PDF (double-sided) - Physics Department, UCSB - University of ...
PDF (double-sided) - Physics Department, UCSB - University of ... PDF (double-sided) - Physics Department, UCSB - University of ...
1.2 The Power of Quantum Computers The power of quantum computers roots in two revolutionary concepts that quantum mechanics introduced: Superpositions and Entanglement. 1.2.1 Superpositions According to quantum mechanics any system is described by a set of discrete states in which it can exist: the system’s “eigenstates”. It is possible for the system to exist in a superposition of these states, i.e. to be in multiple states at the same time. For example, a quantum bit can not only be in the 0 or 1 state, but it can be in both, 0 and 1, at the same time. To describe the full state of a quantum system, each eigenstate is given a complex amplitude that describes its weight, called the “probability amplitude”. A measurement of the system will then force it to “choose” between one of its eigenstates (in the basis of the measurement). The probability for each eigenstate to be chosen is given by the square of its probability amplitude. After the measurement, the system’s state “collapses” to the chosen eigenstate, i.e. the chosen eigenstate’s probability amplitude becomes 1, while all others go to 0. Since measurements always yield an answer, the square of the probability amplitudes for all states needs to sum to 1, i.e. one of the states has to be chosen. 6
In terms of quantum bits, this means that a quantum computer can not only use the two states of the bit (0 and 1) to do binary calculations, but can instead use the complex probability amplitude of the 1 state, which provides two analog values (the relative phase and amplitude of the 0 and 1 state) for calculations. This concept is discussed further in Chapter 3.3.1. 1.2.2 Entanglement Superpositions of single qubits alone do not provide a significant advantage, though, since they can be efficiently simulated by a classical computer by using a collection of classical bits to store the probability amplitudes. The true “magic” happens when several quantum systems are allowed to interact. According to quantum mechanics, the state of a collection of interacting quantum systems can no longer be described as a collection of the states of the individual systems, but instead needs to be described in terms of a new set of states that consists of all possible combinations of the individual states. For example, for three quantum bits, the combined system is not described in terms of the three qubits’ individual states that each are 0 or 1, but instead by the eight new states 000, 001, 010, 011, 100, 101, 110, and 111. In general, a system consisting of n interacting quantum bits needs to be described in terms of 2 n quantum states. A quantum computer can then be in a superposition of these 2 n 7
- Page 1: UNIVERSITY of CALIFORNIA Santa Barb
- Page 5: Benchmarking the Superconducting Jo
- Page 8 and 9: viii
- Page 11 and 12: Curriculum Vitæ Markus Ansmann Edu
- Page 13 and 14: 99:187006 Lisenfeld, J., Lukashenko
- Page 15 and 16: Abstract Benchmarking the Supercond
- Page 17 and 18: Contents Contents List of Figures L
- Page 19 and 20: 4.1.3 Readout Squid Parameters . .
- Page 21 and 22: 7.5.5 Grapher . . . . . . . . . . .
- Page 23 and 24: 11.5 Analysis and Verification . .
- Page 25 and 26: List of Figures 2.1 Inductor-Capaci
- Page 27 and 28: List of Tables 3.1 Transition Matri
- Page 29 and 30: Chapter 1 Quantum Computation 1.1 M
- Page 31 and 32: for such problems include factoring
- Page 33: if present encrypted data will rema
- Page 37 and 38: 1.2.3 Implications - The EPR Parado
- Page 39 and 40: proposed architecture of quantum bi
- Page 41 and 42: “coherence times”, i.e. the tim
- Page 43 and 44: Chapter 2 Superconducting Josephson
- Page 45 and 46: of the glue-circuitry needed to con
- Page 47 and 48: Figure 2.1: Inductor-Capacitor Osci
- Page 49 and 50: • The circuit needs to be cooled
- Page 51 and 52: Figure 2.2: Josephson Tunnel Juncti
- Page 53 and 54: the trace along the V-axis, gives c
- Page 55 and 56: Figure 2.4: Josephson Qubits: Sligh
- Page 57 and 58: the cosine forms a local minimum al
- Page 59 and 60: Figure 2.5: Example Qubit Coupling
- Page 61 and 62: Readout schemes can further be cate
- Page 63: states in the qubit’s inductor, t
- Page 66 and 67: at time t. r is not restricted to b
- Page 68 and 69: 3.1.2 Effects of a Time Dependent P
- Page 70 and 71: In some cases, it is possible to so
- Page 72 and 73: Figure 3.1: Examples of Numerical S
- Page 74 and 75: • The energy difference between t
- Page 76 and 77: like this: V = ( V (−1, −1), V
- Page 78 and 79: Figure 3.2: Simulation of LC Oscill
- Page 80 and 81: Table 3.1: Transition Matrix Elemen
- Page 82 and 83: with ω mn = Em−En . Multiplying
In terms <strong>of</strong> quantum bits, this means that a quantum computer can not only<br />
use the two states <strong>of</strong> the bit (0 and 1) to do binary calculations, but can instead<br />
use the complex probability amplitude <strong>of</strong> the 1 state, which provides two analog<br />
values (the relative phase and amplitude <strong>of</strong> the 0 and 1 state) for calculations.<br />
This concept is discussed further in Chapter 3.3.1.<br />
1.2.2 Entanglement<br />
Superpositions <strong>of</strong> single qubits alone do not provide a significant advantage,<br />
though, since they can be efficiently simulated by a classical computer by using a<br />
collection <strong>of</strong> classical bits to store the probability amplitudes. The true “magic”<br />
happens when several quantum systems are allowed to interact.<br />
According to<br />
quantum mechanics, the state <strong>of</strong> a collection <strong>of</strong> interacting quantum systems can<br />
no longer be described as a collection <strong>of</strong> the states <strong>of</strong> the individual systems, but<br />
instead needs to be described in terms <strong>of</strong> a new set <strong>of</strong> states that consists <strong>of</strong> all<br />
possible combinations <strong>of</strong> the individual states.<br />
For example, for three quantum bits, the combined system is not described in<br />
terms <strong>of</strong> the three qubits’ individual states that each are 0 or 1, but instead by<br />
the eight new states 000, 001, 010, 011, 100, 101, 110, and 111. In general, a system<br />
consisting <strong>of</strong> n interacting quantum bits needs to be described in terms <strong>of</strong> 2 n<br />
quantum states. A quantum computer can then be in a superposition <strong>of</strong> these 2 n<br />
7
Change language