The errors caused by qubit displacements from their prescribed locations in an ensemble of spin chains are estimated analytically and calculated numerically for a quantum computer based on phosphorus donors in silicon. We show that it is possible to polarize (initialize) the nuclear spins even with displaced qubits by using Controlled NOT gates between the electron and nuclear spins of the same phosphorus atom. However, a Controlled NOT gate between the displaced electron spins is implemented with large error because of the exponential dependence of exchange interaction constant on the distance between the qubits. If quantum computation is implemented on an ensemble of many spin chains, the errors can be small if the number of chains with displaced qubits is small.
We describe how to implement quantum logic operations in a silicon-based quantum computer with phosphorus atoms serving as qubits. The information is stored in the states of nuclear spins and the conditional logic operations are implemented through the electron spins using nuclear-electron hyperfine and electron-electron exchange interactions. The electrons in our computer should stay coherent only during implementation of one Control-Not gate. The exchange interaction is constant and selective excitations are provided by a magnetic field gradient. The quantum logic operations are implemented …
Entanglement is a fundamental property of quantum mechanics, and is a primary resource in quantum information systems. Its manipulation remains a central challenge in the development of quantum technology. In this work, we demonstrate a device which can generate, manipulate, and analyse two-qubit entangled states, using miniature and mass-manufacturable silicon photonics. By combining four photon-pair sources with a reconfigurable six-mode interferometer, embedding a switchable entangling gate, we generate two-qubit entangled states, manipulate their entanglement, and analyse them, all in the …
The quality of quantum bits (qubits) in silicon is highly vulnerable to charge noise that is omni-present in semiconductor devices and is in principle hard to be suppressed. For a realistically sized quantum dot system based on a silicon-germanium heterostructure whose confinement is manipulated with electrical biases imposed on top electrodes, we computationally explore the noise-robustness of 2-qubit entangling operations with a focus on the controlled-X (CNOT) logic that is essential for designs of gate-based universal quantum logic circuits. With device simulations based on the physics of …
Control of entanglement between qubits at distant quantum processors using a two-qubit gate is an essential function of a scalable, modular implementation of quantum computation. Among the many qubit platforms, spin qubits in silicon quantum dots are promising for large-scale integration along with their nanofabrication capability. However, linking distant silicon quantum processors is challenging as two-qubit gates in spin qubits typically utilize short-range exchange coupling, which is only effective between nearest-neighbor quantum dots. Here we demonstrate a two-qubit gate between spin qub…
Quantum computation requires many qubits that can be coherently controlled and coupled to each other. Qubits that are defined using lithographic techniques are often argued to be promising platforms for scalability, since they can be implemented using semiconductor fabrication technology. However, leading solid-state approaches function only at temperatures below 100 mK, where cooling power is extremely limited, and this severely impacts the perspective for practical quantum computation. Recent works on spins in silicon have shown steps towards a platform that can be operated at higher tempera…
Stabilization of encoded logical qubits using quantum error correction is key to the realization of reliable quantum computers. While qubit codes require many physical systems to be controlled, oscillator codes offer the possibility to perform error correction on a single physical entity. One powerful encoding for oscillators is the grid state or GKP encoding, which allows small displacement errors to be corrected. Here we introduce and implement a dissipative map designed for physically realistic finite GKP codes which performs quantum error correction of a logical qubit implemented in the mo…
Casimir forces are of fundamental interest because they originate from quantum fluctuations of the electromagnetic field. Apart from controlling the Casimir force via the optical properties of the materials, a number of novel geometries have been proposed to generate repulsive and/or non-monotonic Casimir forces between bodies separated by vacuum gaps. Experimental realization of these geometries, however, is hindered by the difficulties in alignment when the bodies are brought into close proximity. Here, using an on-chip platform with integrated force sensors and actuators, we circumvent the …
Quantum error correction is of crucial importance for fault-tolerant quantum computers. As an essential step towards the implementation of quantum error-correcting codes, quantum non-demolition (QND) measurements are needed to efficiently detect the state of a logical qubit without destroying it. Here we implement QND measurements in a Si/SiGe two-qubit system, with one qubit serving as the logical qubit and the other serving as the ancilla. Making use of a two-qubit controlled-rotation gate, the state of the logical qubit is mapped onto the ancilla, followed by a destructive readout of the an…
Quantum technologies based on photons are anticipated in the areas of information processing, communication, metrology, and lithography. While there have been impressive proof-of-principle demonstrations in all of these areas, future technologies will likely require an integrated optics architecture for improved performance, miniaturization and scalability. We demonstrated high- fidelity silica-on-silicon integrated optical realizations of key quantum photonic circuits, including two-photon quantum interference with a visibility of 94.8(5)%; a controlled-NOT gate with logical basis fidelity of…
Quantum computation requires qubits that can be coupled and realized in a scalable manner, together with universal and high-fidelity one- and two-qubit logic gates \cite{DiVincenzo2000, Loss1998}. Strong effort across several fields have led to an impressive array of qubit realizations, including trapped ions \cite{Brown2011}, superconducting circuits \cite{Barends2014}, single photons\cite{Kok2007}, single defects or atoms in diamond \cite{Waldherr2014, Dolde2014} and silicon \cite{Muhonen2014}, and semiconductor quantum dots \cite{Veldhorst2014}, all with single qubit fidelities exceeding th…
Interferometers enable ultrasensitive measurement in a wide array of applications from gravitational wave searches to force microscopes. The role of quantum mechanics in the metrological limits of interferometers has a rich history, and a large number of techniques to surpass conventional limits have been proposed. In a typical measurement configuration, the tradeoff between the probe's shot noise (imprecision) and its quantum backaction results in what is known as the standard quantum limit (SQL). In this work we investigate how quantum correlations accessed by modifying the readout of the in…
We consider quantum gates for trapped ions using state-selective displacement of the ions. We generalize earlier work in order to treat arbitrary separations between the traps. This requires the impact of anharmonicity arising from the Coulomb interaction to be estimated. We show that its effects are always small enough to allow high fidelity. In particular, the method can be applied to two ions in the same trap. We also show that gates between non-neighbour ions, and hence a Toffoli (three-qubit controlled-NOT) gate, can be achieved. We discuss how the gate can be applied to logical qubits en…
Modeling Logical Gates and Read-Out of Superconducting Gottesman-Kitaev-Preskill Qubits
ARC Centre of Excellence for Engineered Quantum Systems, School of Physics, The University of Sydney（悉尼大学工程量子系统卓越研究中心物理学院）；QuTech, Delft University of Technology（代尔夫特理工大学QuTech）；Faculty of EEMCS, Delft University of Technology（代尔夫特理工大学EEMCS学院）；AWS Center for Quantum Computing（亚马逊云科技量子计算中心）；California Institute of Technology（加州理工学院）
Benchmarking and characterising quantum states and logic gates is essential in the development of devices for quantum computing. We introduce a Bayesian approach to self-consistent process tomography, called fast Bayesian tomography (FBT), and experimentally demonstrate its performance in characterising a two-qubit gate set on a silicon-based spin qubit device. FBT is built on an adaptive self-consistent linearisation that is robust to model approximation errors. Our method offers several advantages over other self-consistent tomographic methods. Most notably, FBT can leverage prior informatio…
We apply the full power of modern electronic band structure engineering and epitaxial heterostructures to design a transistor that can sense and control a single donor electron spin. Spin resonance transistors may form the technological basis for quantum information processing. One and two qubit operations are performed by applying a gate bias. The bias electric field pulls the electron wave function away from the dopant ion into layers of different alloy composition. Owing to the variation of the g-factor (Si:g=1.995, Ge:g=1.563), this displacement changes the spin Zeeman energy, allowing sin…
In analogy to the Coulomb and the Pauli spin blockade, based on the electrostatic repulsion and the Pauli exclusion principle respectively, the concept of valley blockade in Silicon nanostructures is explored. The valley parity operator is defined. Valley blockade is determined by the parity conservation of valley composition eigenvectors in quantum transport. A Silicon quantum changeover switch based on a triple of donor quantum dots capable to separate electrons having opposite valley parity by virtue of the valley parity conservation is proposed. The quantum changeover switch represents a n…
Silicon-based quantum logic is a promising technology to implement universal quantum computing. It is widely believed that a millikelvin cryogenic environment will be necessary to accommodate silicon-based qubits. This prompts a question of the ultimate scalability of the technology due to finite cooling capacity of refrigeration systems. In this work, we answer this question by studying energy dissipation due to interactions between nuclear spin impurities and qubit control pulses. We demonstrate that this interaction constrains the sustainable number of single-qubit operations per second for…
We suggest an architecture for quantum computing with spin-pair encoded qubits in silicon. Electron-nuclear spin-pairs are controlled by a dc magnetic field and electrode-switched on and off hyperfine interaction. This digital processing is insensitive to tuning errors and easy to model. Electron shuttling between donors enables multi-qubit logic. These hydrogenic spin qubits are transferable to nuclear spin-pairs, which have long coherence times, and electron spin-pairs, which are ideally suited for measurement and initialization. The architecture is scalable to highly parallel operation.
An architecture for a quantum computer is presented in which spins associated with donors in silicon function as qubits. Quantum operations on the spins are performed using a combination of voltages applied to gates adjacent to the spins and radio frequency applied magnetic fields resonant with spin transitions. Initialization and measurement of electron spins is made by electrostatic probing of a two electron system, whose orbital configuration must depend on the spin states of the electrons because of the Pauli Principle. Specific devices will be discussed which perform all the necessary ope…
We design and analyze a logical qubit composed of a linear array of electron spins in semiconductor quantum dots. To avoid the difficulty of fully controlling a two-dimensional array of dots, we adapt spin control and error correction to a one-dimensional line of silicon quantum dots. Control speed and efficiency are maintained via a scheme in which electron spin states are controlled globally using broadband microwave pulses for magnetic resonance while two-qubit gates are provided by local electrical control of the exchange interaction between neighboring dots. Error correction with two-, th…
We present two strategies for performing two-qubit operations on the electron spins of an exchange-coupled pair of phosphorus donors in silicon, using the ability to set the donor nuclear spins in arbitrary states. The effective magnetic detuning of the two electron qubits is provided by the hyperfine interaction when the $^{31}$P nuclei are prepared in opposite spin states. This can be exploited to switch on and off SWAP operations with modest tuning of the electron exchange interaction. Furthermore, the hyperfine detuning enables high-fidelity conditional rotation gates based on selective re…
A fault-tolerant quantum processor may be configured using stationary qubits interacting only with their nearest neighbours, but at the cost of significant overheads in physical qubits per logical qubit. Such overheads could be reduced by coherently transporting qubits across the chip, allowing connectivity beyond immediate neighbours. Here we demonstrate high-fidelity coherent transport of an electron spin qubit between quantum dots in isotopically-enriched silicon. We observe qubit precession in the inter-site tunnelling regime and assess the impact of qubit transport using Ramsey interferom…
Donor spin in silicon have achieved record values of coherence times and single-qubit gate fidelities. The next stage of development involves demonstrating high-fidelity two-qubit logic gates, where the most natural coupling is the exchange interaction. To aid the efficient design of scalable donor-based quantum processors, we model the two-electron wave function using a full configuration interaction method within a multi-valley effective mass theory. We exploit the high computational efficiency of our code to investigate the exchange interaction, valley population, and electron densities for…
Spin-orbit effects, inherent to electrons confined in quantum dots at a silicon heterointerface, provide a means to control electron spin qubits without the added complexity of on-chip, nanofabricated micromagnets or nearby coplanar striplines. Here, we demonstrate a novel singlet-triplet qubit operating mode that can drive qubit evolution at frequencies in excess of 200 MHz. This approach offers a means to electrically turn on and off fast control, while providing high logic gate orthogonality and long qubit dephasing times. We utilize this operational mode for dynamical decoupling experiment…
We present the experimental observation of a large exchange coupling $J \approx 300$ $μ$eV between two $^{31}$P electron spin qubits in silicon. The singlet and triplet states of the coupled spins are monitored in real time by a Single-Electron Transistor, which detects ionization from tunnel-rate-dependent processes in the coupled spin system, yielding single-shot readout fidelities above 95%. The triplet to singlet relaxation time $T_1 \approx 4$ ms at zero magnetic field agrees with the theoretical prediction for $J$-coupled $^{31}$P dimers in silicon. The time evolution of the 2-electron s…
We resolve the thermal motion of a high-stress silicon nitride nanobeam at frequencies far below its fundamental flexural resonance (3.4 MHz) using cavity-enhanced optical interferometry. Over two decades, the displacement spectrum is well-modeled by that of a damped harmonic oscillator driven by a $1/f$ thermal force, suggesting that the loss angle of the beam material is frequency-independent. The inferred loss angle at 3.4 MHz, $ϕ= 4.5\cdot 10^{-6}$, agrees well with the quality factor ($Q$) of the fundamental beam mode ($ϕ= Q^{-1}$). In conjunction with $Q$ measurements made on higher orde…
Developing devices that can reliably and accurately demonstrate the principles of superposition and entanglement is an on-going challenge for the quantum computing community. Modeling and simulation offer attractive means of testing early device designs and establishing expectations for operational performance. However, the complex integrated material systems required by quantum device designs are not captured by any single existing computational modeling method. We examine the development and analysis of a multi-staged computational workflow that can be used to design and characterize silicon…
Silicon nanoelectronic devices can host single-qubit quantum logic operations with fidelity better than 99.9%. For the spins of an electron bound to a single donor atom, introduced in the silicon by ion implantation, the quantum information can be stored for nearly 1 second. However, manufacturing a scalable quantum processor with this method is considered challenging, because of the exponential sensitivity of the exchange interaction that mediates the coupling between the qubits. Here we demonstrate the conditional, coherent control of an electron spin qubit in an exchange-coupled pair of $^{…
Individual donors in silicon chips are used as quantum bits with extremely low error rates. However, physical realizations have been limited to one donor because their atomic size causes fabrication challenges. Quantum dot qubits, in contrast, are highly adjustable using electrical gate voltages. This adjustability could be leveraged to deterministically couple donors to quantum dots in arrays of qubits. In this work, we demonstrate the coherent interaction of a $^{31}$P donor electron with the electron of a metal-oxide-semiconductor quantum dot. We form a logical qubit encoded in the spin sin…
Single electron spins confined in silicon quantum dots hold great promise as a quantum computing architecture with demonstrations of long coherence times, high-fidelity quantum logic gates, basic quantum algorithms and device scalability. While single-shot spin detection is now a laboratory routine, the need for quantum error correction in a large-scale quantum computing device demands a quantum non-demolition (QND) implementation. Unlike conventional counterparts, the QND spin readout imposes minimal disturbance to the probed spin polarization and can therefore be repeated to extinguish measu…
Proposed Silicon-based quantum computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing infrastructure of the powerful Si technology. Quantitative understanding of and precise physical control over donor (e.g. Phosphorus) exchange are crucial elements in the physics underlying the proposed Si-based quantum computer hardware. An important potential problem in this context is that inter-valley interference originating from the degeneracy in the Si conduction band …
