All reports by Author Qisheng Wang:

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TR24-167
| 31st October 2024
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François Le Gall, Yupan Liu, Harumichi Nishimura, Qisheng Wang#### Space-bounded quantum interactive proof systems

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TR24-157
| 17th October 2024
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Yupan Liu, Qisheng Wang#### On estimating the trace of quantum state powers

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TR23-117
| 9th August 2023
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François Le Gall, Yupan Liu, Qisheng Wang#### Space-bounded quantum state testing via space-efficient quantum singular value transformation

Revisions: 1

François Le Gall, Yupan Liu, Harumichi Nishimura, Qisheng Wang

We introduce two models of space-bounded quantum interactive proof systems, $\mathbf{QIPL}$ and $\mathbf{QIP_\mathrm{U}L}$. The $\mathbf{QIP_\mathrm{U}L}$ model, a space-bounded variant of quantum interactive proofs ($\mathbf{QIP}$) introduced by Watrous (CC 2003) and Kitaev and Watrous (STOC 2000), restricts verifier actions to unitary circuits. In contrast, $\mathbf{QIPL}$ allows logarithmically many intermediate measurements per ... more >>>

Yupan Liu, Qisheng Wang

We investigate the computational complexity of estimating the trace of quantum state powers $\text{tr}(\rho^q)$ for an $n$-qubit mixed quantum state $\rho$, given its state-preparation circuit of size $\text{poly}(n)$. This quantity is closely related to and often interchangeable with the Tsallis entropy $\text{S}_q(\rho) = \frac{1-\text{tr}(\rho^q)}{q-1}$, where $q = 1$ corresponds to ... more >>>

François Le Gall, Yupan Liu, Qisheng Wang

Driven by exploring the power of quantum computation with a limited number of qubits, we present a novel complete characterization for space-bounded quantum computation, which encompasses settings with one-sided error (unitary coRQL) and two-sided error (BQL), approached from a quantum (mixed) state testing perspective:

- The first family of natural ...
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