Many-body quantum magic

• URL: http://arxiv.org/abs/2010.13817v4
• Date: Thu, 12 May 2022 18:37:04 GMT
• Title: Many-body quantum magic
• Authors: Zi-Wen Liu, Andreas Winter
• Abstract summary: We show that the maximum magic of an $n$-qubit state is essentially $n$, simultaneously for a range of "good" magic measures. In the quest for explicit, scalable cases of highly entangled states whose magic can be understood, we connect the magic of hypergraph states with the second-order nonlinearity of their underlying Boolean functions. We show that $n$-qubit states with nearly $n$ magic, or indeed almost all states, cannot supply nontrivial speedups over classical computers.
• Score: 0.609170287691728
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Magic (non-stabilizerness) is a necessary but "expensive" kind of "fuel" to drive universal fault-tolerant quantum computation. To properly study and characterize the origin of quantum "complexity" in computation as well as physics, it is crucial to develop a rigorous understanding of the quantification of magic. Previous studies of magic mostly focused on small systems and largely relied on the discrete Wigner formalism (which is only well behaved in odd prime power dimensions). Here we present an initiatory study of the magic of genuinely many-body quantum states that may be strongly entangled, with focus on the important case of many qubits, at a quantitative level. We first address the basic question of how "magical" a many-body state can be, and show that the maximum magic of an $n$-qubit state is essentially $n$, simultaneously for a range of "good" magic measures. We then show that, in fact, almost all $n$-qubit pure states have magic of nearly $n$. In the quest for explicit, scalable cases of highly entangled states whose magic can be understood, we connect the magic of hypergraph states with the second-order nonlinearity of their underlying Boolean functions. Next, we go on and investigate many-body magic in practical and physical contexts. We first consider a variant of MBQC where the client is restricted to Pauli measurements, in which magic is a necessary feature of the initial "resource" state. We show that $n$-qubit states with nearly $n$ magic, or indeed almost all states, cannot supply nontrivial speedups over classical computers. We then present an example of analyzing the magic of "natural" condensed matter systems of physical interest. We apply the Boolean function techniques to derive explicit bounds on the magic of certain representative 2D SPT states, and comment on possible further connections between magic and the quantum complexity of phases of matter.

Related papers

• Noise robustness and threshold of many-body quantum magic [0.5524804393257919]
  We investigate how noise affects magic properties in entangled many-body quantum states. We show that interactions facilitated by high-degree gates are fragile to noise. We also discuss the qudit case based on the discrete Wigner formalism.
  arXiv  Detail & Related papers  (2024-10-28T17:01:47Z)
• Quantum magic dynamics in random circuits [1.9568111750803001]
  Magic refers to the degree of "quantumness" in a system that cannot be fully described by stabilizer states and Clifford operations alone. In quantum computing, stabilizer states and Clifford operations can be efficiently simulated on a classical computer.
  arXiv  Detail & Related papers  (2024-10-28T15:29:21Z)
• On the Hardness of Measuring Magic [0.4601544125705421]
  Measuring the amount of magic used by a device allows us to quantify its potential computational power. We introduce Pauli instability as a measure of magic and experimentally measure it on the IBM Eagle quantum processor. Our results suggest that one may only measure magic when a quantum computer does not provide a speed-up.
  arXiv  Detail & Related papers  (2024-08-03T04:29:34Z)
• Magic of quantum hypergraph states [6.3109948645563465]
  We analytically investigate the magic resource of archetypal multipartite quantum states -- quantum hypergraph states. Our study advances the understanding of multipartite quantum magic and could lead to applications in quantum computing and quantum many-body physics.
  arXiv  Detail & Related papers  (2023-08-03T17:21:55Z)
• Schr\"odinger cat states of a 16-microgram mechanical oscillator [54.35850218188371]
  The superposition principle is one of the most fundamental principles of quantum mechanics. Here we demonstrate the preparation of a mechanical resonator with an effective mass of 16.2 micrograms in Schr"odinger cat states of motion. We show control over the size and phase of the superposition and investigate the decoherence dynamics of these states.
  arXiv  Detail & Related papers  (2022-11-01T13:29:44Z)
• The power of noisy quantum states and the advantage of resource dilution [62.997667081978825]
  Entanglement distillation allows to convert noisy quantum states into singlets. We show that entanglement dilution can increase the resilience of shared quantum states to local noise.
  arXiv  Detail & Related papers  (2022-10-25T17:39:29Z)
• Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
  Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle. We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm. We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
  arXiv  Detail & Related papers  (2022-05-26T20:32:36Z)
• Irreducible magic sets for $n$-qubit systems [0.0]
  Magic sets of observables capture quantum state-independent advantage for systems of $nge 2$ qubits. An open question is whether there are magic sets that cannot be reduced to the square or the pentagram. We identify magic sets which cannot be reduced to the square or the pentagram and require $n=3,4,5$, or $6$ qubits.
  arXiv  Detail & Related papers  (2022-02-26T13:35:18Z)
• Quantifying Qubit Magic Resource with Gottesman-Kitaev-Preskill Encoding [58.720142291102135]
  We define a resource measure for magic, the sought-after property in most fault-tolerant quantum computers. Our formulation is based on bosonic codes, well-studied tools in continuous-variable quantum computation.
  arXiv  Detail & Related papers  (2021-09-27T12:56:01Z)
• Operational Resource Theory of Imaginarity [48.7576911714538]
  We show that quantum states are easier to create and manipulate if they only have real elements. As an application, we show that imaginarity plays a crucial role for state discrimination.
  arXiv  Detail & Related papers  (2020-07-29T14:03:38Z)
• Quantum Gram-Schmidt Processes and Their Application to Efficient State Read-out for Quantum Algorithms [87.04438831673063]
  We present an efficient read-out protocol that yields the classical vector form of the generated state. Our protocol suits the case that the output state lies in the row space of the input matrix. One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
  arXiv  Detail & Related papers  (2020-04-14T11:05:26Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.