Creating entangled logical qubits in the heavy-hex lattice with topological codes

• URL: http://arxiv.org/abs/2404.15989v1
• Date: Wed, 24 Apr 2024 17:02:35 GMT
• Title: Creating entangled logical qubits in the heavy-hex lattice with topological codes
• Authors: Bence Hetényi, James R. Wootton,
• Abstract summary: In this work we show how this bug can be turned into a feature. We demonstrate entanglement between logical qubits with code distance up to $d = 4$. We verify the violation of Bell's inequality for both the $d=2$ case with post selection featuring a fidelity of $94%$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Designs for quantum error correction depend strongly on the connectivity of the qubits. For solid state qubits, the most straightforward approach is to have connectivity constrained to a planar graph. Practical considerations may also further restrict the connectivity, resulting in a relatively sparse graph such as the heavy-hex architecture of current IBM Quantum devices. In such cases it is hard to use all qubits to their full potential. Instead, in order to emulate the denser connectivity required to implement well-known quantum error correcting codes, many qubits remain effectively unused. In this work we show how this bug can be turned into a feature. By using the unused qubits of one code to execute another, two codes can be implemented on top of each other, allowing easy application of fault-tolerant entangling gates and measurements. We demonstrate this by realizing a surface code and a Bacon-Shor code on a 133 qubit IBM Quantum device. Using transversal CX gates and lattice surgery we demonstrate entanglement between these logical qubits with code distance up to $d = 4$ and five rounds of stabilizer measurement cycles. The nonplanar coupling between the qubits allows us to simultaneously measure the logical $XX$, $YY$, and $ZZ$ observables. With this we verify the violation of Bell's inequality for both the $d=2$ case with post selection featuring a fidelity of $94\%$, and the $d=3$ instance using only quantum error correction.

Related papers

• Demonstrating real-time and low-latency quantum error correction with superconducting qubits [52.08698178354922]
  We demonstrate low-latency feedback with a scalable FPGA decoder integrated into a superconducting quantum processor. We observe logical error suppression as the number of decoding rounds is increased. The decoder throughput and latency developed in this work, combined with continued device improvements, unlock the next generation of experiments.
  arXiv  Detail & Related papers  (2024-10-07T17:07:18Z)
• Quantum error correction below the surface code threshold [107.92016014248976]
  Quantum error correction provides a path to reach practical quantum computing by combining multiple physical qubits into a logical qubit. We present two surface code memories operating below a critical threshold: a distance-7 code and a distance-5 code integrated with a real-time decoder. Our results present device performance that, if scaled, could realize the operational requirements of large scale fault-tolerant quantum algorithms.
  arXiv  Detail & Related papers  (2024-08-24T23:08:50Z)
• Entangling four logical qubits beyond break-even in a nonlocal code [0.0]
  Quantum error correction protects logical quantum information against environmental decoherence. We encode the GHZ state in four logical qubits with fidelity $ 99.5 pm 0.15 % le F le 99.7 pm 0.1% $ (after postselecting on over 98% of outcomes) Our results are a first step towards realizing fault-tolerant quantum computation with logical qubits encoded in geometrically nonlocal quantum low-density parity check codes.
  arXiv  Detail & Related papers  (2024-06-04T18:00:00Z)
• 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)
• Fault-tolerant hyperbolic Floquet quantum error correcting codes [0.0]
  We introduce a family of dynamically generated quantum error correcting codes that we call "hyperbolic Floquet codes" One of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a $[[400,52,8]]$ code. At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder.
  arXiv  Detail & Related papers  (2023-09-18T18:00:02Z)
• High-threshold and low-overhead fault-tolerant quantum memory [4.91491092996493]
  We present an end-to-end quantum error correction protocol based on a family of LDPC codes with a high encoding rate. We show that 12 logical qubits can be preserved for nearly one million syndrome cycles using 288 physical qubits.
  arXiv  Detail & Related papers  (2023-08-15T17:55:12Z)
• Quantum computation on a 19-qubit wide 2d nearest neighbour qubit array [59.24209911146749]
  This paper explores the relationship between the width of a qubit lattice constrained in one dimension and physical thresholds. We engineer an error bias at the lowest level of encoding using the surface code. We then address this bias at a higher level of encoding using a lattice-surgery surface code bus.
  arXiv  Detail & Related papers  (2022-12-03T06:16:07Z)
• Protecting Expressive Circuits with a Quantum Error Detection Code [0.0]
  We develop a quantum error detection code for implementations on existing trapped-ion computers. By encoding $k$ logical qubits into $k+2$ physical qubits, this code presents fault-tolerant state initialisation and syndrome measurement circuits.
  arXiv  Detail & Related papers  (2022-11-12T16:46:35Z)
• Suppressing quantum errors by scaling a surface code logical qubit [147.2624260358795]
  We report the measurement of logical qubit performance scaling across multiple code sizes. Our system of superconducting qubits has sufficient performance to overcome the additional errors from increasing qubit number. Results mark the first experimental demonstration where quantum error correction begins to improve performance with increasing qubit number.
  arXiv  Detail & Related papers  (2022-07-13T18:00:02Z)
• Fault-tolerant Coding for Quantum Communication [71.206200318454]
  encode and decode circuits to reliably send messages over many uses of a noisy channel. For every quantum channel $T$ and every $eps>0$ there exists a threshold $p(epsilon,T)$ for the gate error probability below which rates larger than $C-epsilon$ are fault-tolerantly achievable. Our results are relevant in communication over large distances, and also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise.
  arXiv  Detail & Related papers  (2020-09-15T15:10:50Z)
• Describing quantum metrology with erasure errors using weight distributions of classical codes [9.391375268580806]
  We consider using quantum probe states with a structure that corresponds to classical $[n,k,d]$ binary block codes of minimum distance. We obtain bounds on the ultimate precision that these probe states can give for estimating the unknown magnitude of a classical field.
  arXiv  Detail & Related papers  (2020-07-06T16:22:40Z)

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.