|  Introduction to Quantum Computation Bruce Kane Foundations and Frontiers in Physics Seminar November 8, 1999 | 

Quantum Logic Any quantum computation can be reduced to a sequence of 1 and 2 qubit operations: H|in> = H1 H2 H3 .... Hn |in> Conventional operations: NOT, AND Quantum operations: NOT, CNOT

1. Create state which is a superposition of all possible Grover’s Algorithm 1. Create state which is a superposition of all possible phone numbers:  = (1/n)×(|000-0000 + |000-0001 + …|314-1592 + ...|999-9999 1/n |000-0000 |000-0001 |314-1592

2. Invert the ‘marked’ state: Average 3. Invert the wave function about its average value: Average

4. Repeat Steps 2 and 3 n times: 1 |314-1592 Wave function is in the ‘marked’ state with >50% probability!

Consensus until 1995: thinking about quantum computation is entirely an academic exercise.

Quantum Error Correction While the amplitudes of states in a wave function are continuous variables, measurement outcomes are always discrete: 0 or 1 |> = |0> + |1> Measurement To do quantum error correction a computation is performed on the state which determines the answer to the question: Has bit #4 (for example) been flipped? A measurement of the answer must either be ‘yes’ or ‘no’ If ‘no’ do nothing to the state; if yes flip bit #4. The original quantum state has been restored exactly!

Quantum error correction means that ‘perfect’ quantum computation can be performed despite errors and imperfections in the computer. Accuracy threshold for continuous quantum computation  1 error every 10,000 steps. Consensus in 1999: building a quantum computer may still be a difficult (or impossible) enterprise, but the issue can only be resolved by doing experiments on real systems that may be capable of doing quantum computation.

Intel P6 Microprocessor

Contention: Spins in silicon are a strong candidate to be the qubits in a future quantum computer. But quantum computing using Josephson junctions is also being pursued at U. of MD. Talk to Chris Lobb, Fred Wellstood or Bob Anderson to learn more.

Things necessary for a spin quantum computer: 1. Long lived spin states 2. Single spin operations (Q NOT) controlled spin interactions with an external field 3. Two spin operations (Q CNOT) controlled interactions between spins 4. Single spin preparation and detection controlled interactions with external reservoirs Ideally, each of these operations would be controlled by externally applied electric fields on gates of a semiconductor device

G. Feher c. 1956 (ENDOR) In Si:P at Temperature (T)=1K: electron relaxation time (T1 ) = 1 hour nuclear relaxation time = 1013 hours

“A Silicon-based nuclear spin quantum computer” B. E. Kane, Nature, May 14, 1998 ~200 Å

SINGLE SPIN OPERATIONS (QUANTUM NOT)

TWO SPIN OPERATIONS (QUANTUM CNOT)

Scanned Tunneling Microscope “Bottom up” Nanofabrication Scanned Tunneling Microscope Images Single atom Manipulation using an STM

Ion Implantation of Donors Taken from Vrijen, Yablonovich et al.

SINGLE SPIN MEASUREMENT Assertion: An effective and rapid means of measuring single electron spins will rely on effective spin interactions that are a manifestation of the Pauli Principle, rather than on detecting a magnetic field generated by the electron spin.

SINGLE SPIN MEASUREMENT

Single Electron Transistor (SET) Coupled to a Double Donor Two Electron System Fast SET’s: Schoelkopf et al. Science 280, 1238 (1998). Scanned-probe SET’s: Yoo et al. Science 276, 579 (1997). Quantum Measurements with SET’s: Shnirman et al. Phys. Rev. B 57, 15400 (1998). “Single spin measurement using single electron transistors to probe two electron systems”, B. E. Kane et al. To be published in PRB (cond-mat/9903371)

Single electron capacitance measurements R. Ashoori Demonstrated Sensitivity of single electron transistor: 10-4 e/ Hz 10-6 e/ Hz may be possible.

Band Edge Profile vs. Depth

The current state of experimental quantum computation. A quantum computer exceeding the capabilities of conventional computers using Shor’s or Grover’s algorithms.

Quantum Information: Physics World, March 1998  (http://www.physicsweb.org/toc/11/3)