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Quantum mechanics provides a highly accurate description of a wide variety of physical systems. However, a demonstration that quantum mechanics applies equally to macroscopic mechanical systems has been a long-standing challenge, hindered by the difficulty of cooling a mechanical mode to its quantum ground state. The temperatures required are typically far below those attainable with standard cryogenic methods, so significant effort has been devoted to developing alternative cooling techniques. Once in the ground state, quantum-limited measurements must then be demonstrated. Here, using conventional cryogenic refrigeration, we show that we can cool a mechanical mode to its quantum ground state by using a microwave-frequency mechanical oscillator—a ‘quantum drum’—coupled to a quantum bit, which is used to measure the quantum state of the resonator. We further show that we can controllably create single quantum excitations (phonons) in the resonator, thus taking the first steps to complete quantum control of a mechanical system. Quantum mechanics you can see The bizarre, often counter-intuitive predictions of quantum mechanics have been observed in atomic-scale optical and electrical systems, but efforts to demonstrate that quantum mechanics applies equally to a mechanical system, especially one large enough to be seen with the naked eye, have proved challenging. The difficulty is cooling a mechanical system to its quantum ground state, where all classical noise is eliminated. A team at the Department of Physics at the University of California, Santa Barbara, has overcome this obstacle. Using conventional cryogenic refrigeration, they cool a mechanical resonator with a very high oscillation frequency to one-fortieth of a degree above absolute zero. This resonator, called a 'quantum drum', is coupled to a superconducting quantum bit that acts as a quantum thermometer to detect whether there are any excitations left in the resonator. When it is confirmed there are none, it is further shown that a single quantum of excitation, a phonon, can be introduced in this system and exchanged between resonator and qubit many times, thereby taking the first steps towards complete quantum control of a mechanical system. Quantum mechanics provides an accurate description of a wide variety of physical systems but it is very challenging to prove that it also applies to macroscopic (classical) mechanical systems. This is because it has been impossible to cool a mechanical mode to its quantum ground state, in which all classical noise is eliminated. Recently, various mechanical devices have been cooled to a near-ground state, but this paper demonstrates the milestone result of a piezoelectric resonator with a mechanical mode cooled to its quantum ground state.

Super states The superposition principle is a fundamental tenet of quantum mechanics, allowing a quantum system to be 'in two places at the same time'. The preparation and use of superposed states forms the basis of quantum computation and simulation. Max Hofheinz and colleagues now demonstrate the technically challenging preparation and measurement of arbitrary quantum states in an electromagnetic resonator. States with different numbers of photons are superposed in a completely controlled and deterministic manner. The superposition principle is a fundamental tenet of quantum mechanics, allowing a quantum system to be 'in two places at the same time'. Here, the preparation and measurement of arbitrary quantum states in an electromagnetic resonator is demonstrated; states with different numbers of photons are superposed in a completely controlled and deterministic manner. The superposition principle is a fundamental tenet of quantum mechanics. It allows a quantum system to be ‘in two places at the same time’, because the quantum state of a physical system can simultaneously include measurably different physical states. The preparation and use of such superposed states forms the basis of quantum computation and simulation 1 . The creation of complex superpositions in harmonic systems (such as the motional state of trapped ions 2 , microwave resonators 3 , 4 , 5 or optical cavities 6 ) has presented a significant challenge because it cannot be achieved with classical control signals. Here we demonstrate the preparation and measurement of arbitrary quantum states in an electromagnetic resonator, superposing states with different numbers of photons in a completely controlled and deterministic manner. We synthesize the states using a superconducting phase qubit to phase-coherently pump photons into the resonator, making use of an algorithm 7 that generalizes a previously demonstrated method of generating photon number (Fock) states in a resonator 8 . We completely characterize the resonator quantum state using Wigner tomography, which is equivalent to measuring the resonator’s full density matrix.

Cavity quantum electrodynamics: Fock states represent quantum purity In cavity quantum electrodynamics (QED), light–matter interactions between a single emitter (an atom or an atom-like system with discrete energy levels) and a resonant optical cavity are investigated at a fundamental level. Recent advances in solid-state implementations, which offer great design flexibility, have given this field considerable momentum. An outstanding important question has been which features in such a system show true quantum behaviour and cannot be explained with classical models. Hofheinz et al . study a 'circuit' QED system where a superconducting qubit acts as an atom-like two-energy level system and is embedded in a microwave transmission circuit, acting as the optical cavity. They demonstrate in this system the creation of pure quantum states, known as Fock states, which give specific numbers of energy quanta, in this case photons. Fock states with up to six photons are prepared and analysed. The results are important because cavity QED is expected to play a crucial role in the development of quantum information processing and communication applications. A 'circuit' quantum electrodynamics system where a superconducting qubit acts as an atom-like two-energy level system and is embedded in a microwave transmission circuit (acting as the optical cavity) is studied. In this system, it is demonstrated that the creation of pure quantum states, known as Fock states, which give specific numbers of energy quanta, in this case photons. Fock states with up to six photons are prepared and analysed. Spin systems and harmonic oscillators comprise two archetypes in quantum mechanics 1 . The spin-1/2 system, with two quantum energy levels, is essentially the most nonlinear system found in nature, whereas the harmonic oscillator represents the most linear, with an infinite number of evenly spaced quantum levels. A significant difference between these systems is that a two-level spin can be prepared in an arbitrary quantum state using classical excitations, whereas classical excitations applied to an oscillator generate a coherent state, nearly indistinguishable from a classical state 2 . Quantum behaviour in an oscillator is most obvious in Fock states, which are states with specific numbers of energy quanta, but such states are hard to create 3 , 4 , 5 , 6 , 7 . Here we demonstrate the controlled generation of multi-photon Fock states in a solid-state system. We use a superconducting phase qubit 8 , which is a close approximation to a two-level spin system, coupled to a microwave resonator, which acts as a harmonic oscillator, to prepare and analyse pure Fock states with up to six photons. We contrast the Fock states with coherent states generated using classical pulses applied directly to the resonator.

Demonstration of quantum entanglement, a key resource in quantum computation arising from a nonclassical correlation of states, requires complete measurement of all states in varying bases. By using simultaneous measurement and state tomography, we demonstrated entanglement between two solid-state qubits. Single qubit operations and capacitive coupling between two super-conducting phase qubits were used to generate a Bell-type state. Full two-qubit tomography yielded a density matrix showing an entangled state with fidelity up to 87%. Our results demonstrate a high degree of unitary control of the system, indicating that larger implementations are within reach.

Defects in Josephson junctions are considered a nuisance when it comes to using superconducting circuits as building blocks for a quantum-information processor. But if the interaction between the circuit and defects is accurately controlled—as has been demonstrated now—the imperfections might be useful, serving as memory elements. A quantum computer will require quantum bits (qubits) with good coherence that can be coupled together to form logic gates 1 , 2 . Superconducting circuits offer a novel solution 3 , 4 , 5 , 6 , 7 , 8 , 9 because qubits can be connected in elaborate ways through simple wiring, much like that of conventional integrated circuits. However, this ease of coupling is offset by coherence times shorter than those observed in molecular and atomic systems. Hybrid architectures could help skirt this fundamental trade-off between coupling and coherence by using macroscopic qubits for coupling and atom-based qubits for coherent storage 10 , 11 . Here, we demonstrate the first quantum memory operation 12 on a Josephson-phase qubit by transferring an arbitrary quantum state to a two-level state 13 (TLS), storing it there for some time, and later retrieving it. The qubit is used to probe the coherence of the TLS by measuring its energy relaxation and dephasing times. Quantum process tomography 2 , 14 completely characterizes the memory operation, yielding an overall process fidelity of 79%. Although the uncontrolled distribution of TLSs precludes their direct use in a scalable architecture, the ability to coherently couple a macroscopic device with an atomic-sized system motivates a search for designer molecules that could replace the TLS in future hybrid qubits.

Quantum process tomography provides a means of benchmarking the components and algorithms of a quantum computer in a quantitative fashion, independent of the particular architecture used. Such a procedure has now been demonstrated for a universal entangling gate in a solid-state system. Quantum gates must perform reliably when operating on standard input basis states and on complex superpositions thereof. Experiments using superconducting qubits have validated truth tables for particular implementations of, for example, the controlled-NOT gate 1 , 2 , but have not fully characterized gate operation for arbitrary superpositions of input states. Here we demonstrate the use of quantum process tomography 3 , 4 (QPT) to fully characterize the performance of a universal entangling gate between two superconducting qubits. Process tomography permits complete gate analysis, but requires precise preparation of arbitrary input states, control over the subsequent qubit interaction and ideally simultaneous single-shot measurement of output states. In recent work, it has been proposed to use QPT to probe noise properties 5 and time dynamics 6 of qubit systems and to apply techniques from control theory to create scalable qubit benchmarking protocols 7 , 8 . We use QPT to measure the fidelity and noise properties 5 of an entangling gate. In addition to demonstrating a promising fidelity, our entangling gate has an on-to-off ratio of 300, a level of adjustable coupling that will become a requirement for future high-fidelity devices. This is the first solid-state demonstration of QPT in a two-qubit system, as QPT has previously been demonstrated only with single solid-state qubits 9 , 10 , 11 .

Measurement is one of the fundamental building blocks of quantum-information processing systems. Partial measurement, where full wavefunction collapse is not the only outcome, provides a detailed test of the measurement process. We introduce quantum-state tomography in a superconducting qubit that exhibits high-fidelity single-shot measurement. For the two probabilistic outcomes of partial measurement, we find either a full collapse or a coherent yet nonunitary evolution of the state. This latter behavior explicitly confirms modern quantum-measurement theory and may prove important for error-correction algorithms in quantum computation.

Quantum behaviour in electrical circuits Bell inequalities provide a quantitative measure that can distinguish classically determined correlations from stronger quantum correlations. Experiments on microscopic systems such as atoms and photons strongly favour the quantum description, but there has been no Bell test in a solid-state system. This paper reports clear evidence for violation of a Bell inequality (and thus quantum behaviour) in a macroscopic electrical circuit consisting of superconducting phase qubits. Bell inequalities are a quantitative measure that can distinguish classically determined correlations from stronger quantum correlations, and their measurement provides strong experimental evidence that quantum mechanics provides a complete description. The violation of a Bell inequality is now demonstrated in a solid-state system; the experiment provides further strong evidence that a macroscopic electrical circuit is really a quantum system. The measurement process plays an awkward role in quantum mechanics, because measurement forces a system to ‘choose’ between possible outcomes in a fundamentally unpredictable manner. Therefore, hidden classical processes have been considered as possibly predetermining measurement outcomes while preserving their statistical distributions 1 . However, a quantitative measure that can distinguish classically determined correlations from stronger quantum correlations exists in the form of the Bell inequalities, measurements of which provide strong experimental evidence that quantum mechanics provides a complete description 2 , 3 , 4 . Here we demonstrate the violation of a Bell inequality in a solid-state system. We use a pair of Josephson phase qubits 5 , 6 , 7 acting as spin-1/2 particles, and show that the qubits can be entangled 8 , 9 and measured so as to violate the Clauser–Horne–Shimony–Holt (CHSH) version of the Bell inequality 10 . We measure a Bell signal of 2.0732 ± 0.0003, exceeding the maximum amplitude of 2 for a classical system by 244 standard deviations. In the experiment, we deterministically generate the entangled state, and measure both qubits in a single-shot manner, closing the detection loophole 11 . Because the Bell inequality was designed to test for non-classical behaviour without assuming the applicability of quantum mechanics to the system in question, this experiment provides further strong evidence that a macroscopic electrical circuit is really a quantum system 7 .

Cavity quantum electrodynamics: Fock states represent quantum purity

We calculate the energy decay rate of Josephson qubits and superconducting resonators from non-equilibrium quasiparticles. The decay rates from experiments are shown to be consistent with predictions based on a prior measurement of the quasiparticle density n_qp = 10/um^3, which suggests that non-equilibrium quasiparticles are an important decoherence source for Josephson qubits. Calculations of the energy-decay and diffusion of quasiparticles also indicate that prior engineered gap and trap structures, which reduce the density of quasiparticles, should be redesigned to improve their efficacy. This model also explains a striking feature in Josephson qubits and resonators - a small reduction in decay rate with increasing temperature.