A log-depth in-place quantum Fourier transform that rarely needs ancillas

• URL: http://arxiv.org/abs/2505.00701v1
• Date: Thu, 01 May 2025 17:58:36 GMT
• Title: A log-depth in-place quantum Fourier transform that rarely needs ancillas
• Authors: Gregory D. Kahanamoku-Meyer, John Blue, Thiago Bergamaschi, Craig Gidney, Isaac L. Chuang,
• Abstract summary: It can be cheaper to achieve a good approximation on most inputs than on all inputs.<n>We formalize this idea, and propose that such "optimistic quantum circuits" are often sufficient in the context of larger quantum algorithms.
• Score: 0.08113005007481719
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: When designing quantum circuits for a given unitary, it can be much cheaper to achieve a good approximation on most inputs than on all inputs. In this work we formalize this idea, and propose that such "optimistic quantum circuits" are often sufficient in the context of larger quantum algorithms. For the rare algorithm in which a subroutine needs to be a good approximation on all inputs, we provide a reduction which transforms optimistic circuits into general ones. Applying these ideas, we build an optimistic circuit for the in-place quantum Fourier transform (QFT). Our circuit has depth $O(\log (n / \epsilon))$ for tunable error parameter $\epsilon$, uses $n$ total qubits, i.e. no ancillas, is logarithmically local for input qubits arranged in 1D, and is measurement-free. The circuit's error is bounded by $\epsilon$ on all input states except an $O(\epsilon)$-sized fraction of the Hilbert space. The circuit is also rather simple and thus may be practically useful. Combined with recent QFT-based fast arithmetic constructions [arXiv:2403.18006], the optimistic QFT yields factoring circuits of nearly linear depth using only $2n + O(n/\log n)$ total qubits. Applying our reduction technique, we also construct the first approximate QFT to achieve the asymptotically optimal depth of $O(\log (n/\epsilon))$ with a sublinear number of ancilla qubits, well-controlled error on all inputs, and no intermediate measurements.

Related papers

• Quantum Algorithms for Non-smooth Non-convex Optimization [30.576546266390714]
  This paper considers the problem for finding the $(,epsilon)$-Goldstein stationary point of Lipschitz continuous objective. We construct a zeroth-order quantum estimator for the surrogate oracle function.
  arXiv  Detail & Related papers  (2024-10-21T16:52:26Z)
• Nearly Optimal Circuit Size for Sparse Quantum State Preparation [0.0]
  A quantum state is said to be $d$-sparse if it has only $d$ non-zero amplitudes.<n>We prove for the first time a trade-off between the number of ancillary qubits and the circuit size.
  arXiv  Detail & Related papers  (2024-06-23T15:28:20Z)
• Calculating response functions of coupled oscillators using quantum phase estimation [40.31060267062305]
  We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. Our proposed quantum algorithm operates in the standard $s-sparse, oracle-based query access model. We show that a simple adaptation of our algorithm solves the random glued-trees problem in time.
  arXiv  Detail & Related papers  (2024-05-14T15:28:37Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Space-Efficient and Noise-Robust Quantum Factoring [10.974556218898435]
  Two improvements to Regev's recent quantum factoring algorithm.<n>Regev's circuit requires $O(n3/2)$ qubits and $O(n3/2 log n)$ gates.<n>Regev's analysis of his classical postprocessing procedure requires all $approx sqrtn$ runs to be successful.
  arXiv  Detail & Related papers  (2023-10-02T04:31:21Z)
• Spacetime-Efficient Low-Depth Quantum State Preparation with Applications [93.56766264306764]
  We show that a novel deterministic method for preparing arbitrary quantum states requires fewer quantum resources than previous methods. We highlight several applications where this ability would be useful, including quantum machine learning, Hamiltonian simulation, and solving linear systems of equations.
  arXiv  Detail & Related papers  (2023-03-03T18:23:20Z)
• Asymptotically optimal synthesis of reversible circuits [0.0]
  We propose an algorithm to implement an arbitrary $n$wire circuit with no more than $ (2n n/log n)$ elementary gates.
  arXiv  Detail & Related papers  (2023-02-13T03:08:55Z)
• A lower bound on the space overhead of fault-tolerant quantum computation [51.723084600243716]
  The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation. We prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude noise.
  arXiv  Detail & Related papers  (2022-01-31T22:19:49Z)
• 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)
• Asymptotically Optimal Circuit Depth for Quantum State Preparation and General Unitary Synthesis [24.555887999356646]
  The problem is of fundamental importance in quantum algorithm design, Hamiltonian simulation and quantum machine learning, yet its circuit depth and size complexity remain open when ancillary qubits are available. In this paper, we study efficient constructions of quantum circuits with $m$ ancillary qubits that can prepare $psi_vrangle$ in depth. Our circuits are deterministic, prepare the state and carry out the unitary precisely, utilize the ancillary qubits tightly and the depths are optimal in a wide range of parameter regime.
  arXiv  Detail & Related papers  (2021-08-13T09:47:11Z)
• Low-depth Quantum State Preparation [3.540171881768714]
  A crucial subroutine in quantum computing is to load the classical data of $N$ complex numbers into the amplitude of a superposed $n=lceil logNrceil$-qubit state. Here we investigate this space-time tradeoff in quantum state preparation with classical data. We propose quantum algorithms with $mathcal O(n2)$ circuit depth to encode any $N$ complex numbers.
  arXiv  Detail & Related papers  (2021-02-15T13:11:43Z)
• Trading T gates for dirty qubits in state preparation and unitary synthesis [0.0]
  We present a quantum algorithm for preparing any dimension-$N$ pure quantum state specified by a list of $N$ classical numbers. Our scheme uses $mathcalO(fracNlambda+lambdalogfracNepsilonlogfraclogNepsilon)$ to reduce the T-gate cost to $mathcalO(fracNlambda+lambdalogfracNepsilonlogfraclogNepsilon)$
  arXiv  Detail & Related papers  (2018-12-03T18:24:32Z)

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.