Extending the lifetime of a quantum bit with error correction in superconducting circuits (original) (raw)
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Experimental Demonstration of Fault-Tolerant State Preparation with Superconducting Qubits
Physical review letters, 2017
Robust quantum computation requires encoding delicate quantum information into degrees of freedom that are hard for the environment to change. Quantum encodings have been demonstrated in many physical systems by observing and correcting storage errors, but applications require not just storing information; we must accurately compute even with faulty operations. The theory of fault-tolerant quantum computing illuminates a way forward by providing a foundation and collection of techniques for limiting the spread of errors. Here we implement one of the smallest quantum codes in a five-qubit superconducting transmon device and demonstrate fault-tolerant state preparation. We characterize the resulting code words through quantum process tomography and study the free evolution of the logical observables. Our results are consistent with fault-tolerant state preparation in a protected qubit subspace.
Realization of three-qubit quantum error correction with superconducting circuits
Quantum computers could be used to solve certain problems exponentially faster than classical computers, but are challenging to build because of their increased susceptibility to errors. However, it is possible to detect and correct errors without destroying coherence, by using quantum error correcting codes 1. The simplest of these are three-quantum-bit (three-qubit) codes, which map a one-qubit state to an entangled three-qubit state; they can correct any single phase-flip or bit-flip error on one of the three qubits, depending on the code used 2. Here we demonstrate such phase-and bit-flip error correcting codes in a superconducting circuit. We encode a quantum state 3,4 , induce errors on the qubits and decode the error syndrome—a quantum state indicating which error has occurred—by reversing the encoding process. This syndrome is then used as the input to a three-qubit gate that corrects the primary qubit if it was flipped. As the code can recover from a single error on any qubit, the fidelity of this process should decrease only quadratically with error probability. We implement the correcting three-qubit gate (known as a conditional-conditional NOT, or Toffoli, gate) in 63 nanoseconds, using an interaction with the third excited state of a single qubit. We find 85 6 1 per cent fidelity to the expected classical action of this gate, and 78 6 1 per cent fidelity to the ideal quantum process matrix. Using this gate, we perform a single pass of both quantum bit-and phase-flip error correction and demonstrate the predicted first-order insensitivity to errors. Concatenation of these two codes in a nine-qubit device would correct arbitrary single-qubit errors. In combination with recent advances in superconducting qubit coherence times 5,6 , this could lead to scalable quantum technology. Quantum error correction relies on detecting the presence of errors without gaining knowledge of the encoded quantum state. In the three-qubit error-correcting code, the subspace of the two additional 'ancilla' qubits uniquely encodes which of the four possible single-qubit errors has occurred, including the possibility of no flip. Crucially, errors consisting of finite rotations can also be corrected using these schemes because the error syndromes are allowed to be in superpositions of the possible outcomes, flipped and not flipped 2. Previous works implementing error correcting codes in liquid-7–9 and solid-state 10 NMR and with trapped ions 11,12 have demonstrated two possible strategies for using the error syndromes. The first is to measure the ancillas (thereby projecting the syndrome) and use a classical logic operation to correct the detected error. This 'feed-forward' capability is challenging in superconducting circuits as it requires a fast and high-fidelity quantum non-demolition measurement, but is probably a necessary component to achieve scalable fault tolerance 2,13. The second strategy, as recently demonstrated with trapped ions 12 and used here, is to replace the classical logic with a quantum controlled-controlled NOT (CCNOT) gate that performs the correction coherently, leaving the entropy associated with the error in the ancilla qubits, which can then be reset 14 if the code is to be repeated. The CCNOT gate performs exactly the action that would follow the measurement in the first scheme: flipping the primary qubit if and only if the ancillas encode the associated error syndrome. The CCNOT gate is also vital for a wide variety of applications such as Shor's factoring algorithm 15 and has attracted substantial experimental interest, with recent implementations in linear optics 16 , trapped ions 17 and superconducting circuits 18,19. Here we use the circuit quantum electrodynamics architecture 20 to couple four super-conducting transmon qubits 21 to a single microwave cavity bus 22 , where each qubit transition frequency can be controlled on nano-second timescales with individual flux bias lines 23 and collectively measured by interrogating transmission through the cavity 24. (The details of the device can be found in Methods Summary and in ref. 3.) The frequencies of the qubits, labelled Q 1 –Q 4 , are tuned respectively to 6, 7, 7.85 and ,13 GHz, with Q 4 unused. In this Letter, we first demonstrate the three-qubit interaction used in the gate, which is an extension of interactions used in previous two-qubit gates 3,23,25 , and show how this interaction can be used to create the desired CCNOT gate. We then verify its action and use it to demonstrate error correction for an error on a single qubit with the bit-flip code and then for simultaneous errors on all three qubits with the phase-flip code. We find a quadratic dependence of process fidelity on error probability, indicating that the algorithm is correcting errors as predicted. Our three-qubit gate uses an interaction with the third excited state of one transmon. Specifically, it relies on the unique capability among computational states (eigenstates of the Pauli operator Z) of j111ae to interact with the non-computational state j003ae (the notation jabcae refers to the excitation levels of Q 1 –Q 3 , respectively). As the direct interaction of these states is prohibited to first order, we first transfer the quantum amplitude of j111ae to the intermediate state j102ae, which itself couples strongly to j003ae. Calculated energy levels and time-domain data showing interaction between j011ae and j002ae (which is identical to that between j111ae and j102ae except for a 6-GHz offset) as a function of the flux bias on Q 2 are shown in Fig. 1a. Once the amplitude of j111ae has been transferred to j102ae with a sudden swap interaction , a three-qubit phase is acquired by moving Q 1 up in frequency adiabatically, near the avoided crossing with j003ae. Figure 1b shows the avoided crossing between these states as a function of the flux bias on Q 1. This crossing shifts the frequency of j102ae relative to the sum of the frequencies of j100ae and j002ae to yield the three-qubit phase. The detailed procedure of the gate is shown in Fig. 2a, and is implemented in 63 ns. Further details can be found in Supplementary Information. We demonstrate the gate by first measuring its classical action. The controlled-controlled phase (CCPhase) gate, which maps j111ae to 2j111ae, has no effect on pure computational states so we implement a CCNOT gate by concatenating pre-and post-gate rotations on Q 2 , as indicated in the unshaded regions of Fig. 2a. Such a gate ideally swaps j101ae and j111ae and does nothing to the remaining states. To verify this, we prepare the eight computational states, implement the gate and measure its output using three-qubit state tomography 3 to generate the classical truth table. The intended state is reached with 85 6 1% fidelity on average. This measurement is sensitive only to classical action, however, so we complete our verification by performing full quantum process tomography on the CCPhase gate, which can detect
Superconducting quantum circuits at the surface code threshold for fault tolerance
Nature, 2014
A quantum computer can solve hard problems -such as prime factoring 1,2 , database searching 3,4 , and quantum simulation 5 -at the cost of needing to protect fragile quantum states from error. Quantum error correction 6 provides this protection, by distributing a logical state among many physical qubits via quantum entanglement. Superconductivity is an appealing platform, as it allows for constructing large quantum circuits, and is compatible with microfabrication. For superconducting qubits the surface code 7 is a natural choice for error correction, as it uses only nearest-neighbour coupling and rapidly-cycled entangling gates. The gate fidelity requirements are modest: The per-step fidelity threshold is only about 99%. Here, we demonstrate a universal set of logic gates in a superconducting multi-qubit processor, achieving an average single-qubit gate fidelity of 99.92% and a two-qubit gate fidelity up to 99.4%. This places Josephson quantum computing at the fault-tolerant threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbour coupling. As a further demonstration, we construct a five-qubit Greenberger-Horne-Zeilinger (GHZ) state 8,9 using the complete circuit and full set of gates. The results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.
Removing leakage-induced correlated errors in superconducting quantum error correction
Nature Communications, 2021
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 the qubits can become excited, creating leakage states that are long-lived and mobile. Particularly for superconducting transmon qubits, this leakage opens a path to errors that are correlated in space and time. Here, we report a reset protocol that returns a qubit to the ground state from all relevant higher level states. We test its performance with the bit-flip stabilizer code, a simplified version of the surface code for quantum error correction. We investigate the accumulation and dynamics of leakage during error correction. Using this protocol, we find lower rates of logical errors and an improved scaling and stability of error suppression with increasing qubit number. This demonstration provides a key step on the path towards scalable quantum computing.
Physical Review A, 2017
The implementation of a scalable quantum computer requires quantum error correction (QEC). An important step toward this goal is to demonstrate the effectiveness of QEC where the fidelity of an encoded qubit is higher than that of the physical qubits. Therefore, it is important to know the conditions under which QEC code is effective. In this study, we analyze the simple three-qubit and nine-qubit QEC codes for quantum-dot and superconductor qubit implementations. First, we carefully analyze QEC codes and find the specific range of memory time to show the effectiveness of QEC and the best QEC cycle time. Second, we run a detailed error simulation of the chosen error-correction codes in the amplitude damping channel and confirm that the simulation data agreed well with the theoretically predicted accuracy and minimum QEC cycle time. We also realize that since the SWAP gate worked rapidly on the quantum-dot qubit, it did not affect the performance in terms of the spatial layout.
2016
Quantum information processing has experienced dramatic experimental breakthroughs over the last couple of years in many physical platforms. With current attained metrics, the horizon appears promising for building increasingly powerful quantum processors. In this talk I will review recent progress on quantum error detection and correction on superconducting qubit systems at IBM. Our experiments, which are implemented within the stabilizer formalism present in the surface code architecture, aim at demonstrating quantum error correcting protocols for fault-tolerant quantum computing. As a conclusion, I will describe and reflect on the main experimental hurdles our field will have to tackle in the incoming years.
Superconducting Circuits for Quantum Information: An Outlook
Science, 2013
The performance of superconducting qubits has improved by several orders of magnitude in the past decade. These circuits benefit from the robustness of superconductivity and the Josephson effect, and at present they have not encountered any hard physical limits. However, building an error-corrected information processor with many such qubits will require solving specific architecture problems that constitute a new field of research. For the first time, physicists will have to master quantum error correction to design and operate complex active systems that are dissipative in nature, yet remain coherent indefinitely. We offer a view on some directions for the field and speculate on its future.
2021
Building from the classical Shannon's entropy, this chapter introduces Pauli Group and quantum error correction mechanisms in correcting bit-flip, phase-flip, and mixed errors that can typically occur in quantum circuits. After building the theoretical framework, this chapter introduces the Gottesman-Knill theorem and the stabilizer formalism. The stabilizer formalism is then applied to Shor's 9-qubit error correction code, CSS code, and Steane's 7-qubit error correction code.While discussing the path towards fault-tolerant quantum systems, this chapter explores ways to solve measurement errors and introduces the toric code and the surface code.Protected qubits such as 0-π qubit, Fluxon-parity protected superconducting qubit, and parity protected superconducting-semiconductor qubit discussed in the closing sections of this chapter explain to the readers how qubits can be protected from errors at the physical level.