Adaptive Quantum Homeopathy

• URL: http://arxiv.org/abs/2510.08129v1
• Date: Thu, 09 Oct 2025 12:14:58 GMT
• Title: Adaptive Quantum Homeopathy
• Authors: Lennart Bittel, Lorenzo Leone,
• Abstract summary: We present a protocol, named Quantum Homeopathy, able to generate unitary $k$-designs on $n$ qubits.<n>Inspired by the principle of homeopathy, our method applies a $k$-design only to a subsystem of size $Theta(k)$, independent of $n$.<n>We prove that this construction achieves full quantum security against adaptive adversaries using only $tildeO(k2 logvarepsilon-1)$ non-Clifford gates.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Randomness is a fundamental resource in quantum information, with crucial applications in cryptography, algorithms, and error correction. A central challenge is to construct unitary $k$-designs that closely approximate Haar-random unitaries while minimizing the costly use of non-Clifford operations. In this work, we present a protocol, named Quantum Homeopathy, able to generate unitary $k$-designs on $n$ qubits, secure against any adversarial quantum measurement, with a system-size-independent number of non-Clifford gates. Inspired by the principle of homeopathy, our method applies a $k$-design only to a subsystem of size $\Theta(k)$, independent of $n$. This "seed" design is then "diluted" across the entire $n$-qubit system by sandwiching it between two random Clifford operators. The resulting ensemble forms an $\varepsilon$-approximate unitary $k$-design on $n$ qubits. We prove that this construction achieves full quantum security against adaptive adversaries using only $\tilde{O}(k^2 \log\varepsilon^{-1})$ non-Clifford gates. If one requires security only against polynomial-time adaptive adversaries, the non-Clifford cost decreases to $\tilde{O}(k + \log^{1+c} \varepsilon^{-1})$. This is optimal, since we show that at least $\Omega(k)$ non-Clifford gates are required in this setting. Compared to existing approaches, our method significantly reduces non-Clifford overhead while strengthening security guarantees to adaptive security as well as removing artificial assumptions between $n$ and $k$. These results make high-order unitary designs practically attainable in near-term fault-tolerant quantum architectures.

Related papers

• Clifford+V synthesis for multi-qubit unitary gates [0.0]
  We develop a general framework for synthesizing target gates by using a finite set of basic gates.<n>We introduce a suboptimal but short run-time algorithm for synthesizing multi-qubit controlled gates.
  arXiv  Detail & Related papers  (2025-10-09T14:57:55Z)
• Reducing T Gates with Unitary Synthesis [0.41873449350124814]
  This work presents a novel FT synthesis algorithm that directly synthesizes arbitrary single-qubit unitaries.<n>By leveraging tensor network-based search, our approach enables native $U3$ synthesis, reducing the $T$ count, Clifford gate count, and approximation error.
  arXiv  Detail & Related papers  (2025-03-20T04:53:54Z)
• Cloning Games, Black Holes and Cryptography [50.022147589030304]
  We introduce a new toolkit for analyzing cloning games.<n>This framework allows us to analyze a new cloning game based on binary phase states.<n>We show that the binary phase variantally optimal bound offers quantitative insights into information scrambling in idealized models of black holes.
  arXiv  Detail & Related papers  (2024-11-07T14:09:32Z)
• Quantum Error Suppression with Subgroup Stabilisation [3.4719087457636792]
  Quantum state purification is the functionality that, given multiple copies of an unknown state, outputs a state with increased purity. We propose an effective state purification gadget with a moderate quantum overhead by projecting $M$ noisy quantum inputs to their subspace. Our method, applied in every short evolution over $M$ redundant copies of noisy states, can suppress both coherent and errors by a factor of $1/M$, respectively.
  arXiv  Detail & Related papers  (2024-04-15T17:51:47Z)
• Simulation of IBM's kicked Ising experiment with Projected Entangled Pair Operator [71.10376783074766]
  We perform classical simulations of the 127-qubit kicked Ising model, which was recently emulated using a quantum circuit with error mitigation. Our approach is based on the projected entangled pair operator (PEPO) in the Heisenberg picture. We develop a Clifford expansion theory to compute exact expectation values and use them to evaluate algorithms.
  arXiv  Detail & Related papers  (2023-08-06T10:24:23Z)
• Transversal Injection: A method for direct encoding of ancilla states for non-Clifford gates using stabiliser codes [55.90903601048249]
  We introduce a protocol to potentially reduce this overhead for non-Clifford gates. Preliminary results hint at high quality fidelities at larger distances.
  arXiv  Detail & Related papers  (2022-11-18T06:03:10Z)
• Random quantum circuits transform local noise into global white noise [118.18170052022323]
  We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially. If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
  arXiv  Detail & Related papers  (2021-11-29T19:26:28Z)
• Quantum copy-protection of compute-and-compare programs in the quantum random oracle model [48.94443749859216]
  We introduce a quantum copy-protection scheme for a class of evasive functions known as " compute-and-compare programs" We prove that our scheme achieves non-trivial security against fully malicious adversaries in the quantum random oracle model (QROM) As a complementary result, we show that the same scheme fulfils a weaker notion of software protection, called "secure software leasing"
  arXiv  Detail & Related papers  (2020-09-29T08:41:53Z)
• Efficient unitary designs with a system-size independent number of non-Clifford gates [2.387952453171487]
  It takes exponential resources to produce Haar-random unitaries drawn from the full $n$-qubit group. Unitary $t-designs mimic the Haar-$-th moments. We derive novel bounds on the convergence time of random Clifford circuits to the $t$-th moment of the uniform distribution on the Clifford group.
  arXiv  Detail & Related papers  (2020-02-21T19:41:07Z)
• Locally Private Hypothesis Selection [96.06118559817057]
  We output a distribution from $mathcalQ$ whose total variation distance to $p$ is comparable to the best such distribution. We show that the constraint of local differential privacy incurs an exponential increase in cost. Our algorithms result in exponential improvements on the round complexity of previous methods.
  arXiv  Detail & Related papers  (2020-02-21T18:30:48Z)

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.