# Browsing by Author "Brown, Kenneth R"

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Item Open Access Fault-tolerant control of an error-corrected qubit.(Nature, 2021-10) Egan, Laird; Debroy, Dripto M; Noel, Crystal; Risinger, Andrew; Zhu, Daiwei; Biswas, Debopriyo; Newman, Michael; Li, Muyuan; Brown, Kenneth R; Cetina, Marko; Monroe, ChristopherQuantum error correction protects fragile quantum information by encoding it into a larger quantum system^{1,2}. These extra degrees of freedom enable the detection and correction of errors, but also increase the control complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while controlling the logical qubit, and are essential for realizing error suppression in practice^{3-6}. Although fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. Here we experimentally demonstrate fault-tolerant circuits for the preparation, measurement, rotation and stabilizer measurement of a Bacon-Shor logical qubit using 13 trapped ion qubits. When we compare these fault-tolerant protocols to non-fault-tolerant protocols, we see significant reductions in the error rates of the logical primitives in the presence of noise. The result of fault-tolerant design is an average state preparation and measurement error of 0.6 per cent and a Clifford gate error of 0.3 per cent after offline error correction. In addition, we prepare magic states with fidelities that exceed the distillation threshold^{7}, demonstrating all of the key single-qubit ingredients required for universal fault-tolerant control. These results demonstrate that fault-tolerant circuits enable highly accurate logical primitives in current quantum systems. With improved two-qubit gates and the use of intermediate measurements, a stabilized logical qubit can be achieved.Item Open Access Improving Circuit Performance in a Trapped-Ion Quantum Computer(2021) Zhang, BichenA quantum circuit is a widely used model for quantum computation. It consists of quantum registers, which we refer to as qubits, and quantum gates. To build a large-scale trapped ion quantum computer, the performance of executing quantum circuits is a bottleneck. Atomic ions are great qubit candidates. However, high-fidelity two-qubit gates extending over all qubits with individual control in a large-scale trapped-ion system have not been achieved. Moreover, coherent gate errors in deep quantum circuits exaggerate the error since they accumulate quadratically. This thesis presents the effort to build a trapped-ion quantum computing system that possesses individual qubit control, scalable high-fidelity two-qubit gates, and the capability to run quantum circuits with multiple qubits. This thesis shows that we realize and characterize high-fidelity two-qubit gates in a system with up to 4 ions using radial modes. The ions are individually addressed by two tightly focused beams steered using micro-electromechanical system (MEMS) mirrors. We accomplish the highest two-qubit gate fidelity using radial motional modes to date. Two methods of robust frequency-modulated two-qubit gate pulse design are introduced. With the state-of-the-art scalable two-qubit gates, we propose a compilation technique, which we refer to as hidden inverses, that creates circuits robust to residual coherent errors. We present experimental data showing that hidden inverses suppress both overrotation and phase misalignment errors in our trapped-ion system, resulting in improved quantum circuit performance.

Item Open Access Quantum Error Correction for Physically Inspired Error Models(2021) Debroy, DriptoIn this dissertation we will discuss methods for creating error-robust logical qubits which have been optimized for trapped ion quantum computers. We will cover the basic building blocks of quantum information and develop an understanding of the standard techniques for building fault-tolerant quantum computers through the use of quantum error correcting codes. We will then focus on trapped ion systems, although many of the errors we consider also occur in other hardware implementations.

The majority of this dissertation is concerned with taking advantage of the structure found in experimental errors to maximize system performance. Using numerical simulation, we study the interplay of structured error models and quantum error correction. We then cover optimizations to the standard quantum error correction framework, both through gate compilation and code design, to correct coherent gate overrotation and dephasing errors. The latter section will also include experiments run on a quantum computer at the University of Maryland which verify the effectiveness of our ideas. We will end with a discussion of a method for quantum error detection in near-term systems by extending the flag gadget framework often used in quantum error correction.

Through this body of work we hope to provide evidence for the value, within the context of quantum error correction, of detailed understanding of our physical systems. Oftentimes, codes and protocols are designed without actual implementation in mind. While these studied often produce useful results, more effective methods can sometimes be found when the physics is kept in mind. Our hope is that this dissertation motivates further study of the physical error processes present in quantum computing architectures, as well as development of novel methods to correct them.

Item Open Access Robust 2-Qubit Gates in a Linear Ion Crystal Using a Frequency-Modulated Driving Force.(Physical review letters, 2018-01) Leung, Pak Hong; Landsman, Kevin A; Figgatt, Caroline; Linke, Norbert M; Monroe, Christopher; Brown, Kenneth RIn an ion trap quantum computer, collective motional modes are used to entangle two or more qubits in order to execute multiqubit logical gates. Any residual entanglement between the internal and motional states of the ions results in loss of fidelity, especially when there are many spectator ions in the crystal. We propose using a frequency-modulated driving force to minimize such errors. In simulation, we obtained an optimized frequency-modulated 2-qubit gate that can suppress errors to less than 0.01% and is robust against frequency drifts over ±1 kHz. Experimentally, we have obtained a 2-qubit gate fidelity of 98.3(4)%, a state-of-the-art result for 2-qubit gates with five ions.Item Open Access Robust Ion Trap Quantum Computation Enabled by Quantum Control(2020) Leung, Pak Hong (James)The advent of quantum computation foretells a new era in science and technology, but the fragility of quantum bits (qubits) and the unreliability of gates hinder the realization of functioning quantum computers. For ion trap quantum computers in particular, 2-qubit operations relying on the M\o lmer-S\o rensen interaction have the greatest error rates. This dissertation introduces frequency-modulated (FM) pulses as a measure to maximize 2-qubit gate fidelity and a way to calibrate gate errors through the measurement of circuit performance.

A key challenge of two-qubit gates in ion chains is unwanted residual entanglement between the ion spin and its motion. Frequency-modulated pulses are developed to achieve such goal. This theoretical advance has led to high-fidelity 2-qubit gates that are robust against small frequency drifts in a 5-ion experiment. Combining frequency and amplitude modulation, numerical calculations suggest that entanglement between an arbitrary pair of qubits are possible in a lattice with up to 50 ions. More recently, long-distance 2-qubit gates have been realized within a 17-ion chain.

Quantum circuit calibration is proposed to improve quantum circuits using feedback from measurement results. A relationship between the error parameters and measured observables can be established to identify systematic circuit errors. The calibration of a 6-qubit parity check circuit targeting 2-qubit overrotations has been implemented using measurement results from an experimental 15-ion trap. This improvement is conducive to quantum error correction protocols which involve high-weight stabilizers. A 4-bit Toffoli circuit with an error vector of length 6 is calibrated using a custom circuit simulator, reducing the average error size by a factor of 4. Using linear and quadratic approximation, a 6-bit Toffoli circuit with 12 error parameters is calibrated in the presence of 3 ancilla qubits.

Item Open Access Stabilizer Slicing: Coherent Error Cancellations in Low-Density Parity-Check Stabilizer Codes.(Physical review letters, 2018-12) Debroy, Dripto M; Li, Muyuan; Newman, Michael; Brown, Kenneth RCoherent errors are a dominant noise process in many quantum computing architectures. Unlike stochastic errors, these errors can combine constructively and grow into highly detrimental overrotations. To combat this, we introduce a simple technique for suppressing systematic coherent errors in low-density parity-check stabilizer codes, which we call stabilizer slicing. The essential idea is to slice low-weight stabilizers into two equally weighted Pauli operators and then apply them by rotating in opposite directions, causing their overrotations to interfere destructively on the logical subspace. With access to native gates generated by three-body Hamiltonians, we can completely eliminate purely coherent overrotation errors, and for overrotation noise of 0.99 unitarity we achieve a 135-fold improvement in the logical error rate of surface-17. For more conventional two-body ion trap gates, we observe an 89-fold improvement for Bacon-Shor-13 with purely coherent errors which should be testable in near-term fault-tolerance experiments. This second scheme takes advantage of the prepared gauge degrees of freedom, and to our knowledge is the first example in which the state of the gauge directly affects the robustness of a code's memory. This Letter demonstrates that coherent noise is preferable to stochastic noise within certain code and gate implementations when the coherence is utilized effectively.Item Open Access Validation of Attaining a Higher Threshold Using Double-Pass MWPM Decoding of CSS Codes Using X/Z Correlations(2023) Pendse, Ruchi AnantIn this report we validate that Minimum Weight Perfect Matching (MWPM) decoding ofa surface code helps attain a higher code threshold than standard decoding by taking into account the correlations of errors that occur on the lattice. Correlated decoding cannot be directly performed using MWPM due to the presence of hyperedges in the graph. Decomposing correlated errors into simultaneous X and Z excitations, along with considering an asymmetric code for optimal performance of this scheme, yields a codecapacity threshold of 15% for standard depolarizing error by updating the weights of one decoding graph based on the corrections of another.