Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session L33: FaultTolerance, Gates, and LeakageFocus Live

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Sponsoring Units: DQI Chair: Guanyu Zhu, IBM TJ Watson Research Center 
Wednesday, March 17, 2021 8:00AM  8:12AM Live 
L33.00001: Towards faulttolerant quantum error correction with spin qubits in diamond Mohamed Abobeih, Yang Wang, Joe Randall, Sjoerd Loenen, Conor Bradley, Barbara Terhal, Tim Hugo Taminiau Quantum error correction (QEC) is essential for reliable largescale quantum information processing. Pioneering experiments have demonstrated QEC codes that could only correct specific types of errors using various physical platforms [1,2]. However, full experimental demonstration of a faulttolerant QEC code that can correct any type of singlequbit error remains an open challenge. Here, I will present our results towards the implementation of a faulttolerant QEC code using a solidstate spin register in diamond. Recently, we have demonstrated that such a register can hold up to 10 qubits with highfidelity universal control, coherence times up to one minute, and genuine multipartite entanglement [3,4]. Building upon these results, I will show how we can use multiple nondestructive parity measurements to encode logical states in C13 nuclearspin qubits in diamond. These parity measurements might be further used to detect and correct arbitrary singlequbit errors on the encoded states, and are therefore an important step towards faulttolerant quantum information processing. 
Wednesday, March 17, 2021 8:12AM  8:24AM Live 
L33.00002: Focus Beyond Quadratic Speedup for ErrorCorrected Quantum Advantage Ryan Babbush, Jarrod McClean, Craig M Gidney, Sergio Boixo, Hartmut Neven We discuss conditions under which it would be possible for a modest faulttolerant quantum computer to realize a runtime advantage by executing a quantum algorithm with only a small polynomial speedup over the best classical alternative. The challenge is that the computation must finish within a reasonable amount of time while being difficult enough that the small quantum scaling advantage would compensate for the large constant factor overheads associated with errorcorrection. We compute several examples of such runtimes using stateoftheart surface code constructions for superconducting qubits under a variety of assumptions. We conclude that quadratic speedups will not enable quantum advantage on early generations of such faulttolerant devices unless there is a significant improvement in how we would realize quantum errorcorrection. While this conclusion persists even if we were to increase the rate of logical gates in the surface code by more than an order of magnitude, we also repeat this analysis for speedups by other polynomial degrees and find that quartic speedups look significantly more practical. 
Wednesday, March 17, 2021 8:24AM  8:36AM Live 
L33.00003: Magic State Distillation for Surface Code for Biased Noise Qubits Shraddha Singh, Shruti Puri Ultrahigh fidelity magic states are required for universal faulttolerant quantum computing with surface code. However, the error probability of the injected magic state on the surface code lattice is proportional to the physical error rate and does not reduce with code distance. Consequently, several noisy states have to be distilled via magic state distillation to get one high fidelity state, thereby increasing the overhead cost for universal, faulttolerant computation. Here we show how the structure of noise in the qubits and entangling gates can be exploited to suppress errors in the injected magic state and reduce the overall resource overheads for magic state distillation. 
Wednesday, March 17, 2021 8:36AM  8:48AM Live 
L33.00004: Scalable, pipelined stabilizer measurement scheme and highfidelity logical operations in a distance2 surface code Jorge Marques, Miguel S Moreira, Hany Ali, Nandini Muthusubramanian, Wouter Vlothuizen, Marc Beekman, Chris Zachariadis, Nadia Haider, Alessandro Bruno, Leonardo DiCarlo The ability to perform simultaneous multiround stabilizer measurements and highfidelity logical operations are necessary to realize quantum error correction. We present the realization and comparison of highfidelity faulttolerant and nonfault tolerant logical operations (initialization, gates and measurement) in Surface7, the distance2 surface code, implemented in a superconducting quantum processor. We demonstrate superior performance of the pipelined [Versluis et al., Phys. Rev. Applied 8, 034021, (2017)] implementation of multiround error detection over the parallel alternative, a key step enabling scalability to larger surface codes. 
Wednesday, March 17, 2021 8:48AM  9:00AM Live 
L33.00005: Correlation matrix tool for error diagnostics in QEC experiments Juan Atalaya, Dvir Kafri, Matthew McEwen, Zijun Chen, Rami Barends, Julian Kelly, Yu Chen, Vadim Smelyanskiy, Alexander N. Korotkov Identification and mitigation of nonconventional errors such as leakage and crosstalk in repetition and surface code experiments is essential to achieve exponential suppression of logical errors with increasing the code distance. In this talk, we introduce an errordiagnostic tool that allows us to characterize longrange as well as longtime errors on the error graph caused by, e.g., crosstalk or leakage to noncomputational states. The probability p_ij of an error involving arbitrary nodes i and j of the error graph is extracted from correlation of the error detection events at these nodes. The matrix p_ij can be used to identify particular error mechanisms and their strengths. In addition, these probabilities can provide accurate edge weights for minimumweightperfectmatching decoders. 
Wednesday, March 17, 2021 9:00AM  9:12AM Live 
L33.00006: Toward a topological CNOT between two Kerrcat qubits: part 1/2 Rodrigo Cortiñas, Nicholas Frattini, Shruti Puri, Owen Duke, Chan U Lei, Steven Girvin, Michel Devoret Schrödinger cat states, superpositions of coherent states in an oscillator, can encode a noisebiased qubit that is naturally protected against one Pauli error channel. Such a protected "cat qubit" has the ability to significantly reduce the overhead associated with quantum error correction in, for instance, a surfacecodestyle architecture. This overhead reduction relies on the ability to perform any gate in a manner that preserves the noise bias. Unlike pure twolevel systems, exchanging coherent states in one oscillator conditioned on the second oscillator's state generates a noisebiased CNOT. Such an exchangebased topological gate does not depend on the path or the speed, but only presence or absence of exchange. This exchange can also be understood as correlated motion of 4 coherent states in a 4D phase space. 
Wednesday, March 17, 2021 9:12AM  9:24AM Live 
L33.00007: Toward a topological CNOT between two Kerrcat qubits: part 2/2 Nicholas Frattini, Rodrigo Cortiñas, Shruti Puri, Owen Duke, Chan U Lei, Steven Girvin, Michel Devoret Schrödinger cat states, superpositions of coherent states in an oscillator, can encode a noisebiased qubit that is naturally protected against one Pauli error channel. Such a protected "cat qubit" has the ability to significantly reduce the overhead associated with quantum error correction in, for instance, a surfacecodestyle architecture. This overhead reduction relies on the ability to perform any gate in a manner that preserves the noise bias. Unlike pure twolevel systems, exchanging coherent states in one oscillator conditioned on the second oscillator's state generates a noisebiased CNOT. Such an exchangebased topological gate does not depend on the path or the speed, but only presence or absence of exchange. This exchange can also be understood as correlated motion of 4 coherent states in a 4D phase space. In part two, we focus on the experimental design and preliminary results. 
Wednesday, March 17, 2021 9:24AM  9:36AM Live 
L33.00008: A hardwareefficient leakagereduction scheme for a transmonbased surface code Francesco Battistel, Boris Varbanov, Barbara Terhal Leakage in superconducting transmon qubits poses a threat to quantum error correction (QEC) as leakage errors cannot be decomposed into standard Pauli errors. Furthermore, leakage can last for many QEC cycles, propagating many correlated errors through the code. Leakagereduction units can shorten the average leakage lifetime by bringing the qubit back to the computational subspace. However, many of the units investigated so far for transmons either require changes in hardware or increase the QECcycle time. 
Wednesday, March 17, 2021 9:36AM  10:12AM Live 
L33.00009: Practical Quantum Error Correction with SurfaceCats Invited Speaker: Shruti Puri In quantum error correction, faulttolerant circuits limit the ways in which errors spread in a system and are essential for reliable execution of quantum algorithms using unreliable devices. Unfortunately, faulttolerance comes at the cost of large resource overheads. In fact, the penalty in the overhead can be so serious that it can suppress potential speedups in many quantum algorithms. Therefore, we need to find ways to achieve faulttolerance in a hardwareefficient manner. Most of the work towards faulttolerance relies on generic noise models for qubit operations and is agnostic to realistic errors in specific hardware platforms. In this talk I will show how we can achieve substantial reductions in the overheads for faulttolerant quantum error correction by exploiting the underlying structure of noise in qubits encoded in bosonic degrees of freedom. I will focus on the planar surface code realized using the bosonic Kerrcat qubit and present numerical results to demonstrate improvements in the resource requirements for faulttolerance. 
Wednesday, March 17, 2021 10:12AM  10:24AM Live 
L33.00010: Pathindependent quantum gates: general formalism and algebraic structure WenLong Ma, Liang Jiang Ancilla systems are often indispensable to universal control of a nearly isolated central system. However, ancilla systems are typically more vulnerable to environmental noise, limiting the performance of such ancillaassisted control. To address this challenge, we propose a general class of pathindependent (PI) quantum gates [1], which integrate quantum error correction and quantum control and therefore can be resilient to ancilla noise. Furthermore, we reveal the underlying algebraic structure for such PI gates, which we call the PI matrix algebra. The PI matrix algebra is defined on both the ancilla and central systems but isomorphic to the ordinary matrix algebra defined on the ancilla system alone. With such an algebraic structure, we provide a unifying criterion for PI gates against general ancilla errors, with ancilla dephasing and relaxation errors as typical examples. 
Wednesday, March 17, 2021 10:24AM  10:36AM Live 
L33.00011: Removing leakageinduced correlated errors in superconducting quantum error correction  Theory Dvir Kafri, Matthew McEwen, Zijun Chen, Juan Atalaya, Kevin Satzinger, Chris Quintana, Paul V Klimov, Daniel Sank, Craig Gidney, Austin G Fowler, Yu Chen, Vadim Smelyanskiy, John Martinis, Hartmut Neven, Julian Kelly, Alexander N. Korotkov, Andre Petukhov, Rami Barends Quantum computing can become scalable through error correction, but logical error rates only decrease with system size when physical errors are sufficiently uncorrelated. During computation, unused high energy levels of superconducting qubits can become excited, creating leakage states that are longlived and mobile. Here, we report a multilevel reset protocol that returns a transmon superconducting qubit to the ground state from all relevant higher level states. The protocol is based on an adiabatic transfer of photons from each transmon to its readout resonator. We develop a threephase semiclassical model describing the protocol and find good agreement with experiment. We then discuss application of the reset gate to the bit flip repetition code. 
Wednesday, March 17, 2021 10:36AM  10:48AM Live 
L33.00012: Removing leakageinduced correlated errors in superconducting quantum error
correction  Experiment Matthew McEwen, Dvir Kafri, Zijun Chen, Juan Atalaya, Kevin Satzinger, Chris Quintana, Paul V Klimov, Daniel Sank, Craig Gidney, Austin G Fowler, Yu Chen, Vadim Smelyanskiy, John Martinis, Hartmut Neven, Julian Kelly, Alexander N. Korotkov, Andre Petukhov, Rami Barends Removing excitations from noncomputational states is an essential challenge in achieving stable quantum error correction. We present the experimental realisation of a multilevel reset protocol that produces the ground state with an error below 5e3 within 250 ns, starting from the qubit being in any of the first three excited levels. We deploy this gate in the context of the bitflip stabilizer code, and demonstrate a significant reduction in the population of leakage built up over time while running the code. We show that the removal of leakage reduces the incidence of timecorrelated errors, and significantly improves the logical error rate as well as the error suppression factor Λ. This provides the first demonstration of error suppression that is stable over large numbers of rounds. 
Wednesday, March 17, 2021 10:48AM  11:00AM On Demand 
L33.00013: Universal FaultTolerant Quantum Computing with Stabiliser Code Families Paul Webster, Michael Vasmer, Thomas Scruby, Stephen D Bartlett Scalable universal quantum computing requires faulttolerant implementations of a universal set of logical operators. Several important results constraining this goal exist in specific contexts, along with particular methods for overcoming these constraints, but no broadly applicable framework has been developed. We address this by defining a general notion of fault tolerance of quantum channels on scalable quantum errorcorrecting code families. With this definition, we present a nogo theorem that precludes a universal set of unitary faulttolerant logical operator implementations for a wide range of stabiliser code families, including concatenated codes and conventional topological stabiliser codes such as surface and colour codes. Deriving this theorem also illuminates a general approach for how nonunitary channels can circumvent its constraints, which we show is manifested in a range of apparently distinct universal, faulttolerant schemes. 
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