arXiv subjects

Fedor Simkovic IV

Publications and source records attributed to Fedor Simkovic IV.

8 recordsLinked to original sources

arXiv2026

Quantum Channel Polynomial Processing

We introduce a quantum algorithmic framework based on probabilistic mixtures of unitary channels that, similar to the framework of quantum singular value transformations, enables the application of arbitrary polynomials of hermitian operators onto arbitrary initial states. We show that our framework supports a flexible tradeoff between sample- and query complexity ranging from optimal query complexity, meaning logarithmic in the error, and exponentially scaling sample complexity to sub-polynomial query complexity in the error and polynomial sample complexity. Combined with the considerably lower quantum circuit complexity, compared to quantum singular value transformations with a linear combination of unitaries block encoding, we argue that our framework can be seamlessly scaled from NISQ to fault-tolerant quantum computing.

quant-ph↗

arXiv2025

Quantum error detection in qubit-resonator star architecture

Achieving industrial quantum advantage is unlikely without the use of quantum error correction (QEC). Other QEC codes beyond surface code are being experimentally studied, such as color codes and quantum Low-Density Parity Check (qLDPC) codes, that could benefit from new quantum processing unit (QPU) architectures. We introduce the six-qubit star lattice architecture that offers parallelism and effective local all-to-all connectivity and thus enables hardware-efficient implementation of certain QEC codes. As a first demonstration of this new architecture, we encode two logical qubits in a six-qubit superconducting QPU with a star-topology using the [[4, 2, 2]] code and characterize the logical states with the classical shadow framework. Logical life-time and logical error rate are measured over repeated quantum error detection cycles for various logical states including a logical Bell state. We measure logical state fidelities above 96 % for every cardinal logical state, find logical life-times above the best physical element, and logical error-per-cycle values ranging from 0.25(2) % to 0.91(3) %. In future, such star QPU can be tiled to enable QEC codes with high-weight and overlapping stabilizers for improved encoding rates.

quant-ph↗

arXiv2024

Anderson impurity solver integrating tensor network methods with quantum computing

Solving the Anderson impurity model typically involves a two-step process, where one first calculates the ground state of the Hamiltonian, and then computes its dynamical properties to obtain the Green's function. Here we propose a hybrid classical/quantum algorithm where the first step is performed using a classical computer to obtain the tensor network ground state as well as its quantum circuit representation, and the second step is executed on the quantum computer to obtain the Green's function. Our algorithm exploits the efficiency of tensor networks for preparing ground states on classical computers, and takes advantage of quantum processors for the evaluation of the time evolution, which can become intractable on classical computers. We demonstrate the algorithm using 24 qubits on a quantum computing emulator for SrVO$_3$ with a multi-orbital Anderson impurity model within the dynamical mean field theory. The tensor network based ground state quantum circuit preparation algorithm can also be performed for up to 60 qubits with our available computing resources, while the state vector emulation of the quantum algorithm for time evolution is beyond what is accessible with such resources. We show that, provided the tensor network calculation is able to accurately obtain the ground state energy, this scheme does not require a perfect reproduction of the ground state wave function on the quantum circuit to give an accurate Green's function. This hybrid approach may lead to quantum advantage in materials simulations where the ground state can be computed classically, but where the dynamical properties cannot.

quant-ph↗

arXiv2024

Operator-Projected Variational Quantum Imaginary Time Evolution

Variational Quantum Imaginary Time Evolution (VQITE) is a leading technique for ground state preparation on quantum computers. A significant computational challenge of VQITE is the determination of the quantum geometric tensor. We show that requiring the imaginary-time evolution to be correct only when projected onto a chosen set of operators allows to achieve a twofold reduction in circuit depth by bypassing fidelity estimations, and reduces measurement complexity from quadratic to linear in the number of parameters. We demonstrate by a simulation of the transverse-field Ising model that our algorithm achieves a several orders of magnitude improvement in the number of measurements required for the same accuracy.

quant-ph↗

arXiv2024

Contextual Subspace Auxiliary-Field Quantum Monte Carlo: Improved bias with reduced quantum resources

Using trial wavefunctions prepared on quantum devices to reduce the bias of auxiliary-field quantum Monte Carlo (QC-AFQMC) has established itself as a promising hybrid approach to the simulation of strongly correlated many body systems. Here, we further reduce the required quantum resources by decomposing the trial wavefunction into classical and quantum parts, respectively treated by classical and quantum devices, within the contextual subspace projection formalism. Importantly, we show that our algorithm is compatible with the recently developed matchgate shadow protocol for efficient overlap calculation in QC-AFQMC. Investigating the nitrogen dimer and the reductive decomposition of ethylene carbonate in lithium-based batteries, we observe that our method outperforms a number of established algorithm for ground state energy computations, while reaching chemical accuracy with less than half of the original number of qubits.

quant-ph↗

arXiv2024

Low-Weight High-Distance Error Correcting Fermionic Encodings

We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high minimum distance, low-weight fermionic logical operators, a small qubit to fermionic mode ratio and a simple qubit connectivity graph including ancilla qubits for the measurement of stabilizers. Our strategy consists of a three-step procedure in which we: first generate encodings with code distances up to $d\leq4$ by a brute-force enumeration technique; subsequently, we use these encodings as starting points and apply Clifford deformations to them which allows us to identify higher-distance codes with $d\leq7$; finally, we optimize the hardware connectivity graphs of resulting encodings in terms of the graph thickness and the number of connections per qubit. We report multiple promising high-distance encodings which significantly improve the weights of stabilizers and logical operators compared to previously reported alternatives.

quant-ph↗

arXiv2020

Spin and charge correlations across the metal-to-insulator crossover in the half-filled $2d$ Hubbard model

The $2d$ Hubbard model with nearest-neighbour hopping on the square lattice and an average of one electron per site is known to undergo an extended crossover from metallic to insulating behavior driven by proliferating antiferromagnetic correlations. We study signatures of this crossover in spin and charge correlation functions and present results obtained with controlled accuracy using diagrammatic Monte Carlo in the range of parameters amenable to experimental verification with ultracold atoms in optical lattices. The qualitative changes in charge and spin correlations associated with the crossover are observed at well-separated temperature scales, which encase the intermediary regime of non-Fermi-liquid character, where local magnetic moments are formed and non-local fluctuations in both channels are essential.

cond-mat.str-el↗

arXiv2020

Real-space cluster dynamical mean-field theory: Center focused extrapolation on the one- and two particle level

We revisit the cellular dynamical mean-field theory (CDMFT) for the single band Hubbard model on the square lattice at half filling, reaching real-space cluster sizes of up to 9 x 9 sites. Using benchmarks against direct lattice diagrammatic Monte Carlo at high temperature, we show that the self-energy obtained from a cluster center focused extrapolation converges faster with the cluster size than the periodization schemes previously introduced in the literature. The same benchmark also shows that the cluster spin susceptibility can be extrapolated to the exact result at large cluster size, even though its spatial extension is larger than the cluster size.

cond-mat.str-el↗