Efficient simulatability of continuous-variable circuits with large
Wigner negativity
- URL: http://arxiv.org/abs/2005.12026v2
- Date: Mon, 22 Mar 2021 12:57:39 GMT
- Title: Efficient simulatability of continuous-variable circuits with large
Wigner negativity
- Authors: Laura Garc\'ia-\'Alvarez, Cameron Calcluth, Alessandro Ferraro, Giulia
Ferrini
- Abstract summary: Wigner negativity is known to be a necessary resource for computational advantage in several quantum-computing architectures.
We identify vast families of circuits that display large, possibly unbounded, Wigner negativity, and yet are classically efficiently simulatable.
We derive our results by establishing a link between the simulatability of high-dimensional discrete-variable quantum circuits and bosonic codes.
- Score: 62.997667081978825
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Discriminating between quantum computing architectures that can provide
quantum advantage from those that cannot is of crucial importance. From the
fundamental point of view, establishing such a boundary is akin to pinpointing
the resources for quantum advantage; from the technological point of view, it
is essential for the design of non-trivial quantum computing architectures.
Wigner negativity is known to be a necessary resource for computational
advantage in several quantum-computing architectures, including those based on
continuous variables (CVs). However, it is not a sufficient resource, and it is
an open question under which conditions CV circuits displaying Wigner
negativity offer the potential for quantum advantage. In this work we identify
vast families of circuits that display large, possibly unbounded, Wigner
negativity, and yet are classically efficiently simulatable, although they are
not recognized as such by previously available theorems. These families of
circuits employ bosonic codes based on either translational or rotational
symmetries (e.g., Gottesman-Kitaev-Preskill or cat codes), and can include both
Gaussian and non-Gaussian gates and measurements. Crucially, within these
encodings, the computational basis states are described by intrinsically
negative Wigner functions, even though they are stabilizer states if considered
as codewords belonging to a finite-dimensional Hilbert space. We derive our
results by establishing a link between the simulatability of high-dimensional
discrete-variable quantum circuits and bosonic codes.
Related papers
- Characterizing randomness in parameterized quantum circuits through expressibility and average entanglement [39.58317527488534]
Quantum Circuits (PQCs) are still not fully understood outside the scope of their principal application.
We analyse the generation of random states in PQCs under restrictions on the qubits connectivities.
We place a connection between how steep is the increase on the uniformity of the distribution of the generated states and the generation of entanglement.
arXiv Detail & Related papers (2024-05-03T17:32:55Z) - QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum
Circuits [82.50620782471485]
QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits.
It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness.
Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
arXiv Detail & Related papers (2024-01-10T22:33:00Z) - Minimizing the negativity of quantum circuits in overcomplete
quasiprobability representations [0.6428333375712125]
We develop an approach for minimizing the total negativity of a given quantum circuit with respect to quasiprobability representations, that are overcomplete.
Our approach includes both optimization over equivalent quasistochastic vectors and matrices, which appear due to the overcompleteness.
We also study the negativity minimization of noisy brick-wall random circuits via a combination of increasing frame dimension and applying gate merging technique.
arXiv Detail & Related papers (2023-06-19T08:02:00Z) - A learning theory for quantum photonic processors and beyond [0.0]
We consider the tasks of learning quantum states, measurements and channels generated by continuous-variable quantum circuits.
We establish efficient learnability guarantees for such classes, by computing bounds on their pseudo-dimension or covering numbers.
Our results establish that CV circuits can be trained efficiently using a number of training samples that, unlike their finite-dimensional counterpart, does not scale with the circuit depth.
arXiv Detail & Related papers (2022-09-07T11:28:17Z) - Fundamental limitations on optimization in variational quantum
algorithms [7.165356904023871]
A leading paradigm to establish such near-term quantum applications is variational quantum algorithms (VQAs)
We prove that for a broad class of such random circuits, the variation range of the cost function vanishes exponentially in the number of qubits with a high probability.
This result can unify the restrictions on gradient-based and gradient-free optimizations in a natural manner and reveal extra harsh constraints on the training landscapes of VQAs.
arXiv Detail & Related papers (2022-05-10T17:14:57Z) - Quantum circuit debugging and sensitivity analysis via local inversions [62.997667081978825]
We present a technique that pinpoints the sections of a quantum circuit that affect the circuit output the most.
We demonstrate the practicality and efficacy of the proposed technique by applying it to example algorithmic circuits implemented on IBM quantum machines.
arXiv Detail & Related papers (2022-04-12T19:39:31Z) - Gaussian initializations help deep variational quantum circuits escape
from the barren plateau [87.04438831673063]
Variational quantum circuits have been widely employed in quantum simulation and quantum machine learning in recent years.
However, quantum circuits with random structures have poor trainability due to the exponentially vanishing gradient with respect to the circuit depth and the qubit number.
This result leads to a general belief that deep quantum circuits will not be feasible for practical tasks.
arXiv Detail & Related papers (2022-03-17T15:06:40Z) - Circuit Symmetry Verification Mitigates Quantum-Domain Impairments [69.33243249411113]
We propose circuit-oriented symmetry verification that are capable of verifying the commutativity of quantum circuits without the knowledge of the quantum state.
In particular, we propose the Fourier-temporal stabilizer (STS) technique, which generalizes the conventional quantum-domain formalism to circuit-oriented stabilizers.
arXiv Detail & Related papers (2021-12-27T21:15:35Z) - Quantum amplitude damping for solving homogeneous linear differential
equations: A noninterferometric algorithm [0.0]
This work proposes a novel approach by using the Quantum Amplitude Damping operation as a resource, in order to construct an efficient quantum algorithm for solving homogeneous LDEs.
We show that such an open quantum system-inspired circuitry allows for constructing the real exponential terms in the solution in a non-interferometric.
arXiv Detail & Related papers (2021-11-10T11:25:32Z) - On exploring practical potentials of quantum auto-encoder with
advantages [92.19792304214303]
Quantum auto-encoder (QAE) is a powerful tool to relieve the curse of dimensionality encountered in quantum physics.
We prove that QAE can be used to efficiently calculate the eigenvalues and prepare the corresponding eigenvectors of a high-dimensional quantum state.
We devise three effective QAE-based learning protocols to solve the low-rank state fidelity estimation, the quantum Gibbs state preparation, and the quantum metrology tasks.
arXiv Detail & Related papers (2021-06-29T14:01:40Z)
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.