Related papers: Learning t-doped stabilizer states
We employed the techniques from [Phys. Rev. A \textbf{70}, 052328 (2004)/arXiv:0406196] to analytically study two set of quantum circuits containing one $T$ gate/magic $|T\rangle = \frac{|0\rangle+\sqrt{i}|1\rangle}{\sqrt{2}}$ state. These…
We evaluate the usefulness of holographic stabilizer codes for practical purposes by studying their allowed sets of fault-tolerantly implementable gates. We treat them as subsystem codes and show that the set of transversally implementable…
We investigate Clifford+$T$ quantum circuits with a small number of $T$-gates. Using the sparsification lemma, we identify time complexity lower bounds in terms of $T$-gate count below which a strong simulator would improve on the…
The classical simulation of highly-entangling quantum dynamics is conjectured to be generically hard. Thus, recently discovered measurement-induced transitions between highly entangling and low-entanglement dynamics are phase transitions in…
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…
We prove that magic states from the Clifford hierarchy give optimal solutions for tasks involving nonlocality and entropic uncertainty with respect to Pauli measurements. For both the nonlocality and uncertainty tasks, stabilizer states are…
We present an algorithm for verifying the local unitary (LU) equivalence of graph and stabilizer states. Our approach reduces the problem to solving a system of linear equations in modular arithmetic. Furthermore, we demonstrate that any LU…
We prove that on any two-dimensional lattice of qudits of a prime dimension, every translation invariant Pauli stabilizer group with local generators and with code distance being the linear system size, is decomposed by a local Clifford…
Bounding the cost of classically simulating the outcomes of universal quantum circuits to additive error $\delta$ is often called weak simulation and is a direct way to determine when they confer a quantum advantage. Weak simulation of the…
How entangled is a randomly chosen bipartite stabilizer state? We show that if the number of qubits each party holds is large the state will be close to maximally entangled with probability exponentially close to one. We provide a similar…
We apply the cutting stabiliser decomposition techniques [arXiv:2403.10964] to the quantum states generated from magic state cultivation [arXiv:2409.17595], post-selected upon all $+1$ measured values for simplicity. The resultant states to…
We propose a robust and efficient algorithm for computing bound states of infinite tight-binding systems that are made up of a finite scattering region connected to semi-infinite leads. Our method uses wave matching in close analogy to the…
We propose a learning method for estimating unknown pure quantum states. The basic idea of our method is to learn a unitary operation $\hat{U}$ that transforms a given unknown state $|\psi_\tau\rangle$ to a known fiducial state $|f\rangle$.…
Randomly-doped silicon has many competitive advantages for quantum computation; not only is it fast to fabricate but it could naturally contain high numbers of qubits and logic gates as a function of doping densities. We determine the…
In the task of quantum state learning, one receives some data about measurements performed on a state, and using that, must make predictions on the outcomes of unseen measurements. Computing a prediction is generally hard but it has been…
We analyze the complexity of learning $n$-qubit quantum phase states. A degree-$d$ phase state is defined as a superposition of all $2^n$ basis vectors $x$ with amplitudes proportional to $(-1)^{f(x)}$, where $f$ is a degree-$d$ Boolean…
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…
A powerful feature of stabiliser error correcting codes is the fact that stabiliser measurement projects arbitrary errors to Pauli errors, greatly simplifying the physical error correction process as well as classical simulations of code…
The vast and complicated large-qubit state space forbids us to comprehensively capture the dynamics of modern quantum computers via classical simulations or quantum tomography. Recent progress in quantum learning theory prompts a crucial…
Policy iteration is one of the classical frameworks of reinforcement learning, which requires a known initial stabilizing control. However, finding the initial stabilizing control depends on the known system model. To relax this requirement…