The large overhead imposed by quantum error correction is a critical challenge to the realization of quantum computers, and motivates searching for alternative error correcting codes and fault-tolerant circuit constructions. Postselection is a powerful tool that builds large programs out of probabilistically generated sub-circuits, and has been shown to increase the threshold of quantum error correction based on fusing fixed-size resource states or concatenated codes. In this work, we present an approach to lower the overhead of quantum computing using scalable postselection, based on directly postselecting sub-circuits with a size extensive in the code distance using decoder soft information. We introduce a metric, the partial gap, that estimates what the logical gap of a resource state will be after it is consumed, and show that postselection based on the partial gap leads to scalable improvements in the logical error rate. In the specific context of implementing logical gates via teleportation through a cluster state, we demonstrate that scalable postselection provides a $4\times$ reduction in the overhead per logical gate, at the same logical error probability.
Experimental demonstration of scalable cross-entropy benchmarking to detect measurement-induced phase transitions on a superconducting quantum processor
Multi-mode NOON states have been attracting increasing attentions recently for their abilities of obtaining supersensitive and superresolved measurements for simultaneous multiple-phase estimation. In this paper, four different methods of generating multi-mode NOON states with high photon number are proposed. The first method is a linear optical approach that makes use of the Fock state filtration to reduce lower-order Fock state terms from the coherent state inputs, which are jointly combined to produce a multi-mode NOON state with the triggering of single-photon coincidence detections (SPCD)…
Quantum error correction is an essential component for practical quantum computing on noisy quantum hardware. However, logical operations on error-corrected qubits require a significant resource overhead, especially for high-precision and high-fidelity non-Clifford rotation gates. To address this issue, we propose a postselection-based algorithm to efficiently prepare resource states for gate teleportation. Our algorithm achieves fault tolerance, demonstrating the exponential suppression of logical errors with code distance, and it applies to any stabilizer codes. We provide analytical derivat…
Continuous-variable systems realized in quantum optics play a major role in quantum information processing, and it is also one of the promising candidates for a scalable quantum computer. We introduce a resource theory for continuous-variable systems relevant to universal quantum computation. In our theory, easily implementable operations---Gaussian operations combined with feed-forward---are chosen to be the free operations, making the convex hull of the Gaussian states the natural free states. Since our free operations and free states cannot perform universal quantum computation, genuine non…
Nonstabilizerness and Error Resilience in Noisy Quantum Circuits
University of Augsburg（奥格斯堡大学）；Joint Center for Quantum Information and Computer Science, NIST and University of Maryland（量子信息与计算机科学联合中心，美国国家标准与技术研究院和马里兰大学）
Non-stabilizerness or magic resource characterizes the amount of non-Clifford operations needed to prepare quantum states. It is a crucial resource for quantum computing and a necessary condition for quantum advantage. However, quantifying magic resource beyond a few qubits has been a major challenge. Here, we introduce efficient measures of magic resource for pure quantum states with a sampling cost that is independent of the number of qubits. Our method uses Bell measurements over two copies of a state, which we implement in experiment together with a cost-free error mitigation scheme. We sh…
Scalable Simulation of Fermionic Encoding Performance on Noisy Quantum Computers
Institute for Quantum Computing, University of Waterloo（量子计算研究所，滑铁卢大学）；David R. Cheriton School of Computer Science, University of Waterloo（大卫·R·切里顿计算机科学学院，滑铁卢大学）；Perimeter Institute for Theoretical Physics（理论物理前沿研究所）；Department of Physics and Astronomy, University of Waterloo（物理与天文学系，滑铁卢大学）
A Resource Comparison of Logical T-State Preparation
School of Physics, Peking University（北京大学物理学院）；Center on Frontiers of Computing Studies, School of Computer Science, Peking University（北京大学计算机科学学院前沿计算研究中心）
Time-reversal Interferometry Using Cat States with Scalable Entangling Resources
DEVCOM Army Research Laboratory（美国国防部陆军研究实验室）；MIT-Harvard Center for Ultracold Atoms and Research Laboratory of Electronics, Massachusetts Institute of Technology（麻省理工学院哈佛超冷原子中心及电子研究实验室）；Department of Applied Physics, Stanford University（斯坦福大学应用物理系）；Department of Physics, University of Connecticut（康涅狄格大学物理系）；Institute of Quantum Physics and Center for Integrated Quantum Science and Technology (IQST), Ulm University（乌尔姆大学量子物理研究所及集成量子科学与技术中心）
While the Rydberg-blockade regime provides the natural setting for creating $W$-type entanglement with cold neutral atoms, it is demonstrated here that a scalable entanglement resource of this type can even be obtained under completely different physical circumstances. To be more precise, a special instance of twisted $W$ states -- namely, $π$-twisted ones -- can be engineered in one-dimensional arrays of cold neutral atoms with Rydberg-dressed resonant dipole-dipole interaction. In particular, it is shown here that this is possible even when a (dressed) Rydberg excitation is coupled to the mo…
The question of how quantities, like entanglement and coherence, depend on the number of copies of a given state $ρ$ is addressed. This is a hard problem, often involving optimizations over Hilbert spaces of large dimensions. Here, we propose a way to circumvent the direct evaluation of such quantities, provided that the employed measures satisfy a self-similarity property. We say that a quantity ${\cal E}(ρ^{\otimes N})$ is {\it scalable} if it can be described as a function of the variables $\{{\cal E}(ρ^{\otimes i_1}),\dots,{\cal E}(ρ^{\otimes i_q}); N\}$ for $N>i_j$, while, preserving the …
Linear optical quantum computing is beset by the lack of deterministic entangling operations besides photon loss. Motivated by advancements at the experimental front in deterministic generation of various kinds of multiphoton entangled states, we propose an architecture for linear-optical quantum computing that harnesses the availability of three-photon Greenberger-Horne-Zeilinger (GHZ) states. Our architecture and its subvariants use polarized photons in GHZ states, polarization beam splitters, delay lines, optical switches and on-off detectors. We concatenate topological quantum error correc…
We propose a scheme to implement general quantum measurements, also known as Positive Operator Valued Measures (POVMs) in dimension $d$ using only classical resources and a single ancillary qubit. Our method is based on the probabilistic implementation of $d$-outcome measurements which is followed by postselection of some of the received outcomes. We conjecture that the success probability of our scheme is larger than a constant independent of $d$ for all POVMs in dimension $d$. Crucially, this conjecture implies the possibility of realizing arbitrary nonadaptive quantum measurement protocol o…
The security of code based constructions is usually assessed by Information Set Decoding (ISD) algorithms. In the quantum setting, amplitude amplification yields an asymptotic square root gain over the classical analogue. However, it is still unclear whether a real quantum circuit could yield actual improvements or suffer an enormous overhead due to its implementation. This leads to different considerations of these quantum attacks in the security analysis of code based proposals. In this work we clarify this doubt by giving the first quantum circuit design of the fully-fledged ISD procedure, …
