Program with Abstracts > Thursday PM + posters

BBGKY hierarchy for quantum error mitigation 

Theo Saporiti et al.  (CEA)    —  Th 15:00-15:30

The confinement/deconfinement phase transition of QCD at finite densities is still numerically inaccessible by classical computations. Quantum computers, with their potential for exponential speedup, could overcome this challenge. However, their current physical implementations are affected by quantum noise. In my talk, I will introduce a novel quantum error mitigation technique based on a BBGKY-like hierarchy, which is applicable to any arbitrary digital quantum simulation. The core idea is to improve zero-noise extrapolations by incorporating additional constraints from the hierarchy equations associated to the digital spin system. Our results indicate that the mitigation scheme systematically improves the quality of the (1+1)-Schwinger model measurements.

Teleporting quantum errors: Knill error correction in the era of modern quantum processors

Michael Vasmer et al.  (INRIA Paris, U.Waterloo, Perimeter Institute)     —   Th 16:00-16:30

Quantum computing hardware has continued its advance in recent years, with modern processors capable of executing larger circuits with reduced noise. However, these processors remain too limited to run large-scale algorithms such as Shor's algorithm. To achieve scalable fault-tolerant quantum computation, it is widely believed that quantum error correction will be essential. In this talk, we focus on an approach to quantum error correction based on quantum teleportation, due to Knill.This approach offers many advantages, such as reducing the impact of leakage and coherent errors, and simplifying the decoding problem. Notably, we show that in Knill's approach the decoding problem for circuit-level noise is essentially the same as the decoding problem for channel noise, which means that code and decoder pairs optimised for channel noise also perform well under circuit noise. We illustrate this property by decoding a family of (high-rate) lifted product codes using belief propagation, without additional decoding layers such as OSD.

Roundtable  featuring session speakers, Paris quantum company Alice&Bob     —  Th  16:30-17:00

Michele Vischi (U Trieste)

We present a novel method for simulating the noisy behavior of quantum computers, which allows to efficiently incorporate environmental effects in the driven evolution implementing the gates acting on the qubits. We show how to modify the noiseless gate executed by the computer to include any Markovian noise, hence resulting in what we will call a noisy gate. We compare our method with the IBM qiskit simulator, and show that it follows more closely both the analytical solution of the Lindblad equation as well as the behavior of a real quantum computer, where we ran algorithms involving up to 18 qubits; as such, our protocol offers a more accurate simulator for NISQ devices. The method is flexible enough to potentially describe any noise, including non-Markovian ones. The noise simulator based on this work is available as a python package at the link, https://pypi.org/project/quantum-gates.

 Orbit dimensions of Fock states in quantum optics

Eliott Mamon (LIP6)

Both linear and Gaussian quantum optics are bases of platforms explored for quantum computing. However, by default they are sub-univeral, and thus both require additional costly experimental ingredients to be able to universally drive quantum states in Fock space. In the meantime, preparable states are only able to attain a strict subspace of state space under arbitrary linear or Gaussian unitaries, called the orbit of the state. As preparing specific bosonic states is also experimentally challenging, understanding the structure of orbits of preparable states under these sub-universal unitaries is crucial to gain insight on the state space that current optical platforms can explore.

We propose using the dimension of these orbits as a simple yet powerful measure of their "richness", i.e. how many states an initial state can reach under linear or Gaussian unitaries. This dimension is computable for a wide class of states from the unitary group's Lie algebra, and is invariant under the action of the group. We demonstrate this approach for Fock basis states and show how orbit dimension offers both a diagnostic for state convertibility and an experimental witness of non-Gaussianity.

Efficient quantum circuits for quantum state preparation, diagonal operators and multi-controlled gates

Julien Zylberman  (Observatoire de Paris)

Many quantum algorithms rely on the assumption that efficient quantum routines exist for tasks such as quantum state preparation (the process of encoding classical data into qubit states), unitary and non-unitary diagonal operators, and multi-controlled operations. Implementing these routines on a quantum computer necessitates the synthesis of quantum circuits, where efficiency is gauged by circuit size, depth, and the number of ancilla qubits required. However, existing methods for exact quantum circuit synthesis, particularly for quantum state preparation and diagonal operators, often scale exponentially with the number of qubits. In this poster, we present novel routines with efficient complexity scalings leveraging parallelization and approximation methods [1][2]. Additionally, we present the first quantum circuit for n-controlled gates with sublinear-in-n circuit depth without ancilla [3].    

Ref: [1] PRA 109(4), 042401 [2] ACM 10.1145/3718348 [3] Nature Communications 15:5886

Advantage of Quantum Machine Learning from General Computational Advantages

Natsuto Isogai et al. (Tokyo University)

An overarching milestone of quantum machine learning (QML) is to demonstrate the advantage of QML over all possible classical learning methods in accelerating a common type of learning task as represented by supervised learning with classical data. In supervised learning, in terms of the PAC learning model, learning complexity is defined for a class of functions, called a concept class, reduced to the computational complexity when the class has only one function. Therefore, advantages of computational complexity does not straight forwardly imply advantages of learning complexity. The provable advantages of QML in supervised learning have been known so far only for the learning tasks designed for using the advantage of specific quantum algorithms, i.e., Shor’s algorithms. Here we explicitly construct an unprecedentedly broader family of supervised learning tasks with classical data to offer the provable advantage of QML based on general quantum computational advantages in the PAC learning model, progressing beyond Shor’s algorithms.

QHC: Ultra Minimal Quantum Hardware with Simplified Circuitry

Omid Faizy (LCMCP, Sorbonne University)

Quantum computing relies on preparing a quantum core in a specific state and measuring the resulting outcome after quantum evolution. In Quantum Hamiltonian Computing (QHC), these essential processes—state preparation (input) and measurement (output)—are fully integrated within the quantum core, embedded directly in its graph topology. This approach sets QHC apart from classical computers, which feature spatially distinct hardware for input, processing, and output, and from qubit-based quantum computers, which, while unifying processing within a quantum core, still employ separate input and output registers. By embedding all computational functions into the quantum graph, QHC achieves an ultra-minimal hardware design with simplified circuitry, eliminating the need for distinct registers and interconnects. Furthermore, the performance of QHC, including its response time to inputs and the strategies for extracting results, is intricately tied to the topology of the quantum graph. This dependence highlights the pivotal role of graph structure in defining the capabilities of this innovative computing paradigm. 

One-to-one Correspondence between Deterministic Port-Based Teleportation and Unitary Estimation

Satoshi Yoshida (Tokyo University)

Port-based teleportation is a variant of quantum teleportation, where the receiver can choose one of the ports in his part of the entangled state shared with the sender, but cannot apply other recovery operations. We show that the optimal fidelity of deterministic port-based teleportation (dPBT) using N=n+1 ports to teleport a d-dimensional state is equivalent to the optimal fidelity of d-dimensional unitary estimation using n calls of the input unitary operation. From any given dPBT, we can explicitly construct the corresponding unitary estimation protocol achieving the same optimal fidelity, and vice versa. Using the obtained one-to-one correspondence between dPBT and unitary estimation, we derive the asymptotic optimal fidelity of port-based teleportation given by 1 – O(d⁴N^-2)  ≤ F ≤  1 – (d⁴N^-2), which improves the previously known result given by 1 – O(d⁵N^-2)  ≤ F ≤  1 – (d²N^-2).

We also show that the optimal fidelity of unitary estimation for the case n ≤ d –1 is  F = (n +1)/d², and this fidelity is equal to the optimal fidelity of unitary inversion with n ≤ d –1 calls of the input unitary operation even if we allow indefinite causal order among the calls.

Towards an error-protected qubit based on pinhole Josephson junctions

Tien Nguyen Dinh, Joël Griesmar (Ecole Polytechnique)

Transmon-based devices have demonstrated logical qubits that surpass the performance of their physical components. However, scaling quantum error correction (QEC) requires large hardware overhead. Alternatively, intrinsically noise-resilient qubits could reduce such overhead. In this work, we focus on the realisation of a cos 2φ qubit based on high-transmission junctions termed pinhole junctions—a design in which the two ground states reside in distinct parity subspaces, naturally protecting the qubit from local noise and errors. Our immediate objective is to demonstrate quantum coherence by observing Rabi and Ramsey oscillations in the protected regime. Further work will focus on implementing high-fidelity single- and two-qubit gates and extending the architecture to one- and two-dimensional arrays to explore exotic quantum states, such as Gottesman-Kitaev-Preskill states.

Analysis, Synthesis and Measurement of Quantum Linear Time-Invariant Systems

Jacques Ding (IN2P3, CNRS)

From first principles, we develop a general framework to quantize, synthesize and measure any multimode Linear Time-Invariant system from its classical transfer function, thus revealing its fundamental quantum noise, without Markovian assumption or state-space representation. We determine the inherent Lie group structure of such systems. We present a tomography scheme that generalizes homodyne detection for frequency-dependent quantum states.

Benign Overfitting with Quantum Kernels