arXiv subjects
Publications and source records attributed to Francisca Vasconcelos.
We show that 2-fold Forrelation with inverse-polylogarithmic promise gap can be solved, with bounded error, by polynomial-size QAC$^0$ circuits. Unlike the standard oracle-based Forrelation algorithm, our circuits receive the input explicitly, in the same form as the AC$^0$ circuits against which Forrelation is known to be hard. At constant gap, this yields a natural promise-problem separation between QAC$^0$ and AC$^0$.
Dicke states serve as a critical resource in quantum metrology, communication, and computation. However, unitary preparation of Dicke states is limited to logarithmic depth in standard circuit models and existing constant-depth protocols require measurement and feed-forward. In this work, we present the first unitary, constant-depth protocols for exact Dicke state preparation. We overcome the logarithmic-depth barrier by moving beyond the standard circuit model and leveraging global interactions (native to architectures such as neutral atoms and trapped ions). Specifically, utilizing unbounded CZ gates (i.e. within the QAC$^0$ circuit class), we offer circuits for exact computation of constant-weight Dicke states, using polynomial ancillae, and approximation of weight-1 Dicke states (i.e. $W$ states), using only constant ancillae. Granted additional access to the quantum FAN-OUT operation (i.e. upgrading to the QAC$_f^0$ circuit class), we also achieve exact and clean preparation of arbitrary-weight Dicke states, with polynomial ancillae. These protocols distinguish the constant-depth capabilities of quantum architectures based on connectivity and offer a novel path toward resolving a long-standing quantum complexity conjecture.
In this work, we prove the strongest known lower bounds for QAC$^0$, allowing polynomially many gates and ancillae. Our main results show that: (1) Depth-3 QAC$^0$ circuits cannot compute PARITY, and require $\Omega(\exp(\sqrt{n}))$ gates to compute MAJORITY. (2) Depth-2 circuits cannot approximate high-influence Boolean functions (e.g., PARITY) with non-negligible advantage, regardless of size. We develop new classical simulation techniques for QAC$^0$ to obtain our depth-3 bounds. In these results, we relax the output requirement of the quantum circuit to a single bit, making our depth $2$ approximation bound stronger than the previous best bound of Rosenthal (2021). This also enables us to draw natural comparisons with classical AC$^0$ circuits, which can compute PARITY exactly in depth $2$ (exp size). Our techniques further suggest that, for boolean total functions, constant-depth quantum circuits do not necessarily provide more power than their classical counterparts. Our third result shows that depth $2$ QAC$^0$ circuits, regardless of size, cannot exactly synthesize an $n$-target nekomata state (a state whose synthesis is directly related to the computation of PARITY). This complements the depth $2$ exponential size upper bound of Rosenthal (2021) for approximating nekomatas (which is used as a sub-circuit in the only known constant depth PARITY upper bound). Finally, we argue that approximating PARITY in QAC0, with significantly better than 1/poly(n) advantage on average, is just as hard as computing it exactly. Thus, extending our techniques to higher depths would also rule out approximate circuits for PARITY and related problems
Random unitaries are a central object of study in quantum information, with applications to quantum computation, quantum many-body physics, and quantum cryptography. Recent work has constructed unitary designs and pseudorandom unitaries (PRUs) using $\Theta(\log \log n)$-depth unitary circuits with two-qubit gates. In this work, we show that unitary designs and PRUs can be efficiently constructed in several well-studied models of $\textit{constant-time}$ quantum computation (i.e., the time complexity on the quantum computer is independent of the system size). These models are constant-depth circuits augmented with certain nonlocal operations, such as (a) many-qubit TOFFOLI gates, (b) many-qubit FANOUT gates, or (c) mid-circuit measurements with classical feedforward control. Recent advances in quantum computing hardware suggest experimental feasibility of these models in the near future. Our results demonstrate that unitary designs and PRUs can be constructed in much weaker circuit models than previously thought. Furthermore, our construction of PRUs in constant-depth with many-qubit TOFFOLI gates shows that, under cryptographic assumptions, there is no polynomial-time learning algorithm for the circuit class $\mathsf{QAC}^0$. Finally, our results suggest a new approach towards proving that PARITY is not computable in $\mathsf{QAC}^0$, a long-standing question in quantum complexity theory.
Block encodings are a fundamental primitive in quantum algorithms, but can often have large ancilla overhead. In this work, we introduce novel techniques for reducing this overhead in two distinct ways. In Part I, we prove the existence of a "space-time tradeoff" by deriving an algorithm that, for any block encoding, approximately uncomputes all but one of its ancilla (freeing up those ancillae for reuse in later parts of a quantum algorithm). In Part II, we evaluate the minimum number of ancillae required to perform coherent multiplication of block encodings and introduce a "space-accuracy tradeoff". Specfically, we prove that logarithmic ancillae is optimal for exact multiplication of block encodings, but show that (in certain block encoding regimes) approximate multiplication of block encodings can be achieved to high-precision with just one ancilla.
We present the first computationally-efficient algorithm for average-case learning of shallow quantum circuits with many-qubit gates. Specifically, we provide a quasi-polynomial time and sample complexity algorithm for learning unknown QAC$^0$ circuits -- constant-depth circuits with arbitrary single-qubit gates and polynomially many $CZ$ gates of unbounded width -- with at most logarithmic ancilla, up to inverse-polynomially small error. Furthermore, we show that the learned unitary can be efficiently synthesized in poly-logarithmic depth. This work expands the family of efficiently learnable quantum circuits, notably since in finite-dimensional circuit geometries, QAC$^0$ circuits require polynomial depth to implement.
Recent developments in domains such as non-local games, quantum interactive proofs, and quantum generative adversarial networks have renewed interest in quantum game theory and, specifically, quantum zero-sum games. Central to classical game theory is the efficient algorithmic computation of Nash equilibria, which represent optimal strategies for both players. In 2008, Jain and Watrous proposed the first classical algorithm for computing equilibria in quantum zero-sum games using the Matrix Multiplicative Weight Updates (MMWU) method to achieve a convergence rate of $\mathcal{O}(d/\epsilon^2)$ iterations to $\epsilon$-Nash equilibria in the $4^d$-dimensional spectraplex. In this work, we propose a hierarchy of quantum optimization algorithms that generalize MMWU via an extra-gradient mechanism. Notably, within this proposed hierarchy, we introduce the Optimistic Matrix Multiplicative Weights Update (OMMWU) algorithm and establish its average-iterate convergence complexity as $\mathcal{O}(d/\epsilon)$ iterations to $\epsilon$-Nash equilibria. This quadratic speed-up relative to Jain and Watrous' original algorithm sets a new benchmark for computing $\epsilon$-Nash equilibria in quantum zero-sum games.
The circuit class $\mathsf{QAC}^0$ was introduced by Moore (1999) as a model for constant depth quantum circuits where the gate set includes many-qubit Toffoli gates. Proving lower bounds against such circuits is a longstanding challenge in quantum circuit complexity; in particular, showing that polynomial-size $\mathsf{QAC}^0$ cannot compute the parity function has remained an open question for over 20 years. In this work, we identify a notion of the Pauli spectrum of $\mathsf{QAC}^0$ circuits, which can be viewed as the quantum analogue of the Fourier spectrum of classical $\mathsf{AC}^0$ circuits. We conjecture that the Pauli spectrum of $\mathsf{QAC}^0$ circuits satisfies low-degree concentration, in analogy to the famous Linial, Nisan, Mansour theorem on the low-degree Fourier concentration of $\mathsf{AC}^0$ circuits. If true, this conjecture immediately implies that polynomial-size $\mathsf{QAC}^0$ circuits cannot compute parity. We prove this conjecture for the class of depth-$d$, polynomial-size $\mathsf{QAC}^0$ circuits with at most $n^{O(1/d)}$ auxiliary qubits. We obtain new circuit lower bounds and learning results as applications: this class of circuits cannot correctly compute - the $n$-bit parity function on more than $(\frac{1}{2} + 2^{-\Omega(n^{1/d})})$-fraction of inputs, and - the $n$-bit majority function on more than $(1 - \Omega(n^{-1/2}))$-fraction of inputs. Additionally we show that this class of $\mathsf{QAC}^0$ circuits with limited auxiliary qubits can be learned with quasipolynomial sample complexity, giving the first learning result for $\mathsf{QAC}^0$ circuits. More broadly, our results add evidence that "Pauli-analytic" techniques can be a powerful tool in studying quantum circuits.
Implicit neural representations (INRs) have achieved impressive results for scene reconstruction and computer graphics, where their performance has primarily been assessed on reconstruction accuracy. As INRs make their way into other domains, where model predictions inform high-stakes decision-making, uncertainty quantification of INR inference is becoming critical. To that end, we study a Bayesian reformulation of INRs, UncertaINR, in the context of computed tomography, and evaluate several Bayesian deep learning implementations in terms of accuracy and calibration. We find that they achieve well-calibrated uncertainty, while retaining accuracy competitive with other classical, INR-based, and CNN-based reconstruction techniques. Contrary to common intuition in the Bayesian deep learning literature, we find that INRs obtain the best calibration with computationally efficient Monte Carlo dropout, outperforming Hamiltonian Monte Carlo and deep ensembles. Moreover, in contrast to the best-performing prior approaches, UncertaINR does not require a large training dataset, but only a handful of validation images.
Realizing a fully connected network of quantum processors requires the ability to distribute quantum entanglement. For distant processing nodes, this can be achieved by generating, routing, and capturing spatially entangled itinerant photons. In this work, we demonstrate the deterministic generation of such photons using superconducting transmon qubits that are directly coupled to a waveguide. In particular, we generate two-photon N00N states and show that the state and spatial entanglement of the emitted photons are tunable via the qubit frequencies. Using quadrature amplitude detection, we reconstruct the moments and correlations of the photonic modes and demonstrate state preparation fidelities of $84\%$. Our results provide a path towards realizing quantum communication and teleportation protocols using itinerant photons generated by quantum interference within a waveguide quantum electrodynamics architecture.
This article provides an overview of the history, theoretical basis, and different implementations of quantum computers. In Fall 2018, four MIT faculty -- Isaac Chuang, Dirk Englund, Aram Harrow, and William Oliver -- at the forefront of quantum computation and information research were interviewed. They provided personal perspectives on the development of the field, as well as insight to its near-term trajectory. There has been a lot of recent media hype surrounding quantum computation, so in this article we present an academic view of the matter, specifically highlighting progress being made at MIT.
The practical viability of any qubit technology stands on long coherence times and high-fidelity operations, with the superconducting qubit modality being a leading example. However, superconducting qubit coherence is impacted by broken Cooper pairs, referred to as quasiparticles, with a density that is empirically observed to be orders of magnitude greater than the value predicted for thermal equilibrium by the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity. Previous work has shown that infrared photons significantly increase the quasiparticle density, yet even in the best isolated systems, it still remains higher than expected, suggesting that another generation mechanism exists. In this Letter, we provide evidence that ionizing radiation from environmental radioactive materials and cosmic rays contributes to this observed difference, leading to an elevated quasiparticle density that would ultimately limit superconducting qubits of the type measured here to coherence times in the millisecond regime. We further demonstrate that introducing radiation shielding reduces the flux of ionizing radiation and positively correlates with increased coherence time. Albeit a small effect for today's qubits, reducing or otherwise mitigating the impact of ionizing radiation will be critical for realizing fault-tolerant superconducting quantum computers.