Quantum computing is believed to be particularly useful for the simulation of chemistry and materials, among the various applications. In recent years, there have been significant advancements in the development of near-term quantum algorithms for quantum simulation, including VQE and many of its variants. However, for such algorithms to be useful, they need to overcome several critical barriers including the inability to prepare high-quality approximations of the ground state. Current challenges to state preparation, including barren plateaus and the high-dimensionality of the optimization landscape, make state preparation through ansatz optimization unreliable. In this work, we introduce the method of ground state boosting, which uses a limited-depth quantum circuit to reliably increase the overlap with the ground state. This circuit, which we call a booster, can be used to augment an ansatz from VQE or be used as a stand-alone state preparation method. The booster converts circuit depth into ground state overlap in a controllable manner. We numerically demonstrate the capabilities of boosters by simulating the performance of a particular type of booster, namely the Gaussian booster, for preparing the ground state of $N_2$ molecular system. Beyond ground state preparation as a direct objective, many quantum algorithms, such as quantum phase estimation, rely on high-quality state preparation as a subroutine. Therefore, we foresee ground state boosting and similar methods as becoming essential algorithmic components as the field transitions into using early fault-tolerant quantum computers.
Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code
在容错量子计算方案中，开销通常由可靠地准备码字的成本决定。该成本通常与底层量子纠错码的块大小成二次方地增加。因此，大的代码，否则是非常有效的发现有限的容错应用。因此，容错准备电路是优化的重要目标。我们研究了Golay码，这是一种23量子比特的量子纠错码，可以保护逻辑量子比特的距离为7。在模拟中，即使使用一个天真的辅助准备过程中，Golay码是竞争力与其他代码的开销和可容忍的噪声阈值。我们提供了两个简化的电路容错准备戈莱码编码的辅助。新电路最大限度地减少了错误传播，与标准编码电路相比，开销大约减少了四分之一。通过将恶性集计数技术应用于去极化噪声，我们进一步证明了每个门的阈值高于1.32 x 10^{-3}噪声。
Magic state distillation is one of the leading candidates for implementing universal fault-tolerant logical gates. However, the distillation circuits themselves are not fault-tolerant, so there is additional cost to first implement encoded Clifford gates with negligible error. In this paper we present a scheme to fault-tolerantly and directly prepare magic states using flag qubits. One of these schemes uses a single extra ancilla, even with noisy Clifford gates. We compare the physical qubit and gate cost of this scheme to the magic state distillation protocol of Meier, Eastin, and Knill, whic…
Transferring quantum information between distant nodes of a network is a key capability. This transfer can be realized via remote state preparation where two parties share entanglement and the sender has full knowledge of the state to be communicated. Here we demonstrate such a process between heterogeneous nodes functioning with different information encodings, i.e., particle-like discrete-variable optical qubits and wave-like continuous-variable ones. Using hybrid entanglement of light as a shared resource, we prepare arbitrary coherent-state superpositions controlled by measurements on the …
Gottesman-Kitaev-Preskill (GKP) states appear to be amongst the leading candidates for correcting errors when encoding qubits into oscillators. However the preparation of GKP states remains a significant theoretical and experimental challenge. Until now, no clear definitions for fault-tolerantly preparing GKP states have been provided. Without careful consideration, a small number of faults can lead to large uncorrectable shift errors. After proposing a metric to compare approximate GKP states, we provide rigorous definitions of fault-tolerance and introduce a fault-tolerant phase estimation p…
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…
Fault-tolerant quantum computation (FTQC) schemes that use multi-qubit large block codes can potentially reduce the resource overhead to a great extent. A major obstacle is the requirement of a large number of clean ancilla states of different types without correlated errors inside each block. These ancilla states are usually logical stabilizer states of the data code blocks, which are generally difficult to prepare if the code size is large. Previously we have proposed an ancilla distillation protocol for Calderbank-Shor-Steane (CSS) codes by classical error-correcting codes. It was assumed t…
The overhead cost of performing universal fault-tolerant quantum computation for large scale quantum algorithms is very high. Despite several attempts at alternative schemes, magic state distillation remains one of the most efficient schemes for simulating non-Clifford gates in a fault-tolerant way. However, since magic state distillation circuits are not fault-tolerant, all Clifford operations must be encoded in a large distance code in order to have comparable failure rates with the magic states being distilled. In this work, we introduce a new concept which we call redundant ancilla encodin…
Extremely Low-Cost Magic State Preparation toward Fault-Tolerant Quantum Computing
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（北京大学前沿交叉学科研究院计算机学院）
Symmetry-Adapted State Preparation for Quantum Chemistry on Fault-Tolerant Quantum Computers
Graduate School of Engineering Science, The University of Osaka（大阪大学工学研究科）；Center for Quantum Information and Quantum Biology, The University of Osaka（大阪大学量子信息与量子生物学中心）
Entanglement boosting: Low-volume logical Bell pair preparation for distributed fault-tolerant quantum computation
Nanofiber Quantum Technologies, Inc. (NanoQT)（纳米纤维量子技术有限公司）；Clarendon Laboratory, University of Oxford（牛津大学克拉伦登实验室）；Department of Computer Science, Graduate School of Information Science and Technology, The University of Tokyo（东京大学大学院信息理工学研究系计算机科学专业）
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the encoded logical qubit. Fault-tolerant circuits contain the spread of errors while operating the logical qubit, and are essential for realizing error suppression in practice. While fault-tolerant design works in principle, it has not previously been demonstrated in an error-corrected physical system with native noise characteristics. In this work, we experimenta…
Bosonic fault tolerant quantum computing requires preparations of Bosonic code states like cat states and GKP states with high fidelity and reliable quantum certification of these states. Although many proposals on preparing these states have been developed, few investigation has been done on how to reliably certify these experimental states. In this paper, we develop approaches to certify whether a continuous-variable state falls inside a certain Bosonic qubit code space by detecting a witness using Gaussian measurements. Our results can be applied to certification of various cat codes includ…
