particle entangled states with a high degree of…