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Related papers: Spectral Properties Versus Magic Generation in $T$…

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Magic states enable universal, fault-tolerant quantum computation within the stabilizer framework. Their non-stabilizerness supplies the resource needed to bypass the Eastin-Knill theorem while allowing fault-tolerant distillation. Although…

Quantum Physics · Physics 2026-02-27 Muhammad Erew , Moshe Goldstein

Bravyi and Gosset recently gave classical simulation algorithms for quantum circuits dominated by Clifford operations. These algorithms scale exponentially with the number of T-gate in the circuit, but polynomially in the number of qubits…

Quantum Physics · Physics 2019-05-15 Yifei Huang , Peter Love

Quantum circuits consisting of Clifford and matchgates are two classes of circuits that are known to be efficiently simulatable on a classical computer. We introduce a unified framework that shows in a transparent way the special structure…

Quantum Physics · Physics 2024-05-24 Igor Ermakov , Oleg Lychkovskiy , Tim Byrnes

We describe a new method for approximating an arbitrary $n$ qubit unitary with precision $\varepsilon$ using a Clifford and T circuit with $O(4^{n}n(\log(1/\varepsilon)+n))$ gates. The method is based on rounding off a unitary to a unitary…

Quantum Physics · Physics 2013-06-14 Vadym Kliuchnikov

The Clifford group plays a central role in quantum information science. It is the building block for many error-correcting schemes and matches the first three moments of the Haar measure over the unitary group -a property that is essential…

Quantum Physics · Physics 2025-04-17 Lennart Bittel , Jens Eisert , Lorenzo Leone , Antonio A. Mele , Salvatore F. E. Oliviero

Recently it has been shown that Repeat-Until-Success (RUS) circuits can approximate a given single-qubit unitary with an expected number of $T$ gates of about $1/3$ of what is required by optimal, deterministic, ancilla-free decompositions…

Quantum Physics · Physics 2015-06-11 Alex Bocharov , Martin Roetteler , Krysta M. Svore

We prove that local random quantum circuits acting on n qubits composed of O(t^{10} n^2) many nearest neighbor two-qubit gates form an approximate unitary t-design. Previously it was unknown whether random quantum circuits were a t-design…

Quantum Physics · Physics 2019-07-11 Fernando G. S. L. Brandao , Aram W. Harrow , Michal Horodecki

Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. We first show that robustness of magic is a well-behaved magic monotone that operationally quantifies the…

Quantum Physics · Physics 2017-03-16 Mark Howard , Earl T. Campbell

For a quantum computer acting on d-dimensional systems, we analyze the computational power of circuits wherein stabilizer operations are perfect and we allow access to imperfect non-stabilizer states or operations. If the noise rate…

Quantum Physics · Physics 2011-03-21 Wim van Dam , Mark Howard

We introduce an exact mapping of Clifford (stabilizer) random tensor networks (RTNs) and monitored quantum circuits, onto a statistical mechanics model. With Haar unitaries, the fundamental degrees of freedom ('spins') are permutations…

Statistical Mechanics · Physics 2025-04-18 Yaodong Li , Romain Vasseur , Matthew P. A. Fisher , Andreas W. W. Ludwig

Magic or non-stabilizerness is a resource for quantum computing that has been extensively studied in qudit networks. It describes the degree to which Clifford gates cannot generate a given state, capturing the advantage of quantum over…

Let G(A,B) denote the 2-qubit gate which acts as the 1-qubit SU(2) gates A and B in the even and odd parity subspaces respectively, of two qubits. Using a Clifford algebra formalism we show that arbitrary uniform families of circuits of…

Quantum Physics · Physics 2008-11-19 Richard Jozsa , Akimasa Miyake

We investigate non-stabilizerness, also known as ``magic,'' to understand criticality and exceptional points in non-Hermitian quantum many-body systems. Our focus is on parity-time ($\mathcal{PT}$) symmetric spin chains, specifically the…

Quantum Physics · Physics 2025-10-21 Cătălin Paşcu Moca , Doru Sticlet , Balázs Dóra

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…

Quantum Physics · Physics 2019-08-14 Eleanor Crane , Thomas Crane , Nguyen H. Le , Alexander Schuckert , Andrew J. Fisher

Non-Clifford gates are frequently exclusively implemented on fault-tolerant architectures by first distilling magic states in specialised magic-state factories. In the rest of the architecture, the computational space, magic states can then…

Quantum Physics · Physics 2024-03-29 Vadym Kliuchnikov , Eddie Schoute

We find a scaling reduction in the stabilizer rank of the twelve-qubit tensored $T$ gate magic state. This lowers its asymptotic bound to $2^{\sim 0.463 t}$ for multi-Pauli measurements on $t$ magic states, improving over the best…

Quantum Physics · Physics 2022-06-08 Lucas Kocia

We apply periodic orbit theory to a quantum billiard on a torus with a variable number N of small circular scatterers distributed randomly. Provided these scatterers are much smaller than the wave length they may be regarded as sources of…

chao-dyn · Physics 2009-10-31 Per Dahlqvist

In most stabilizer-based quantum computing schemes, so-called magic states are a necessary resource for implementing non-transversal quantum gates. With the resource theory of magic, it is possible to analyze and quantify the generation of…

Quantum Physics · Physics 2026-05-22 Carolin Deckers , Justus Neumann , Hermann Kampermann , Dagmar Bruß

Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random…

Quantum Physics · Physics 2009-11-13 Yaakov S. Weinstein , Winton G. Brown , Lorenza Viola

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…

Statistical Mechanics · Physics 2021-12-03 Ali Lavasani , Yahya Alavirad , Maissam Barkeshli