Related papers: Improved Strong Simulation of Universal Quantum Ci…
While implementing a quantum algorithm it is crucial to reduce the quantum resources, in order to obtain the desired computational advantage. For most fault-tolerant quantum error-correcting codes the cost of implementing the non-Clifford…
As quantum systems expand in size and complexity, manual qubit characterization and gate optimization will be a non-scalable and time-consuming venture. Physical qubits have to be carefully calibrated because quantum processors are very…
We start by studying the subgroup structures underlying stabilizer circuits and we use our results to propose a new normal form for stabilizer circuits. This normal form is computed by induction using simple conjugation rules in the…
Recent developments in classical simulation of quantum circuits make use of clever decompositions of chunks of magic states into sums of efficiently simulable stabiliser states. We show here how, by considering certain non-stabiliser…
We develop classical simulation algorithms for adaptive quantum circuits that produce states with low levels of ``magic'' (i.e., non-stabilizerness). These algorithms are particularly well-suited to circuits with high rates of Pauli…
We generalize the polynomial-time outcome-complete simulation algorithm for stabilizer circuits in arXiv:2309.08676 to track global phases exactly, yielding what we call phased outcome-complete simulation. The original algorithm enabled…
We develop analytical and algorithmic techniques that enable efficient simulation of a broad class of noisy stabilizer circuits. We derive closed-form expressions of expectation values for tensor product of Paulis in circuits with…
Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we…
We present an algorithm for efficiently simulating a quantum circuit in the graph formalism. In the graph formalism, we represent states as a linear combination of graphs with Clifford operations on their vertices. We show how a…
We show that any pseudoentangled state ensemble with a gap of $t$ bits of entropy requires $\Omega(t)$ non-Clifford gates to prepare. This bound is tight up to polylogarithmic factors if linear-time quantum-secure pseudorandom functions…
It has recently been discovered that random quantum circuits provide an avenue to realize rich entanglement phase diagrams, which are hidden to standard expectation values of operators. Here we study (2+1)D random circuits with random…
The Gottesman-Knill theorem asserts that a quantum circuit composed of Clifford gates can be efficiently simulated on a classical computer. Here we revisit this theorem and extend it to quantum circuits composed of Clifford and T gates,…
Stabilizer states are fundamental families of quantum states with crucial applications such as error correction, quantum computation, and simulation of quantum circuits. In this paper, we study the problem of testing how close or far a…
We propose a measurement scheme that validates the preparation of an $n$-qubit stabilizer state. The scheme involves a measurement of $n$ Pauli observables, a priori determined from the stabilizer state and which can be realized using…
In this paper, we study the problem of learning an unknown quantum circuit of a certain structure. If the unknown target is an $n$-qubit Clifford circuit, we devise an efficient algorithm to reconstruct its circuit representation by using…
In this paper we investigate stabilizer quantum error correction codes using controlled phase rotations of strong coherent probe states. We explicitly describe two methods to measure the Pauli operators which generate the stabilizer group…
Quantum circuits of many qubits are extremely difficult to realize; thus, the number of qubits is an important metric in a quantum circuit design. Further, scalable and reliable quantum circuits are based on Clifford + T gates. An efficient…
Determining the best attainable threshold for qudit magic state distillation is directly related to the question of whether or not contextuality is sufficient for universal quantum computation. We show that the performance of a qudit…
We present a comprehensive and self-contained framework for the efficient classical simulation of Clifford circuits acting on $d$-dimensional qudits, including realistic Pauli/Weyl noise via stochastic simulation. Our approach uses the…
Standard randomized benchmarking protocols entail sampling from a unitary 2 design, which is not always practical. In this article we examine randomized benchmarking protocols based on subgroups of the Clifford group that are not unitary 2…