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Achieving fault tolerance on capped color codes with few ancillas

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arXiv 2021年

作者： Tansuwannont, Theerapat Leung, Debbie Institute for Quantum Computing Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada Department of Electrical and Computer Engineering Duke University DurhamNC27708 United States Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo WaterlooONN2L 3G1 Canada Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada

Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits. One major technique that can overcome this problem is the flag technique, in which high-weight errors arising from a few faults can be detected by a few ancillas and distinguished using subsequent syndrome measurements. The technique can be further improved using the fact that for some families of codes, errors of any weight are logically equivalent if they have the same syndrome and weight parity, as previously shown in [1]. In this work, we develop a notion of distinguishable fault set which captures both concepts of flags and weight parities, and extend the use of weight parities in error correction from [1] to families of capped and recursive capped color codes. We also develop fault-tolerant protocols for error correction, measurement, state preparation, and logical T gate implementation via code switching, which are sufficient for performing fault-tolerant Clifford computation on a capped color code, and performing fault-tolerant universal quantum computation on a recursive capped color code. Our protocols for a capped or a recursive capped color code of any distance require only 2 ancillas, assuming that the ancillas can be reused. The concept of distinguishable fault set also leads to a generalization of the definitions of fault-tolerant gadgets proposed by Aliferis, Gottesman, and Preskill. Copyright © 2021, The Authors. All rights reserved.

关键词： Error correction

Improved local spectral gap thresholds for lattices of finite size

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Physical Review B 2020年第16期101卷 165104-165104页

作者： Anurag Anshu Institute for Quantum Computing and Department of Combinatorics and Optimization University of Waterloo Waterloo Ontario Canada N2L 3G1 and Perimeter Institute for Theoretical Physics Waterloo Ontario Canada N2L 2Y5

Knabe's theorem lower bounds the spectral gap of a one-dimensional frustration-free local Hamiltonian in terms of the local spectral gaps of finite regions. It also provides a local spectral gap threshold for Hamiltonians that are gapless in the thermodynamic limit, showing that the local spectral gap must scale inverse linearly with the length of the region for such systems. Recent works have further improved upon this threshold, tightening it in the one-dimensional case and extending it to higher dimensions. Here, we show a local spectral gap threshold for frustration-free Hamiltonians on a finite-dimensional lattice that is optimal up to a constant factor that depends on the dimension of the lattice. Our proof is based on the detectability lemma framework and uses the notion of a coarse-grained Hamiltonian (introduced in [Anshu et al., Phys. Rev. B 93, 205142]) as a link connecting the (global) spectral gap and the local spectral gap.

关键词： 1-dimensional spin chains Strongly correlated systems Spin lattice models

Unified approach to data-driven quantum error mitigation

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Physical Review Research 2021年第3期3卷 033098-033098页

作者： Angus Lowe Max Hunter Gordon Piotr Czarnik Andrew Arrasmith Patrick J. Coles Lukasz Cincio Department of Combinatorics and Optimization and Institute for Quantum Computing University of Waterloo Waterloo Ontario Canada N2L 3G1 Instituto de Física Teórica UAM/CSIC Universidad Autónoma de Madrid 28049 Madrid Spain Theoretical Division Los Alamos National Laboratory Los Alamos New Mexico 87545 USA Quantum Science Center Oak Ridge Tennessee 37931 USA

Achieving near-term quantum advantage will require effective methods for mitigating hardware noise. Data-driven approaches to error mitigation are promising, with popular examples including zero-noise extrapolation (ZNE) and Clifford data regression (CDR). Here, we propose a scalable error mitigation method that conceptually unifies ZNE and CDR. Our approach, called variable-noise Clifford data regression (vnCDR), significantly outperforms these individual methods in numerical benchmarks. vnCDR generates training data first via near-Clifford circuits (which are classically simulable) and second by varying the noise levels in these circuits. We employ a noise model obtained from IBM's Ourense quantum computer to benchmark our method. For the problem of estimating the energy of an 8-qubit Ising model system, vnCDR improves the absolute energy error by a factor of 33 over the unmitigated results and by factors of 20 and 1.8 over ZNE and CDR, respectively. For the problem of correcting observables from random quantum circuits with 64 qubits, vnCDR improves the error by factors of 2.7 and 1.5 over ZNE and CDR, respectively.

关键词： quantum algorithms quantum simulation

Revivals imply quantum many-body scars

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Physical Review B 2020年第20期101卷 205107-205107页

作者： Álvaro M. Alhambra Anurag Anshu Henrik Wilming Perimeter Institute for Theoretical Physics Waterloo Ontario Canada N2L 2Y5 Institute for Quantum Computing and Department of Combinatorics and Optimization University of Waterloo Waterloo Ontario Canada N2L 3G1 Institute for Theoretical Physics ETH Zurich 8093 Zurich Switzerland

We derive general rigorous results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a D-dimensional lattice system of N sites initialized in a low-entangled and short-range correlated state, our results show that a perfect revival of the state after a time of at most O(poly(N)) implies the existence of at least O(N/log2D(N)) “quantum many-body scars”: energy eigenstates with energies placed in an equally spaced ladder and with Rényi entanglement entropy of at most O(log(N))+O(|∂A|) for any region A of the lattice. This shows that quantum many-body scars are a necessary consequence of revivals, independent of particularities of the Hamiltonian leading to them. We also present results for approximate revivals and for revivals of expectation values of observables and prove that the duration of revivals of states has to become vanishingly short with increasing system size.

关键词： Eigenstate thermalization quantum entanglement quantum quench quantum statistical mechanics

Composably secure device-independent encryption with certified deletion

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arXiv 2020年

作者： Kundu, Srijita Tan, Ernest Y.-Z. Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo WaterlooONN2L 3G1 Canada Institute for Theoretical Physics ETH Zürich Switzerland Institute for Quantum Computing Department of Physics and Astronomy University of Waterloo WaterlooONN2L 3G1 Canada

We study the task of encryption with certified deletion (ECD) introduced by Broadbent and Islam [BI20], but in a device-independent setting: we show that it is possible to achieve this task even when the honest parties do not trust their quantum devices. Moreover, we define security for the ECD task in a composable manner and show that our ECD protocol satisfies conditions that lead to composable security. Our protocol is based on device-independent quantum key distribution (DIQKD), and in particular the parallel DIQKD protocol based on the magic square non-local game, given by Jain, Miller and Shi [JMS20]. To achieve certified deletion, we use a property of the magic square game observed by Fu and Miller [FM18], namely that a two-round variant of the game can be used to certify deletion of a single random bit. In order to achieve certified deletion security for arbitrarily long messages from this property, we prove a parallel repetition theorem for two-round non-local games, which may be of independent interest. © 2020, CC BY.

关键词： quantum cryptography

Fast estimation of outcome probabilities for quantum circuits

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arXiv 2021年

作者： Pashayan, Hakop Reardon-Smith, Oliver Korzekwa, Kamil Bartlett, Stephen D. Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo ONN2L 3G1 Canada Perimeter Institute for Theoretical Physics WaterlooONN2L 2Y5 Canada Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University Kraków30-348 Poland Centre for Engineered Quantum Systems School of Physics The University of Sydney SydneyNSW2006 Australia

We present two classical algorithms for the simulation of universal quantum circuits on n qubits constructed from c instances of Clifford gates and t arbitrary-angle Z-rotation gates such as T gates. Our algorithms complement each other by performing best in different parameter regimes. The Estimate algorithm produces an additive precision estimate of the Born rule probability of a chosen measurement outcome with the only source of run-time inefficiency being a linear dependence on the stabilizer extent (which scales like ≈ 1.17t for T gates). Our algorithm is state-of-the-art for this task: as an example, in approximately 13 hours (on a standard desktop computer), we estimated the Born rule probability to within an additive error of 0.03, for a 50-qubit, 60 non-Clifford gate quantum circuit with more than 2000 Clifford gates. Our second algorithm, Compute, calculates the probability of a chosen measurement outcome to machine precision with run-time O (2t−rt) where r is an efficiently computable, circuit-specific quantity. With high probability, r is very close to min {t, n − w} for random circuits with many Clifford gates, where w is the number of measured qubits. Compute can be effective in surprisingly challenging parameter regimes, e.g., we can randomly sample Clifford+T circuits with n = 55, w = 5, c = 105 and t = 80 T gates, and then compute the Born rule probability with a run-time consistently less than 10 minutes using a single core of a standard desktop computer. We provide a C+Python implementation of our algorithms and benchmark them using random circuits, the hidden shift algorithm and the quantum approximate optimization algorithm (QAOA). Copyright © 2021, The Authors. All rights reserved.

关键词： Probability

Optical quantum communication complexity in the simultaneous-message-passing model

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Physical Review A 2020年第6期102卷 062608-062608页

作者： Ashutosh Marwah Dave Touchette Institute for Quantum Computing Department of Physics and Astronomy University of Waterloo 200 University Ave W Waterloo N2L 3G1 ON Canada Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo 200 University Ave W Waterloo N2L 3G1 ON Canada Perimeter Institute for Theoretical Physics 31 Caroline St N Waterloo N2L 2Y5 ON Canada

The communication cost of a classical protocol is typically measured in terms of the number of bits communicated for this determines the time required for communication during the protocol. Similarly, for quantum communication protocols, which use finite-dimensional quantum states, the communication cost is measured in terms of the number of qubits communicated. However, in quantum physics, one can also use infinite-dimensional states, like optical quantum states, for communication protocols. Communication cost measures based on counting the (equivalent) number of qubits transmitted during communication cannot be directly used to measure the cost of such protocols, which use infinite-dimensional states. Moreover, one cannot infer any physical property of infinite-dimensional protocols using such qubit-based communication costs. In this paper, we provide a framework to understand the growth of physical resources in infinite-dimensional protocols. We focus on optical protocols for the sake of concreteness. The time required for communication and the energy expended during communication are identified as the important physical resources of such protocols. In an optical protocol, the time required for communication is determined by the number of time-bin modes that are transmitted from one party to another. The mean photon number of the messages sent determines the energy required during communication in the protocol. We prove a lower bound on the tradeoff between the growth of these two quantities with the growth of the problem size. We call such tradeoff relations optical quantum communication complexity relations.

关键词： quantum communication quantum protocols

Adaptive shot allocation for fast convergence in variational quantum algorithms

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arXiv 2021年

作者： Gu, Andi Lowe, Angus Dub, Pavel A. Coles, Patrick J. Arrasmith, Andrew Theoretical Division Los Alamos National Laboratory Los AlamosNM87545 United States Department of Physics University of California BerkeleyCA94720 United States Department of Combinatorics and Optimization and Institute for Quantum Computing University of Waterloo WaterlooONN2L 3G1 Canada Chemistry Division Los Alamos National Laboratory Los AlamosNM87545 United States

Variational quantum Algorithms (VQAs) are a promising approach for practical applications like chemistry and materials science on near-term quantum computers as they typically reduce quantum resource requirements. However, in order to implement VQAs, an efficient classical optimization strategy is required. Here we present a new stochastic gradient descent method using an adaptive number of shots at each step, called the global Coupled Adaptive Number of Shots (gCANS) method, which improves on prior art in both the number of iterations as well as the number of shots required. These improvements reduce both the time and money required to run VQAs on current cloud platforms. We analytically prove that in a convex setting gCANS achieves geometric convergence to the optimum. Further, we numerically investigate the performance of gCANS on some chemical configuration problems. We also consider finding the ground state for an Ising model with different numbers of spins to examine the scaling of the method. We find that for these problems, gCANS compares favorably to all of the other optimizers we consider. Copyright © 2021, The Authors. All rights reserved.

关键词： Ising model

Reducing the CNOT count for Clifford+T circuits on NISQ architectures

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arXiv 2020年

作者： Gheorghiu, Vlad Huang, Jiaxin Li, Sarah Meng Mosca, Michele Mukhopadhyay, Priyanka Institute for Quantum Computing University of Waterloo WaterlooON Canada SoftwareQ Inc. KitchenerON Canada Faculty of Mathematics University of Waterloo Canada Department of Combinatorics and Optimization University of Waterloo WaterlooON Canada Perimeter Institute for Theoretical Physics Waterloo WaterlooON Canada

While mapping a quantum circuit to the physical layer one has to consider the numerous constraints imposed by the underlying hardware architecture. Connectivity of the physical qubits is one such constraint that restricts two-qubit operations, such as CNOT, to "connected" qubits. SWAP gates can be used to place the logical qubits on admissible physical qubits, but they entail a significant increase in CNOT-count. In this paper we consider the problem of reducing the CNOT-count in Clifford+T circuits on connectivity constrained architectures, like noisy intermediate-scale quantum (NISQ) computing devices. We "slice" the circuit at the position of Hadamard gates and "build" the intermediate {CNOT, T} sub-circuits using Steiner trees, significantly improving on previous methods. We compared the performance of our algorithms while mapping different benchmark and random circuits to some well-known architectures such as 9-qubit square grid, 16-qubit square grid, Rigetti 16-qubit Aspen, 16-qubit IBM QX5 and 20-qubit IBM Tokyo. Our methods give less CNOT-count compared to Qiskit and TKET transpiler as well as using SWAP gates. Assuming most of the errors in a NISQ circuit implementation are due to CNOT errors, then our method would allow circuits with few times more CNOT gates be reliably implemented than the previous methods would permit. © 2020, CC BY-NC-ND.

关键词： Qubits