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Approximating many-body quantum states with quantum circuits and measurements

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arxiv 2403.07604 v3 pith:IVVSJO3C submitted 2024-03-12 quant-ph cond-mat.stat-mech

Lorenzo Piroli , Georgios Styliaris , J. Ignacio Cirac This is my paper · ORCID
classification quant-phcond-mat.stat-mech
keywords quantumstatescircuitsintroducemany-bodypreparationancillasapplied
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We introduce protocols to prepare many-body quantum states with quantum circuits assisted by local operations and classical communication. We show that by lifting the requirement of exact preparation, one can substantially save resources. In particular, the so-called $W$ and, more generally, Dicke states require a circuit depth and number of ancillas per site that are independent of the system size. As a byproduct of our work, we introduce an efficient scheme to implement certain non-local, non-Clifford unitary operators. We also discuss how similar ideas may be applied in the preparation of eigenstates of well-known spin models, both free and interacting.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Tower of Structured Excited States from Measurements

    quant-ph 2024-11 conditional novelty 7.0 of 10

    A phase-estimation measurement of a global charge or momentum projects an easy-to-prepare matrix product state onto towers of quantum many-body scar states and Dicke states in logarithmic circuit depth.

  2. Spin-$s$ $U(1)$-eigenstate preparation

    quant-ph 2026-01 conditional novelty 6.0 of 10

    A Gray-code-based quantum circuit prepares arbitrary fixed-digit-sum (U(1)) eigenstates of spin-s chains, yielding the first preparation of spin-s XXX Bethe states.

  3. Quantum computing in spin-adapted representations for efficient simulations of spin systems

    quant-ph 2024-12 conditional novelty 6.0 of 10

    Spin-path truncation plus symmetric-group rules yields sparse local qubit Hamiltonians for the Heisenberg model, with shallow adiabatic circuits reaching about 99 percent fidelity for N=16.

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