• Corpus ID: 235212336

Qudit circuits with SU(d) symmetry: Locality imposes additional conservation laws

@inproceedings{Marvian2021QuditCW,
  title={Qudit circuits with SU(d) symmetry: Locality imposes additional conservation laws},
  author={Iman Marvian and Hanqing Liu and Austin Hulse},
  year={2021}
}
Local symmetric quantum circuits provide a simple framework to study the dynamics and phases of complex quantum systems with conserved charges. However, some of their basic properties have not yet been understood. Recently, it has been shown that such quantum circuits only generate a restricted subset of symmetric unitary transformations [I. Marvian, Nature Physics, 2022]. In this paper, we consider circuits with 2-local SU(d)invariant unitaries acting on qudits, i.e., d-dimensional quantum… 

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References

SHOWING 1-10 OF 66 REFERENCES
Charge-conserving unitaries typically generate optimal covariant quantum error-correcting codes
Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes covariant with respect to continuous symmetries
Generic Entanglement Entropy for Quantum States with Symmetry
TLDR
This paper extends the well-known concentration formula to the one applicable to any subspace and shows that bipartite entanglement entropy of a quantum state that is drawn uniformly at random from an invariant subspace of a given symmetry is found.
Quantum Information Scrambling on a Superconducting Qutrit Processor
TLDR
The teleportation algorithm, which connects to recent proposals for studying traversable wormholes in the laboratory, demonstrates how quantum information processing technology based on higher dimensional systems can exploit a larger and more connected state space to achieve the resource efficient encoding of complex quantum circuits.
A random unitary circuit model for black hole evaporation
Inspired by the Hayden-Preskill protocol for black hole evaporation, we consider the dynamics of a quantum many-body qudit system coupled to an external environment, where the time evolution is
Noncommuting conserved charges in quantum many-body thermalization.
TLDR
This work introduces noncommuting conserved quantities from QI-theoretic thermodynamics into quantum many-body physics: atomic, molecular, and optical physics and condensed matter.
Efficient symmetry-preserving state preparation circuits for the variational quantum eigensolver algorithm
The variational quantum eigensolver is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this
Convergence conditions for random quantum circuits
TLDR
It is proved that the measure over random circuits converges exponentially (with increasing circuit length) to the uniform (Haar) measure on the unitary group, though the rate for uniform convergence must decrease exponentially with the number of qubits.
A relational quantum computer using only two-qubit total spin measurement and an initial supply of highly mixed single-qubit states
We prove that universal quantum computation is possible using only (i) the physically natural measurement on two qubits which distinguishes the singlet from the triplet subspace and (ii) qubits
Quantum encodings in spin systems and harmonic oscillators
We show that higher-dimensional versions of qubits, or qudits, can be encoded into spin systems and into harmonic oscillators, yielding important advantages for quantum computation. Whereas
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